## Alessandro SPALLICCI

ALESSANDRO SPALLICCI

Professeur des Universités

Université d'Orléans

Observatoire des Sciences de l'Univers

Collegium Sciences et Techniques, Pôle de Physique

Centre Nationale de la Recherche Scientifique

LPC2E, 3A, Avenue de la Recherche Scientifique

45071 Orléans France

alessandro.spallicci@cnrs-orleans.fr

+ 33 238 25 78 32 (office Orléans)

French Chair at the Universidade do Estado de Rio de Janeiro, Departamento de Física Teórica

Editor International Journal of Geometric Methods in Modern Physics

Editor Frontiers in Fundamental Astronomy

Editor Special Issues of Foundation of Physics

Erasmus responsible Orléans Napoli Federico II

Team Leader VESF-Virgo

Team leader LISA-France

## BREAKING NEWS

- An easy vivid way to explain gravitational waves here

- Selection of a gravitational wave mission by ESA. For info LISA France and the eLISA website

- Italians (could hardly) do it better, often without a salary.

Number of publications and citations for researcher.

## RESEARCH

Keywords: General Relativity and Gravitation (motion, self-force, gravitational waves, entropy, two-body problem), Non-Maxwellian Electromagnetism (photons and light propagation), Fundamental Physics Experiments, Cosmology, Mathematical Physics.

SELECTED PUBLICATIONS

Editor

Refereed journals [ACL 22-33, 35-55 Virgo collaboration papers, not listed here]

- [DO1] Blanchet L., SPALLICCI A., Whiting B., 2011. Mass and motion in general relativity, Springer Series on Fundamental Theories of Physics, ISBN: 978-90-481-3014-6. Contributions by Barack, Blanchet, Burko, Damour, Davis, Detweiler, Djouadi, Esposito-Farèse, Gal’tsov, Gourgoulhon, Gralla, Jaekel, Jaramillo, Jennrich, Lämmerzahl, Le Tiec, Nagar, Noui, Poisson, Reynaud, Schäfer, Spallicci, Wald, Whiting. 600 pages, available at Springer.
Downloaded 21568 times as of 26 November 2016.- [OS1] SPALLICCI A., 2011. Free fall and self-force: an historical perspective, in Mass and motion in general relativity, Springer Series on Fundamental Theories of Physics, Blanchet L., SPALLICCI A., Whiting B. Eds., ISBN: 978-90-481-3014-6. arXiv:1005.0611 [physics.hist-ph]
On-going projects and major contributors (General Relativity and Relativistic Astrophysics)

