arXiv subjects

Antoine Folacci

Publications and source records attributed to Antoine Folacci.

At least 19 recordsLinked to original sources

arXiv2021

Quasinormal mode frequencies of Kerr black holes from Regge trajectories

A large portion of the studies concerning the quasinormal mode frequencies of a Kerr black hole have focused only on achieving higher numerical accuracy with limited emphasis on providing their physical interpretation. In this article, we partially address this issue by computing the quasinormal mode frequency spectrum of a Kerr black hole using the theory of Regge poles. By considering the retarded Green's function of the Teukolsky equation, we establish for scalar, electromagnetic and gravitational perturbations an equation linking the Regge poles to the quasinormal frequencies and we solve it in the high-frequency regime to get "semiclassical" relations permitting us to obtain the complex frequencies of the weakly damped quasinormal modes from the Regge trajectories. Numerical results concerning gravitational perturbations ($s=-2$) are displayed. They are in excellent agreement with the "exact" ones in the eikonal regime $(\ell \gg 1)$ and in very good agreement even for lower values of $\ell$. Moreover, the splitting of each Regge pole of the Schwarzschild black hole into an infinite number of Kerr Regge poles explains the breaking of the azimuthal degeneracy of the quasinormal frequencies of the Schwarzschild black hole due to rotation. Our work is a first step to extend to Kerr black holes the approach developed for static spherically symmetric black holes which allowed, from a geometrical interpretation of the Regge poles in terms of the properties of the unstable circular null geodesics lying on the photon sphere, to derive accurate analytical formulas for the Regge trajectories and, as a by-product, for the complex frequencies of the weakly damped quasinormal modes.

gr-qc↗

arXiv2020

Electromagnetic radiation generated by a charged particle falling radially into a Schwarzschild black hole: A complex angular momentum description

By using complex angular momentum techniques, we study the electromagnetic radiation generated by a charged particle falling radially from infinity into a Schwarzschild black hole. We consider both the case of a particle initially at rest and that of a particle projected with a relativistic velocity and we construct complex angular momentum representations and Regge pole approximations of the partial wave expansions defining the Maxwell scalar $\phi_2$ and the energy spectrum $dE/d\omega$ observed at spatial infinity. We show, in particular, that Regge pole approximations involving only one Regge pole provide effective resummations of these partial wave expansions permitting us (i) to reproduce with very good agreement the black hole ringdown without requiring a starting time, (ii) to describe with rather good agreement the tail of the signal and sometimes the pre-ringdown phase, and (iii) to explain the oscillations in the electromagnetic energy spectrum radiated by the charged particle. The present work as well as a previous one concerning the gravitational radiation generated by a massive particle falling into a Schwarzschild black hole [A. Folacci and M. Ould El Hadj, Phys. Rev. D$\textbf{98}$, 064052 (2018), arXiv:1807.09056 [gr-qc]] highlight the benefits of studying radiation from black holes in the complex angular momentum framework (they obviously appear when the approximations obtained involve a small number of Regge poles and have a clear physical interpretation) but also to exhibit the limits of this approach (this is the case when it is necessary to take into account background integral contributions).

gr-qc↗

arXiv2019

Regge pole description of scattering of gravitational waves by a Schwarzschild black hole

We revisit the problem of plane monochromatic gravitational waves impinging upon a Schwarzschild black hole using complex angular momentum techniques. By extending our previous study concerning scalar and electromagnetic waves [A. Folacci and M. Ould El Hadj, Phys.\, Rev.\, D {\bf 99}, 104079, (2019), arXiv:1901.03965], we provide complex angular momentum representations and Regge pole approximations of the helicity-preserving and helicity-reversing scattering amplitudes and of the total differential scattering cross section. We show, in particular, that for high frequencies (i.e., in the short-wavelength regime), a small number of Regge poles permits us to describe numerically with very good agreement the black hole glory and the orbiting oscillations and we then provide a semiclassical approximation that unifies these two phenomena.

gr-qc↗

arXiv2019

Regge pole description of scattering of scalar and electromagnetic waves by a Schwarzschild black hole

We revisit the problem of scalar and electromagnetic waves impinging upon a Schwarzschild black hole from complex angular momentum techniques. We focus more particularly on the associated differential scattering cross sections. We derive an exact representation of the corresponding scattering amplitudes by replacing the discrete sum over integer values of the angular momentum which defines their partial wave expansions by a background integral in the complex angular momentum plane plus a sum over the Regge poles of the $S$-matrix involving the associated residues. We show that, surprisingly, the background integral is numerically negligible for intermediate and high frequencies and, as a consequence, that the cross sections can be reconstructed in terms of Regge poles with very good agreement. We show in particular that, for large values of the scattering angle, a small number of Regge poles permits us to describe the black hole glory and that, by increasing the number of Regge poles, we can reconstruct very efficiently the differential scattering cross sections for small and intermediate scattering angles and therefore describe the orbiting oscillations. In fact, in the short-wavelength regime, the sum over Regge poles allows us to extract by resummation the information encoded in the partial wave expansion defining a scattering amplitude and, moreover, to overcome the difficulties linked to its lack of convergence due to the long-range nature of the fields propagating on the black hole. As a consequence, from asymptotic expressions for the lowest Regge poles and the associated residues based on the correspondence Regge poles -- ``surface waves'' propagating close to the photon sphere, we can provide an analytical approximation describing both the black hole glory and a large part of the orbiting oscillations. We finally discuss the role of the background integral for low frequencies.

