# Alessandro D. Spallicci - Observatoire de la Cote d'Azur, Nice

## Contact Details

NameAlessandro D. Spallicci |
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AffiliationObservatoire de la Cote d'Azur, Nice |
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CityNice |
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CountryFrance |
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## Pubs By Year |
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## Pub CategoriesGeneral Relativity and Quantum Cosmology (22) High Energy Astrophysical Phenomena (12) Mathematics - Mathematical Physics (8) Mathematical Physics (8) Cosmology and Nongalactic Astrophysics (6) High Energy Physics - Phenomenology (5) Physics - Space Physics (2) Astrophysics (2) Physics - General Physics (1) Mathematics - Analysis of PDEs (1) Physics - History of Physics (1) Physics - Classical Physics (1) Instrumentation and Methods for Astrophysics (1) Physics - Statistical Mechanics (1) High Energy Physics - Theory (1) High Energy Physics - Experiment (1) Physics - Plasma Physics (1) |

## Publications Authored By Alessandro D. Spallicci

The gravitational waves emitted by binary systems with extreme mass ratios carry unique astrophysical information expected to be probed by the next generation of gravitational wave detectors such as LISA. The detection of these binaries rely on an accurate modeling of the gravitational self-force that drives their orbital evolution. Although the theoretical formalism to compute the self-force has been largely established, the mathematical tools needed to implement it are still under development, and the self-force computation remains an open problem. Read More

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: $z = 0.19273(8)$. Read More

We show that photons may be redshifted or blueshifted when interacting with the field of an overcritical dipole, which incorporates the one-loop QED corrections coming from vacuum polarization. Using the effective metric, it follows that such effect depends on the polarization of the photon. The shifts, plotted against the azimuthal angle for various values of the magnetic field, may show an intensity comparable to the gravitational redshift for a magnetar. Read More

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). Read More

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. Read More

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 to some standard matter (scalar and electromagnetic) field theories in curved spacetime, 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. Read More

**Category:**General Relativity and Quantum Cosmology

(Short abstract). 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. Otherwise, an additional 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. Read More

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 $m_\gamma$. The dispersion measure (DM) of FRB 150418 is known to $\sim 0.1$%, and there is a claim to have measured its redshift with an accuracy of $\sim 2$%, but the strength of the constraint on $m_\gamma$ 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). Read More

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. Read More

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. Read More

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. Read More

We intend to develop part of the theoretical tools needed for the detection of gravitational waves coming from the capture of a compact object, 1-100 solar masses, by a Supermassive Black Hole, up to a 10 billion solar masses, located at the centre of most galaxies. The analysis of the accretion activity unveils the star population around the galactic nuclei, and tests the physics of black holes and general relativity. The captured small mass is considered a probe of the gravitational field of the massive body, allowing a precise measurement of the particle motion up to the final absorption. Read More

**Authors:**Alessandro D. A. M. Spallicci

Gravitational waves coming from Super Massive Black Hole Binaries (SMBHBs) are targeted by both 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. Read More

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 wave function and its derivatives, iii) the values of the wave function at adjacent cells. Read More

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\textsuperscript{0} 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. Read More

Free fall has signed the greatest markings in the history of physics through the leaning Pisa tower, the Cambridge apple tree and the Einstein lift. The perspectives offered by the capture of stars by supermassive black holes are to be cherished, because the study of the motion of falling stars will constitute a giant step forward in the understanding of gravitation in the regime of strong field. After an account on the perception of free fall in ancient times and on the behaviour of a gravitating mass in Newtonian physics, this chapter deals with last century debate on the repulsion for a Schwarzschild black hole and mentions the issue of an infalling particle velocity at the horizon. Read More

We establish the jump conditions for the wavefunction and its derivatives through the formal solutions of the wave equation. These conditions respond to the requirement of continuity of the perturbations at the position of the particle and they are given for any mode at first order. Using these jump conditions, we then propose a new method for computing the radiated waveform without direct integration of the source term. Read More

In the context of star capture by a black hole, a new noticeable difference between Brans-Dicke theory and general relativity gravitational radiation is pointed out. This feature stems from the non-stationarity of the black hole state, barring Hawking's theorem. Read More

The concept of a measurement of the yet unevaluated Hannay angle, by means of an Earth-bound satellite, adiabatically driven by the Moon, is shown herein. Numerical estimates are given for the angles, the orbital displacements, the shortening of the orbital periods, for different altitudes. It is concluded that the Hannay effect is measurable in high Earth orbits, by means of atomic clocks, accurate Time & Frequency transfer system and precise positioning. Read More

For future configurations, we study the relation between the abatement of the noise sources and the Signal to Noise Ratio (SNR) for coalescing binaries. Our aim is not the proposition of a new design, but an indication of where in the bandwidth or for which noise source, a noise reduction would be most efficient. We take VIRGO as the reference for our considerations, solely applicable to the inspiralling phase of a coalescing binary. Read More

**Affiliations:**

^{1}Dip. Matematica, Univ. di Torino,

^{2}Observatoire de la Cote d'Azur, Nice

Exact solutions, in terms of special functions, of all wave equations $% u_{xx} - u_{tt} = V(x) u(t,x)$, characterised by eight inequivalent time independent potentials and by variable separation, have been found. The real valueness of the solutions from computer algebra programs is not always manifest and in this work we provide ready to use solutions. We discussed especially the potential $\cosh^{-2}x (m_1 + m_2 \sinh x)$. Read More

**Affiliations:**

^{1}Observatoire de la Cote d'Azur, Nice,

^{2}Observatoire de la Cote d'Azur, Nice

This work deals with the motion of a radially falling star in Schwarzschild geometry and correctly identifies radiation reaction terms by the perturbative method. The results are: i) identification of all terms up to first order in perturbations, second in trajectory deviation, and mixed terms including lowest order radiation reaction terms; ii) renormalisation of all divergent terms by the $\zeta$ Riemann and Hurwitz functions. The work implements a method previously identified by one of the authors and corrects some current misconceptions and results. Read More

An analytic solution of the Regge-Wheeler (RW) equation has been found via the Frobenius method at the regular singularity of the horizon 2M, in the form of a time and radial coordinate dependent series. The RW partial differential equation, derived from the Einstein field equations, represents the first order perturbations of the Schwarzschild metric. The known solutions are numerical in time domain or approximate and asymptotic for low or high frequencies in Fourier domain. Read More

**Affiliations:**

^{1}Univ. Salerno at Benvento, Gravitation Research Group

**Category:**General Relativity and Quantum Cosmology

A novel method for calculation of the motion and radiation reaction for the two-body problem (body plus particle, the small parameter m/M being the ratio of the masses) is presented. In the background curvature given by the Schwarzschild geometry rippled by gravitational waves, the geodesic equations insure the presence of radiation reaction also for high velocities and strong field. The method is generally applicable to any orbit, but radial fall is of interest due to the non-adiabatic regime (equality of radiation reaction and fall time scales), in which the particle locally and immediately reacts to the emitted radiation. Read More