- [ACL1] SPALLICCI A., 1990. Orbiting test masses for equivalence principle space experiment, Gen. Rel. Grav., 22, 863.
- [ACL2] SPALLICCI A., 1991. The fifth force in the Schwarzschild metric, in the field equations and the concept of parageodesic motions, Ann. Phys. (Leipzig), 48, 365.
- [ACL3] SPALLICCI A., Brillet A., Busca G., Fuligni F., Nobili A., Roxburgh I., 1993. Equivalence principle, constant of gravitation, special and general relativity experiments in the Columbus program, Class. Q. Grav., 10, S259.
- [ACL4] SPALLICCI A., 1995. Relativistic time and frequency measurements for spacecraft users of GPS system, Aerotec. Missili Spazio, 74, 41.
- [ACL5] Ferraris M., Francaviglia M., SPALLICCI A., 1996. Associated radius, energy and pressure of McVittie's metric, in its astrophysical application, N. Cimento B, 111, 1031.
- [ACL6] SPALLICCI A., Graf E., Perino M., Matteoni M., Piras A., Arduini C., Catastini G., Ellmers F., Hall D., Härendel G., Nobili A., Iess L., Pinto I., Stöcker J., 1997. Microsatellites and space station for science and technology utilization, Acta Astron., 39, 605.
- [ACL7] SPALLICCI A., Krolak A., Frossati G., 1997. Coalescing binaries and large band resonant spherical detectors, Class. Q. Grav., 14, 577.
- [ACL 8] SPALLICCI A., Brillet A., Busca G., Catastini G., Pinto I., Roxburgh I., Salomon C., Soffel M., Veillet C., 1997. Experiments on fundamental physics on the Space Station, Class. Q. Grav. 14, 2971.
- [ACL 9] SPALLICCI A., 1998. Mathematical methods for quasi-static components of natural perturbative accelerations in microgravity environment analysis, J. Spacecraft Techn., 8, 88.
- [ACL 10] Pierro V., Pinto I., SPALLICCI A., Laserra A., Recano F., 2001. Fast and accurate computational tools for gravitational waveforms from binary systems with any orbital eccentricity, Mon. Not. Roy. Astr. Soc., 325, 358. arXiv:gr-qc/0005044
- [ACL 11] Pierro V., Pinto I., SPALLICCI A., 2002. Computation of hyperngeometric functions for gravitationally radiating binary stars, Mon. Not. Roy. Astr. Soc., 334, 855.
- [ACL 12] SPALLICCI A. Aoudia S., 2004. Perturbation method in the assessment of radiation reaction in the capture of stars by black holes, Class. Q. Grav., 21, S563. arXiv:gr-qc/0309039
- [ACL 13] Ferraris M., SPALLICCI A., 2004. Solutions of all one-dimensional wave equations with time independent potential and separable variables, Gen. Rel. Grav., 36, 1955. arXiv:gr-qc/0309038
- [ACL 14] SPALLICCI A., 2004. Satellite measurement of the Hannay angle, N. Cimento B, 119, 1215. arXiv:astro-ph/0409471
- [ACL 15] SPALLICCI A, Morbidelli A., Metris G., 2005. The three-body problem and the Hannay angle, Nonlinearity, 18, 45. arXiv:astro-ph/0312551
- [ACL 17] Chauvineau B., SPALLICCI A., Fournier J.-D., 2005. Brans-Dicke gravity in the capture of stars by black holes: some asymptotic results, Class. Q. Grav., 22, S457. arXiv:gr-qc/0412053
- [ACL 18] SPALLICCI A., Aoudia S., de Freitas Pacheco J., Regimbau T, Frossati G., 2005. Virgo detector optimization for gravitational waves by coalescing binaries, Class. Q. Grav., 22, S461. arXiv:gr-qc/0406076
- [ACL 21] Regimbau T., de Freitas Pacheco J., SPALLICCI A., Vincent S., 2005. Expected coalescence rates of double neutron stars for ground interferometers, Class. Q. Grav., 22, S935. arXiv:gr-qc/0506058
- [ACL 34] de Freitas Pacheco J., Regimbau T., Vincent S., SPALLICCI A., 2006. Expected coalescence rates of NS-NS binaries for laser beam interferometers, Int. J. Mod. Phys. D, 15, 235. arXiv:astro-ph/0510727
- [ACL 56] Aoudia S., SPALLICCI A., 2011. A source-free integration method for black hole perturbations and self-force computation: Radial fall, Phys. Rev. D, 83, 064029. arXiv:1008.2507 [gr-qc]
- [ACL 57] Ritter P., SPALLICCI A., Aoudia S., Cordier S., 2011. Fourth order indirect integration method for black hole perturbations: even modes, Class. Q. Grav., 28, 134012. arXiv:1102.2404 [gr-qc]
- [ACL 58] SPALLICCI A., 2013. On the complementarity of pulsar timing and space laser interferometry for the individual detection of supermassive black hole binaries, Astrophys. J., 764, 187. arXiv:1107.5984 [gr-qc]
- [ACL 59] SPALLICCI A., Ritter P., Aoudia S., 2014. Self-force driven motion in curved spacetime, Int. J. Geom. Meth. Mod. Phys., 11, 1450072. arXiv:1405.4155 [gr-qc]
- [ACL 60] SPALLICCI A., Ritter P., 2014. A fully relativistic radial fall, Int. J. Geom. Meth. Mod. Phys., 11, 1450090. arXiv:1407.5391 [gr-qc]
- [ACL 61] Ritter P., Aoudia S., SPALLICCI A., Cordier S.,2016. Indirect (source-free) integration method. I. Waveforms from geodesic generic orbits of EMRIs, Int. J. Geom. Meth. Mod. Phys., 13, 1650021. arXiv:1511.04252 [gr-qc]
- [ACL 62] Ritter P., Aoudia S., SPALLICCI A., Cordier S. 2016. Indirect (source-free) integration method. II. Self-force consistent radial fall, Int. J. Geom. Meth. Mod. Phys., 13, 1650019. arXiv:1511.04277 [gr-qc]
- [ACL 63] Bonetti L., Ellis J., Mavromatos N.E., Sakharov A.S., Sarkisyan-Grinbaum E.K.G., SPALLICCI A., 2016. Photon mass limits from Fast Radio Bursts, Phys. Lett. B, 757, 548. arXiv:1602.09135 [astro-ph.HE]
- [ACL 64] Retinò A., SPALLICCI A., Vaivads A., 2016. Solar wind test of the de Broglie-Proca's massive photon with Cluster multi-spacecraft data, Astropart. Phys., 82, 49. arXiv:1302.6168 [hep-ph]
- [ACL 65] SPALLICCI A., van Putten M., 2016. Gauge dependence and self-force in Galilean and Einsteinian free falls, Pisa tower and evaporating black holes at general relativity centennial, Int. J. Geom. Meth. Mod. Phys., 13, 1630014, special volume in Memory of Mauro Francaviglia. arXiv:1607.02594 [gr-qc]
- [ACL 66] Oltean M., Bonetti L., SPALLICCI A., Sopuerta C., 2016. Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem, Phys. Rev. D., 94, 064049. arXiv:1607.03118 [gr-qc]
- [ACL 67] Bonetti L., dos Santos Luis R., Helayël-Neto A. J., SPALLICCI A., 2017. Effective photon mass from Super and Lorentz symmetry breaking, Phys. Lett. B, 764, 203. arXiv:1607.08786 [hep-ph]
- [ACL 68] Bentum M., Bonetti L., SPALLICCI A., 2017. Dispersion by pulsars, magnetars and massive electromagnetism at very low radio frequencies, Adv. Space Res, 59, 736. arXiv:1607.08820 [astro-ph.IM]
- [ACL 69] Bonetti L., Ellis J., Mavromatos N.E., Sakharov A.S., Sarkisyan-Grinbaum E.K.G., SPALLICCI A., 2017. FRB 121102 casts new light on the photon mass. arXiv:1701.03097 [astro-ph.HE]

On-going projects and major contributors (Non-Maxwellian Electromagnetism, Astrophysics and Cosmology)

- Ferraris M., SPALLICCI A., Spacetime matching by transition metrics.
- Bonetti L., SPALLICCI A., Newtonian free fall learned at youth revisited with an Einsteinian view.
- Oltean. M., Sopuerta C.F., SPALLICCI A., A frequency-domain pseudospectral method for the computation of the self-force on a charged particle.

Future projects

- Bonetti L., dos Santos Luis R., Helayël-Neto A. J., SPALLICCI A. Photon sector analysis of Super and Lorentz symmetry breaking
Stay tuned. ## LAST ABSTRACTS

[ACL 56] Aoudia S., SPALLICCI A., 2011. A source-free integration method for black hole perturbations and self-force computation: Radial fall, Phys. Rev. D, 83, 064029. arXiv:1008.2507 [gr-qc]

Perturbations of Schwarzschild-Droste black holes in the Regge-Wheeler gauge benefit from the availability of a wave equation and from the gauge invariance of the wave function, but lack smoothness. Nevertheless, the even perturbations belong to the C°continuity class, if the wave function and its derivatives satisfy specific conditions on the discontinuities, known as jump conditions, at the particle position. These conditions suggest a new way for dealing with finite element integration in time domain. The forward time value in the upper node of the (t, r*) grid cell is obtained by the linear combination of the three preceding node values and of analytic expressions based on the jump conditions. The numerical integration does not deal directly with the source term, the associated singularities and the potential. This amounts to an indirect integration of the wave equation. The known wave forms at infinity are recovered and the wave function at the particle position is shown. In this series of papers, the radial trajectory is dealt with first, being this method of integration applicable to generic orbits of EMRI (Extreme Mass Ratio Inspiral).

[ACL 57] Ritter P., SPALLICCI A., Aoudia S., Cordier S., 2011. Fourth order indirect integration method for black hole perturbations: even modes, Class. Q. Grav., 28, 134012. arXiv:1102.2404 [gr-qc]

On the basis of a recently proposed strategy of finite element integration in time domain for partial differential equations with a singular source term, we present a fourth-order algorithm for non-rotating black hole perturbations in the Regge–Wheeler gauge. Herein, we address even perturbations induced by a particle plunging in. The forward time value at the upper node of the (r*,t) grid cell is obtained by an algebraic sum of (i) the preceding node values of the same cell, (ii) analytic expressions, related to the jump conditions on the wavefunction and its derivatives and (iii) the values of the wavefunction at adjacent cells. In this approach, the numerical integration does not deal with the source and potential terms directly, for cells crossed by the particle world line. This scheme has also been applied to circular and eccentric orbits and it will be the object of a forthcoming publication.

[ACL 58] SPALLICCI A., 2013. On the complementarity of pulsar timing and space laser interferometry for the individual detection of supermassive black hole binaries, Astrophys. J., 764, 187. arXiv:1107.5984 [gr-qc]

Gravitational waves coming from Super Massive Black Hole Binaries (SMBHBs) are targeted by b0^{th}Pulsar Timing Array (PTA) and Space Laser Interferometry (SLI). The possibility of a { single} SMBHB being tracked first by PTA, through inspiral, and later by SLI, up to { merger} and { ring down}, has been previously suggested. Although the bounding parameters are drawn by the current PTA or the upcoming Square Kilometer Array (SKA), and by the New Gravitational Observatory (NGO), derived from the Laser Interferometer Space Antenna (LISA), { this paper also addresses} sequential detection beyond specific project constraints. We consider PTA-SKA, which is sensitive from 10^{-9} to px10^{-7} Hz (p=4-8), and SLI, which operates from sx10^{-5} up to 1 Hz (s = 1-3). A SMBHB in the range 2x10^{8} - 2x10^{9} solar masses (the masses are normalised to a (1+z) factor, the red shift lying between z = 0.2 and z=1.5) moves from the PTA-SKA to the SLI band over a period ranging from two months to fifty years. By combining three Super Massive Black Hole (SMBH)-host relations with three accretion prescriptions, nine astrophysical scenarios are formed. They are then related to three levels of pulsar timing residuals (50, 5, 1 ns), generating twenty-seven cases. For residuals of 1 ns, sequential detection probability will never be better than 4.7x10^{-4} y^{-2} or 3.3x10^{-6} y^{-2} (per year to merger and per year of survey), according to the best and worst astrophysical scenarios, respectively; put differently this means one sequential detection every 46 or 550 years for an equivalent maximum time to merger and duration of the survey. The chances of sequential detection are further reduced by increasing values of the s parameter (they vanish for s = 10) and of the SLI noise, and by decreasing values of the remnant spin. The spread in the predictions diminishes when timing precision is improved or the SLI low frequency cut-off is lowered. So while transit times and the SLI Signal to Noise Ratio (SNR) may be adequate, the likelihood of sequential detection is severely hampered by the current estimates on the number - just an handful - of individual inspirals observable by PTA-SKA, and to a lesser extent by the wide gap between the pulsar timing and space interferometry bands, and by the severe requirements on pulsar timing residuals. Optimisation of future operational scenarios for SKA and SLI is briefly dealt with, since a detection of even a single event would be of paramount importance for the understanding of SMBHBs and of the astrophysical processes connected to their formation and evolution.

[ACL 59] SPALLICCI A., Ritter P., Aoudia S., 2014. Self-force driven motion in curved spacetime, Int. J. Geom. Meth. Mod. Phys., 11, 1450072. arXiv:1405.4155 [gr-qc]

We adopt the Dirac-Detweiler-Whiting radiative and regular effective field in curved spacetime. Thereby, we derive straightforwardly the first order perturbative correction to the geodesic of the background in a covariant form, for the extreme mass ratio two-body problem. The correction contains the self-force contribution and a background metric dependent term.

[ACL 60] SPALLICCI A., Ritter P., 2014. A fully relativistic radial fall, Int. J. Geom. Meth. Mod. Phys., 11, 1450090. arXiv:1407.5391 [gr-qc]

Radial fall has historically played a momentous role. It is one of the most classical problems, the solutions of which represent the level of understanding of gravitation in a given epoch. A {\it gedankenexperiment} in a modern frame is given by a small body, like a compact star or a solar mass black hole, captured by a supermassive black hole. The mass of the small body itself and the emission of gravitational radiation cause the departure from the geodesic path due to the back-action, that is the self-force. For radial fall, as any other non-adiabatic motion, the instantaneous identity of the radiated energy and the loss of orbital energy cannot be imposed and provide the perturbed trajectory. In the first part of this letter, we present the effects due to the self-force computed on the geodesic trajectory in the background field. Compared to the latter trajectory, in the Regge-Wheeler, harmonic and all others smoothly related gauges, a far observer concludes that the self-force pushes inward (not outward) the falling body, with a strength proportional to the mass of the small body for a given large mass; further, the same observer notes an higher value of the maximal coordinate velocity, this value being reached earlier on during infall. In the second part of this letter, we implement a self-consistent approach for which the trajectory is iteratively corrected by the self-force, this time computed on osculating geodesics. Finally, we compare the motion driven by the self-force without and with self-consistent orbital evolution. Subtle differences are noticeable, even if self-force effects have hardly the time to accumulate in such a short orbit.

[ACL 61] Ritter P., Aoudia S., SPALLICCI A., Cordier S., 2016. Indirect (source-free) integration method. I. Waveforms from geodesic generic orbits of EMRIs, Int. J. Geom. Meth. Mod. Phys., 13, 1650021. arXiv:1511.04252 [gr-qc]

The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).

[ACL 62] Ritter P., Aoudia S., SPALLICCI A., Cordier S., 2016. Indirect (source-free) integration method. II. Self-force consistent radial fall, Int. J. Geom. Meth. Mod. Phys., 13, 1650019. arXiv:1511.04277 [gr-qc]

We apply our method of indirect integration, described in Part I, at fourth order, to the radial fall affected by the self-force. The Mode-Sum regularisation is performed in the Regge-Wheeler gauge using the equivalence with the harmonic gauge for this orbit. We consider also the motion subjected to a self-consistent and iterative correction determined by the self-force through osculating stretches of geodesics. The convergence of the results confirms the validity of the integration method. This work complements and justifies the analysis and the results appeared in Int. J. Geom. Meth. Mod. Phys., 11, 1450090 (2014).

[ACL 63] Bonetti L., Ellis J., Mavromatos N.E., Sakharov A.S., Sarkisyan-Grinbaum E.K.G., SPALLICCI A., 2016. Photon mass limits from Fast Radio Bursts, Phys. Lett. B, 757, 548. arXiv:1602.09135 [astro-ph.HE]

The frequency-dependent time delays in fast radio bursts (FRBs) can be used to constrain the photon mass, if the FRB redshifts are known, but the similarity between the frequency dependences of dispersion due to plasma effects and a photon mass complicates the derivation of a limit on the photon mass. The dispersion measure (DM) of FRB 150418 is known to about 0.1 %, and there is a claim to have measured its redshift with an accuracy of about 2%, but the strength of the constraint on the photon mass is limited by uncertainties in the modelling of the host galaxy and the Milky Way, as well as possible inhomogeneities in the intergalactic medium (IGM). Allowing for these uncertainties, the recent data on FRB 150418 indicate that the photon mass is less than 1.8 x 10^{-14} eV c^{-2} (3.2 x 10^{-50} kg), if FRB 150418 indeed has a redshift z = 0.492 as initially reported. In the future, the different redshift dependences of the plasma and photon mass contributions to DM can be used to improve the sensitivity to the photon mass if more FRB redshifts are measured. For a fixed fractional uncertainty in the extra-galactic contribution to the DM of an FRB, one with a lower redshift would provide greater sensitivity to the photon mass.

[ACL 64] Retinò A., SPALLICCI A., Vaivads A., 2016. Solar wind test of the de Broglie-Proca's massive photon with Cluster multi-spacecraft data, Astropart. Phys., 82, 49. arXiv:1302.6168 [hep-ph]

Our understanding of the universe at large and small scales relies largely on electromagnetic observations. As photons are the messengers, fundamental physics has a concern in testing their properties, including the absence of mass. We use Cluster four spacecraft data in the solar wind at 1 AU to estimate the mass upper limit for the photon. We look for deviations from Ampère's law, through the curlometer technique for the computation of the magnetic field, and through the measurements of ion and electron velocities for the computation of the current. We show that the upper bound for m_\gamma lies between 1.4 x 10^{-49} and 3.4 x 10^{-51}$ kg, and thereby discuss the currently accepted lower limits in the solar wind.

[ACL 65] SPALLICCI A., van Putten M., 2016. Gauge dependence and self-force in Galilean and Einsteinian free falls, Pisa tower and evaporating black holes at general relativity centennial, Int. J. Geom. Meth. Mod. Phys., 13, 1630014, special volume in Memory of Mauro Francaviglia. arXiv:1607.02594 [gr-qc]

Obviously, in Galilean physics, the universality of free fall implies an inertial frame, which in turns implies that the mass m of the falling body is omitted (because it is a test mass; put otherwise, the centre of mass of the system coincides with the centre of the main, and fixed, mass M; or else, we consider only an homogeneous gravitational field). Otherwise, an additional (in the same or opposite direction) acceleration proportional to $m/M$ would rise either for an observer at the centre of mass of the system, or for an observer at a fixed distance from the centre of mass of M. These elementary, but overlooked, considerations fully respect the equivalence principle and the (local) identity of an inertial or a gravitational pull for an observer in the Einstein cabin. They value as fore-runners of the self-force and gauge dependency in general relativity. Because of its importance in teaching and in the history of physics, coupled to the introductory role to Einstein's equivalence principle, the approximate nature of Galilei's law of free fall is explored herein. When stepping into general relativity, we report how the geodesic free fall into a black hole was the subject of an intense debate again centred on coordinate choice. Later, we describe how the infalling mass and the emitted gravitational radiation affect the free fall motion of a body. The general relativistic self-force might be dealt with to perfectly fit into a geodesic conception of motion. Then, embracing quantum mechanics, real black holes are not classical static objects any longer. Free fall has to handle the Hawking radiation, and leads us to new perspectives on the varying mass of the evaporating black hole and on the varying energy of the falling mass. Along the paper, we also estimate our indings for ordinary masses being dropped from a Galilean or Einsteinian Pisa-like tower with respect to the current state of the art drawn from precise measurements in ground and space laboratories, and to the constraints posed by quantum measurements. The appendix describes how education physics and high impact factor journals discuss the free fall. Finally, case studies conducted on undergraduate students and teachers are reviewed.

[ACL 66] Oltean M., Bonetti L., SPALLICCI A., Sopuerta C., 2016. Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem, Phys. Rev. D, 94, 064049. arXiv:1607.03118 [gr-qc]

In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics, there are theorems which have been proposed for proving the non-existence of entropy in the latter sense. We explicate, clarify and extend the proofs of these theorems, and then we show why these proofs fail in general relativity; due to properties of the gravitational Hamiltonian and phase space measures, the second law of thermodynamics holds. As a concrete application, we focus on the consequences of these results for the gravitational two-body problem, and in particular, we prove the non-compactness of the phase space of perturbed Schwarzschild-Droste spacetimes. We thus identify the lack of recurring orbits in phase space as a distinct sign of dissipation and thus entropy production

[ACL 67] Bonetti L., dos Santos Rodolfo L., Helayël-Neto J., SPALLICCI A., 2017. Effective photon mass from Super and Lorentz symmetry breaking, Phys. Lett. B., 764, 203. arXiv:1607.08786 [hep-ph]

In the context of Standard Model Extensions (SMEs), we analyse four general classes of Super Symmetry (SuSy) and Lorentz Symmetry (LoSy) breaking, leading to observable imprints at our energy scales. The photon dispersion relations show a non-Maxwellian behaviour for the CPT (Charge-Parity-Time reversal symmetry) odd and even sectors. The group velocities exhibit also a directional dependence with respect to the breaking background vector (odd CPT) or tensor (even CPT). In the former sector, the group velocity may decay following an inverse squared frequency behaviour. Thus, we extract a massive and gauge invariant Carroll-Field-Jackiw photon term in the Lagrangian and show that the effective mass is proportional to the breaking vector and moderately dependent on the direction of observation. The breaking vector absolute value is estimated by ground measurements and leads to a photon mass upper limit of 10^{-19} eV or 2 x 10^{-55} kg and thereby to a potentially measurable delay at low radio frequencies.

[ACL 68] Bentum M., Bonetti L, SPALLICCI A., 2017. Dispersion by pulsars, magnetars and massive electromagnetism at very low radio frequencies, Adv. Space Res, 59, 736. arXiv:1607.08820 [astro-ph.IM]

Our understanding of the universe relies mostly on electromagnetism. As photons are the messengers, fundamental physics is concerned in testing their properties. Photon mass upper limits have been earlier set through pulsar observations, but new investigations are offered by the excess of dispersion measure (DM) sometimes observed with pulsar and magnetar data at low frequencies, or with the fast radio bursts (FRBs), of yet unknown origin. Arguments for the excess of DM do not reach a consensus, but are not mutually exclusive. Thus, we remind that for massive electromagnetism, dispersion goes as the inverse of the frequency squared. Thereby, new avenues are offered also by the recently operating ground observatories in 10-80 MHz domain and by the proposed Orbiting Low Frequency Antennas for Radio astronomy (OLFAR). The latter acts as a large aperture dish by employing a swarm of nano-satellites observing the sky for the first time in the 0.1 - 15 MHz spectrum. The swarm must be deployed sufficiently away from the ionosphere to avoid distortions especially during the solar maxima, terrestrial interference and offer stable conditions for calibration during observations.

[ACL 69] Bonetti L., Ellis J., Mavromatos N.E., Sakharov A.S., Sarkisyan-Grinbaum E.K.G., SPALLICCI A., 2017. FRB 121102 casts new light on the photon mass. arXiv:1701.03097 [astro-ph.HE]

The photon mass, m_gamma, can in principle be constrained using measurements of the dispersion measures (DMs) of fast radio bursts (FRBs), once the FRB redshifts are known. The DM of the repeating FRB 121102 is known to <1 %, a host galaxy has now been identified with high confidence,and its redshift, z , has now been determined with high accuracy: z=0.19273(8). Taking into account the plasma contributions to the DM from the Intergalactic medium (IGM) and the Milky Way, we use the data on FRB 121102 to derive the constraint m_gamma < 2.2×10^{-14} eV c^{-2} (3.9 × 10^{-50} kg). Since the plasma and photon mass contributions to DMs have different redshift dependences, they could in principle be distinguished by measurements of more FRB redshifts, enabling the sensitivity to m_gamma to be improved.

## THE ORLEANS LISA TEAM

- Alessandro D.A.M. Spallicci, PR, spallicci@cnrs-orleans.fr (Theoretical and Fundamental (Astro)Physics, Relativity) Université d’Orléans, Obs. Sciences Univers, LPC2E Webpage
- Richard Emilion, PR, richard.emilion@univ-orleans.fr (Data analysis, Statistics) Université d’Orléans, MAPMO Webpage
- Diarra Fall, MdC, diarra.fall@univ-orleans.fr (Data analysis, Statistics) Université d’Orléans, MAPMO Webpage
- Sylvain Jubertie, MdC, sylvain.jubertie@univ-orléans.fr, (Parallel Computing, Informatics) Université d’Orléans, LIFO Webpage
- Luca Bonetti, Doctorate student, luca.bonetti@cnrs-orleans.fr (Theoretical Physics, Cosmology) Université d’Orléans, LPC2E
- Marius Oltean, Doctorate student, marius.oltean@cnrs-orleans.fr (Theoretical Physics, Relativity) Université d’Orléans and Universitat Autònoma de Barcelona, LPC2E
- Past members: PR Stéphane Cordier now at Grenoble-France, Dr Sofiane Aoudia now at Bgayet-Algeria, Dr Patxi Ritter last position in Praha
- Visitors: PR B. Whiting (Univ. Florida) 2008, PR M. van Putten (MIT-LIGO) Chaire Le STUDIUM 2008-2009, MdC S. Aoudia (Golm) 2011, 2012, MdC L. Burko (Univ. Huntsville) 2012, PR C. Sopuerta (IEEC Barcelona) 2013, PR S. Perez-Bergliaffa (UERJ Rio de Janeiro) 2014, 2015.
## TEACHING

Responsible of the following courses at the Université d'Orléans

- Exploration du milieu spatial et systèmes spatiaux (Master 1)

Intervenants : LPC2E, MAPMO, ESA, CNES- Introduction à la gravitation et à l'astrophysique relativiste (Master 1) [Cours-IGAR.pdf][TD-IGAR.pdf]

Intervenants : LPC2E, MAPMO, IAP Paris- Expériences spatiales en physique fondamentale (Master 2)

Intervenants : LPC2E, IAP Paris, APC Paris, ENS Paris, OCA Grasse- Relativité et physique subatomique (Licence Physique L2, L3) [Cours-RPsA.pdf][rpsa-TD-CC-CT.pdf]

- Physique des (astro-)particules (Ouverture Licence L1, L2, L3)

- Relativité, Sciences spatiales, Astrophysique (Ouverture Licence L1, L2, L3) [Cours-RSSA.pdf]
## CURRICULUM VITAE

- Dottore In Ingegneria, Politecnico di Torino, Thesis at Ist. Elettrotecnico Naz. G. Ferraris, Sez. Metrologia Tempo e Frequenza

- Dottore in Fisica, Università di Pavia, Thesis at Ist. Fisica Matematica J.-L. Lagrange, Torino

At the Université d'Orléans from 2006 - then just 700 years old since its creation in 1306 - after having spent a period at the Observatoire de la Côte d’Azur as recipient of the Giuseppe Colombo prize, I have previously held professorships in my home town Alessandria, but also Benevento and Salerno - the first university in the modern sense is believed by some to have been the medical school founded in the 9^{th}century at Salerno [pdf] - and worked at the European Space Research & Technology Centre in Noordwijk (ESTEC). Space as laboratory to test current or propose new foundations for physics abides by my vision of astrophysics. I have therefore pursued my investigations covering topics from theoretical physics to space experiments through fundamental metrology, publishing in a variety of scientific journals.

1986-1996 European Space Research and Technology Centre, Noordwijk

1996-1997 Università di Salerno

1997-2001 Università del Sannio di Benevento

1998-2002 Parco Scientifico e Tecnologico di Salerno

2002-2005 Observatoire de la Côte d'Azur, Nice

2005-2006 Università del Piemonte Orientale, Alessandria

2006-present Université d'Orléans

## DISTINCTIONS AND PRIZES, INVITATIONS (VISITS AND SEMINARS, CONFERENCES)

FOM Prize Mathematische Fysika 1998

ESA European Space Agency Conseiller, 2000-2001

ESA European Space Agency G. Colombo Senior Research Fellow 2002-2004

Visits and Seminars

- Dip. Matematica, Univ. Pisa, 1988-1990 (in fragments).

- Univ. Groningen Univ., 24 Februay 1989.

- Center of Relativity, Univ. of Texas at Austin, 30 April - 4 May 1990.

- Istituto di Fisica dello Spazio Interplanetario, Frascati, 10 July 1990.

- ESTEC Space Science Dept., Noordwijk, 7 December 1990.

- Istituto Nazionale di Fisica Nucleare, Pisa, 14 December 1990.

- Gravitation Research Group, Univ. Salerno, April 1992.

- Physics and Astr. Dept., Univ. of Wales at Cardiff, 6-10 December 1993.

- Ist. di Fisica Matematica, J.-L. Lagrange, Univ. Torino, 1993-1994 (in fragments).

- Gravitation Research Group, Univ. Salerno, 9-14 January 1995.

- Physics and Astr. Dept., Univ. of Wales at Cardiff, 20-22 March 1995.

-Univ. Chicago, Enrico Fermi Inst., 29 May - 2 June 1995 (by S. Chandrasekhar).

- Physics Dept. Univ. of Utah at Salt Lake City, 26-30 October 1995.

- Gravitation Research Group, Univ. Salerno, 6-21 May 1996.

- A. Einstein Max Planck Institut für Gravitationsphysik Potsdam, 10-13 June 1996.

- Gravitation Research Group, Univ. Salerno, 16-26 September 1996.

- Imperial College, London Univ., 14 October 1996.

- Gravitation Research Group, Univ. Salerno, 5-14 February 1997.

- Osservatorio Monte Mario, Roma, 10 March 1997.

- Scuola Ingegneria Aerospaziale, Roma, 12 March 1997.

- Obs. Neuchâtel, March 1997.

- SRON Space Research Organization Nederland, Utrecht, 27 March 1997.

- Dip. Matematica R. Caccioppoli, Univ. Napoli Federico II, 6 June 1997.

- Univ. Bologna, 15 July 1997.

-Nationaal Instituut voor Kernfysica en Hoge-Energie Fysica, Stichting voor Fundamenteel Onderzoek der Materie, Amsterdam, 1998-1999 (in fragments).

- Dipartimento di Matematica G. Castelnuovo Univ. di Roma 1 La Sapienza, 1999-2002 (in fragments).

- Int. Centre of Relativistic Astrophysics, ICRA, Dip. Fisica, Univ. Roma La Sapienza, 2000.

- UTINAM, Obs. Besançon, 18 April 2002.

- LPTA Montpellier, 24 April 2002.

- Inst. Ciencias del Espacio y Inst. d'Estudis Espacials de Catalunya, Barcelona, 30 November 2005.

- LAL Orsay, 10 April 2006.

- APC Paris, 11 April 2006.

- LPCE Orléans, 13 April 2006.

- LAPTH Annecy, 14 April 2006.

- Facoltà di Scienze Mat. Fis. Nat., Univ. del Piemonte Orientale, Alessandria, 14 June 2006.

- Univ. Chicago, E. Fermi Inst., 19 May – 27 May 2009.

- Univ. Southampton, 17-21 August 2009.

- A. Einstein Max Planck Institut für Gravitationsphysik Golm, 7 - 14 April 2010.

-UERJ Universidade do Estado de Rio de Janeiro and CBPF Centro Brasileiro des Pequiscas Fisicas, Rio de Janeiro, 11-18 November 2012.

-UERJ Universidade do Estado de Rio de Janeiro and CBPF Centro Brasileiro des Pequiscas Fisicas, Rio de Janeiro, 29 October - 23 November 2014.

-IPN Instituto Politécnico Nacional and CINVESTAV (Tesis doctoral A. Avalos Vargas, Prof. G. Ares de Parga), Cidad de Mexico, 15-19 December 2014.

-Dipartimento di Fisica, Università di Napoli Federico II, 9-13 February 2015.

-UERJ Universidade do Estado de Rio de Janeiro and CBPF Centro Brasileiro des Pequiscas Fisicas, Rio de Janeiro, 20 April-29 May 2015.

-UERJ Universidade do Estado de Rio de Janeiro and CBPF Centro Brasileiro des Pequiscas Fisicas, Rio de Janeiro, 6-28 September 2015.

-CBPF Centro Brasileiro des Pequiscas Fisicas, Rio de Janeiro, 16 April-26 May 2016.

Conferences and Schools

- Vulcan Science Meeting, 8 September 1986 Noordwijk.

- Vulcan Science Meeting, 24 October 1986 Noordwijk.

- Optical Systems for Space Applications, 30 March - 1 April 1987 Den Haag.

- Vulcan Science Meeting, 3-4 May 1988 Noordwijk.

- 8^{th}It. Conf. on General Relativity and Gravitational Physics, 30 August-3 September 1988 Cavalese, Trento.

- 12^{th}Internat. Conf. on General Relativity and Gravitation, 3-8 July 1989 Boulder.

- Gravitational waves data analysis workshop, 2-5 December 1989 Roma.

- VIRGO Mtg. on software issues, 7-8 January 1991 Annecy.

- 25^{th}Rencontre de Moriond, New and exotic phenomena, 20-27 January 1990 Les Arcs.

- Radio Science Mtg. of URSI, 7-11 May 1990 Dallas.

- 1^{st}Fairbank Mtg. on Relativistic Gravitational Experiments in Space, 10-14 September 1990 Roma.

- 9^{th}It. Conf. on General Relativity and Gravitational Physics, 25-28 September 1990 Capri.

- 6^{th}European Frequency and Time forum, 17-19 March 1992 Noordwijk.

- Data Analysis for Interferometric Gravitational Wave Detectors, 29-30 April 1992 Cardiff.

- Journées Relativistes, 14-16 May 1992 Amsterdam.

- 13th Int. Conf. on Gen. Rel. and Gravitation, 28 June - 4 July 1992 Huerta Grande, Cordoba.

- 10^{th}It. Conf. on General Relativity and Gravitational Physics, 1-5 September 1992 Bardonecchia.

- ESA Gravitational Wave Detection Workshop, 6-7 October 1992 Paris.

- STEP symposium, 6-8 April 1993 Pisa.

- Detection of Gravitational Radiation Workshop, 24 May 1994 Amsterdam.

- 11^{th}It. Conf. on General Relativity and Gravitational Physics, 26-30 September 1994 Trieste.

- GRAIL workshop, 27-29 March 1995 Twente University.

- 3^{rd}Ann.Penn State Conf., Astrophysical sources of gravitational radiation, 7-10 July 1995 Penn State Univ.

- 14^{th}Internat. Conf. on General Relativity and Gravitation, 6-12 August 1995 Firenze.

- Symposium on Fundamental Physics in Space, 16-19 October 1995 London.

- 12^{th}It. Conf. on General Relativity and Gravitational Physics, 23-27 September 1996 Roma.

- 1^{st}Symp. on the Utilization of the International Space Station, 30 September - 2 October 1996 Darmstadt.

- TAMA Workshop on Gravitational Waves Detection, 12-14 November 1996 Saitama.

- 11^{th}European Frequency and Time forum, 7 March 1997 Neuchâtel.

- Problemi Attuali di Fisica Teorica, Onde Gravitazionali, 21 March 1997 Vietri sul Mare, Salerno.

- 8^{th}Marcel Grossmann Mtg., 22-28 June 1997 Jerusalem.

- 2^{nd}Amaldi Conf. on Gravitational Waves, 1-4 July 1997 Geneve.

- 48^{th}IAF Congress 6-10 October 1997 Torino.

- 15^{th}Internat. Conf. on General Relativity and Gravitation, 16-21 December 1997 Pune.

- 13^{th}Italian Conf. on General Rel. and Grav. Physics, 21-25 September 1998 Monopoli, Bari.

- 3^{rd}Capra Mtg. on radiation reaction, 5-9 June 2000 Pasadena.

- 9^{th}Marcel Grossmann Mtg., 2-8 July 2000 Roma.

- 1^{st}Int. Symp. Microgravity Res. & Appl. Physical Sciences Biotechnology, 10-15 September 2000 Sorrento.

- Assemblea scientifica GNFM, 2-3 November 2000 Montecatini Terme, Pistoia.

- 15^{th}European Frequency and Time Forum, 6-8 March 2001 Neuchâtel.

- 5^{th}Amaldi Conf. on Gravitational Waves, 6-11 July 2003 Tirrenia, Pisa.

- Conf. on Sources of gravitational waves, 22-26 September 2003 Trieste.

- GREX Gravitation et Expériences Spatiales, 8-10 October 2003 Paris.

- ASSNA Action Spécifique pour la simulation numérique en astrophysique, 15-18 December 2003 Paris.

- GPS Meeting, 31 March 2004 Paris.

- VIRGO Mtg., 3-5 May 2004 Pisa.

- 7^{th}Capra Mtg. on radiation reaction, 28 May-4 June 2004 Brownsville.

- Galileo Mtg., 16 June 2004 Paris.

- 38^{th}ESLAB Symp., 5^{th}Intern. LISA Symp., 12-15 July 2004 Noordwijk.

- GREX Gravitation et Expérience, 27-29 October 2004 Nice.

- VIRGO Mtg., 2-3 November 2004 Orsay.

- VESF, Virgo Eur. Scientific Forum, 9-10 December 2004 Pisa.

- GWDAW9 15-18 December 2004 Annecy.

- 1e Journées LISA France, 20-21 January 2005 Paris.

- 8^{th}Capra Mtg. on radiation reaction, 11-14 July 2005 Oxford.

- 2^{e}Journées LISA France, 5-6 October 2005 Nice.

- GREX Gravitation et Expériences Spatiales, 12-15 October 2005 Paris.

- LISA Data Analysis Mtg., 31 October 2005 Noordwijk.

- The 1^{st}Bego scientific meeting, 6-15 February 2006 Nice.

- 3^{e}Journées LISA France, 15-16 May 2006 Meudon.

- VESF, Virgo Eur. Scientific Forum, 23-24 April 2007 Pisa.

- 2^{nd}Workshop on Pulsars: theories et observations, 3-4 May 2007 Paris.

- Journés Tourangelles Relativistes, 1 June 2007 Tours.

- 10^{th}Capra Mtg. on radiation reaction, 25-30 June 2007 Huntsville.

- 18^{th}Internat. Conf. on General Relativity and Gravitation, 8-14 July 2007 Sydney.

- 7^{th}Amaldi Conf. on Gravitational Waves, 8-14 July 2007 Sydney.

- 1^{st}Int. Scientific & Fundamental Aspects of the Galileo Progr., 1-4 October 2007 Toulouse.

- 4^{e}Journées LISA France, 13-14 March 2008 Paris.

-Organisation of the Ecole Thématique CNRS sur la Masse et Conf. Internationale Capra in Orléans 23-29 June 2008.

- 3^{rd}Workshop on Pulsars: theories et observations, 24-26 November 2008 Paris.

- Journée GREX sur l’exploration de la gravitation à l’echelle du système solaire, 2 December 2008 Meudon.

- 5^{e}Journées LISA France, 26-27 February 2009 Paris.

- 12^{th}Capra Mtg. on radiation reaction, 15-19 June 2009 Bloomington.

- 21^{st}Rencontre de Blois: Windows on the Universe, 22-26 June 2009 Blois.

- 12^{th}Marcel Grossmann Mtg., 12-18 July 2009 Paris.

- 4^{th}LISA Astro-GR@BCN, 7-11 September 2009 Barcelona.

- Séminaire de prospective – GDR PCHE, 28-29 September 2009 Paris.

- 2^{nd}Int. Scientific & Fundamental Aspects of the Galileo Progr., COSPAR Coll., 14-16 October 2009 Padova.

- Gravitation and Fundamental Physics in Space, GPhyS "Kick-Off " Coll., 20-22 October 2009 Les Houches.

- 6^{e}Journées LISA France, 9-10 November 2009 Nice.

- 7^{e}Journées LISA France, 1-2 June 2010 Chatillon.

- Fundamental Physics Laws: Gravity, Lorentz Symmetry and Quantum Gravity, 2-3 June 2010 Paris.

- 13^{th}Capra Mtg. on radiation reaction (Theory Meets Data Analysis at Comparable and Extreme Mass Ratios), 20-26 June 2010 Waterloo, Toronto.

- 11^{th}Frontiers of Fundamental Physics, 6-9 July 2010 Paris.

- LISA Astro-GR@Paris, 13-17 September 2010 Paris.

- Call for a medium size mission for a lunch in 2022 Briefing Meeting ESTEC, 1 October 2010 Noordwijk.

- Int. Fall Workshop on Geometry and Physics, 29 October 2010 Paris.

- Variation of fundamental constants, IAP, 8 November 2010 Paris.

- Séminaire par G. ‘t Hooft, Univ. Pierre et Marie Curie, 8 November 2010 Paris.

- J. Action Specifique GRAM (Gravitation, Références, Astronomie, Metrologie), 29-30 November 2010 Nice.

- 8^{e}Journées LISA France, APC, 9-10 May 2011 Paris.

- Cosmological frontiers in Fundamental Physics, APC, 14-17 June 2011 Paris.

- 14^{th}Capra Mtg. on radiation reaction, 4-8 July 2011 Southampton.

- 12^{th}Frontiers of Fundamental Physics, 21-23 November 2011 Udine.

- 9^{th}LISA Symposium, 21-25 May 2012 Paris.

- 15^{th}Capra Mtg. on radiation reaction, 11-15 June 2012 Maryland College Park.

- 16^{th}Capra Mtg. on radiation reaction, 15-22 July 2013 Dublin.

- 99^{th}Congr. Naz. Soc. It. Fis., 23-27 September 2013 Trieste.

- Journées LISA France, APC, 7-8 April 2014 Paris.

- Hot topics in Modern Cosmology Spontaneous Workshop VIII, 12-17 May 2014 Carghjese.

- X LISA symposium, 18-23 May 2014 Gainesville.

- 9^{th}IARD Conference, 9-13 June 2014 Storrs.

- 17^{th}Capra Mtg. on radiation reaction, 23-27 June 2014 Pasadena.

- 14^{th}Frontiers of Fundamental Physics, 15-18 July 2014 Marseille.

- 21^{th}It. Conf. on General Relativity and Gravitational Physics, 15-19 September 2014 Alessandria.

- Escola Brasileira de Cosmologia e Gravitação, Vargas Grande, 31 October 2014.

- Fundação Planetário da Cidade do Rio de Janeiro, 19 November 2014, Seminar for the 44^{th}anniversary.

- 14^{th}Marcel Grossmann Mtg., 12-18 July 2015 Roma.

- Journées Scientifiques GRAM, 2-3 June 2016 Paris.

- Estate Quantistica, 13-17 June 2016 Scalea.

- 19^{th}Capra Meeting on Radiation Reaction in General Relativity, 27 June – 1 July 2016 Meudon.

- Cosmology on small scales, 20-23 September 2016 Praha.

## PROJECTS

next

- SILEX Semi conductor Intersatellite Link Experiment

- ESA Study scientist for Time & Frequency Science Utilization and Space Station Study, Contract 11287/94/NL/VK with Un. Stuttgart, CERGA Grasse, Lab. de Spectroscopie Herzienne ENS Paris, Un. Tübingen (Un. Dresden), Un. München, DLR, DASA-RI. The study has conceived ACES, Atomic Clock Ensemble in Space.

- eLISA/NGO Evolved Laser Interferometer Space Antenna / New Gravitational Wave Observatory. LISA France

- Virgo gravitational wave detector. VESF

## SOME DOCTORATE STUDENTS - POST-DOCS

next

- Vincenzo Pierro, post-doc, now Professore Associato at the Università del Sannio, Benevento

- Sofiane Aoudia, Doctorate student, post-doc at the Max Planck Institut für Gravitationphysik A. Einstein, Golm, now Maitre de Conférences at the Université de Béjaïa

- Patxi Ritter, Doctorate student, post-doc in Praha

- Luca Bonetti, Doctorate student from Trento, 2013-

- Marius Oltean, Doctorate student from Canada-Romania in part-time with Barcelona, Eiffel and NRC grants, 2015-

## TEACHING, RESEARCH AND POLITICS IN FRANCE

University Professors are named by the President of the Republic. Though Italian, I was honoured by the former President Jacques Chirac. [pdf]

Foreign researchers are sometime victims of discrimination, as it occurred to one of my previous non-EU students for a visa renewal. Lately, the government had to step back as the Washington Post reports herein.

## LEASURE AND SCIENCE LINKS

La grande bellezza

Tracery

In trutina

The Book human race should save

## MY FULL NAME

Alessandro Domenico Aloisio Maria Spallicci di Filottrano

Nicknames: Mimino, Picitrè, Mimmo, Cicci, Ale, Alex, Sandro

## NOVELIST

Some novels under the title 'Antologia del Fiume Oglio' have appeared in February 2015 by Arnoldo Mondadori Editore, in the 'Gialli' series as winner of the Suzzara prize for unpblished stories.

## WHERE I HANG MOST

My list of best world cities: 1. Venezia, 2. Roma, 3. Amsterdam, 4. Barcelona, 5. London, 6. Fort Cochin, 7. Rio de Janeiro ......

## SOME RELATIVES

Aldo Spallicci

Mario Spallicci

Emilio Spallicci with Sandro Pertini and Oscar Scalfaro [pdf]

## PEOPLE I HAVE MET

Some people I have met [pdf]

## HOW TO GET TO LPC2E

Visit the page of the CNRS campus (in French) herein. Else, once arrived at one of the stations (Les Aubrais or Gare d'Orléans), get bus n. 7 (ticket in the bus), drop off at the stop "Recherche Scientifique", and then walk for 10-15 minutes, see map. It takes 30-40 minutes from the railway station.

## WHO IS LOOKING AT MY WEBPAGE

(CLUSTRMAPS again stuck and not working)Yes – the springtimes needed you. Often a star was waiting for you to notice it. A wave rolled toward you out of the distant past, or as you walked under an open window, a violin yielded itself to your hearing. All this was mission. But could you accomplish it ?

Clustrmaps data 10 Jun 2012 to 16 Mar 2015 before crash server : 2,589 visits, click the pdf link