gr-qc↗

arXiv2018

An alternative description of gravitational radiation from black holes based on the Regge poles of the ${\cal S}$-matrix and the associated residues

We advocate for an alternative description of gravitational radiation from black holes based on complex angular momentum techniques (analytic continuation of partial wave expansions, duality of the ${\cal S}$-matrix and effective resummations involving its Regge poles and the associated residues, Regge trajectories, semiclassical interpretations, etc.). Such techniques, which proved to be very helpful in various areas of physics to describe and analyze resonant scattering, were only marginally used in the context of black hole physics. Here, by considering the multipolar waveform generated by a massive particle falling radially from infinity into a Schwarzschild black hole, we show that they could play a fundamental role in gravitational-wave physics. More precisely, from the multipole expansion defining the Weyl scalar $\Psi_4$, we extract the Fourier transform of a sum over Regge poles and their residues which can be evaluated numerically from the associated Regge trajectories. This Regge pole approximation permits us to reconstruct, for an arbitrary direction of observation, a large part of the multipolar waveform $\Psi_4$. In particular, it can reproduce with very good agreement the quasinormal ringdown as well as with rather good agreement the tail of the signal. This is achieved even if we take into account only one Regge pole and, if a large number of modes are excited, the result can be improved by considering additional poles. Moreover, while quasinormal-mode contributions do not provide physically relevant results at "early times" due to their exponentially divergent behavior as time decreases, it is not necessary to determine from physical considerations a starting time for the Regge ringdown.

gr-qc↗

arXiv2018

Multipolar gravitational waveforms and ringdowns generated during the plunge from the innermost stable circular orbit into a Schwarzschild black hole

We study the gravitational radiation emitted by a massive point particle plunging from slightly below the innermost stable circular orbit into a Schwarzschild black hole. We consider both even- and odd-parity perturbations and describe them using the two gauge-invariant master functions of Cunningham, Price, and Moncrief. We obtain, for arbitrary directions of observation and, in particular, outside the orbital plane of the plunging particle, the regularized multipolar waveforms, i.e., the waveforms constructed by summing over of a large number of modes, and their unregularized counterparts constructed from the quasinormal-mode spectrum. They are in excellent agreement and our results permit us to especially emphasize the impact on the distortion of the waveforms of (i) the harmonics beyond the dominant $(\ell=2,m=\pm 2)$ modes and (ii) the direction of observation, and therefore the necessity to take them into account in the analysis of the last phase of binary black hole coalescence.

gr-qc↗

arXiv2018

Electromagnetic radiation generated by a charged particle plunging into a Schwarzschild black hole: Multipolar waveforms and ringdowns

Electromagnetic radiation emitted by a charged particle plunging from slightly below the innermost stable circular orbit into a Schwarzschild black hole is examined. Both even- and odd-parity electromagnetic perturbations are considered. They are described by using gauge invariant master functions and the regularized multipolar waveforms as well as their unregularized counterparts constructed from the quasinormal-mode spectrum are obtained for arbitrary directions of observation and, in particular, outside the orbital plane of the plunging particle. They are in excellent agreement and the results especially emphasize the impact of higher harmonics on the distortion of the waveforms.

gr-qc↗

arXiv2016

Stueckelberg massive electromagnetism in de Sitter and anti-de Sitter spacetimes: Two-point functions and renormalized stress-energy tensors

By considering Hadamard vacuum states, we first construct the two-point functions associated with Stueckelberg massive electromagnetism in de Sitter and anti-de Sitter spacetimes. Then, from the general formalism developed in [A. Belokogne and A. Folacci, Phys. Rev. D \textbf{93}, 044063 (2016)], we obtain an exact analytical expression for the vacuum expectation value of the renormalized stress-energy tensor of the massive vector field propagating in these maximally symmetric spacetimes.

gr-qc↗

arXiv2016

Waveforms in massive gravity and neutralization of giant black hole ringings

A distorted black hole radiates gravitational waves in order to settle down in a smoother geometry. During that relaxation phase, a characteristic damped ringing is generated. It can be theoretically constructed from both the black hole quasinormal frequencies (which govern its oscillating behavior and its decay) and the associated excitation factors (which determine intrinsically its amplitude) by carefully taking into account the source of the distortion. In the framework of massive gravity, the excitation factors of the Schwarzschild black hole have an unexpected strong resonant behavior which, theoretically, could lead to giant and slowly decaying ringings. If massive gravity is relevant to physics, one can hope to observe these extraordinary ringings by using the next generations of gravitational wave detectors. Indeed, they could be generated by supermassive black holes if the graviton mass is not too small. In fact, by focusing on the odd-parity $\ell=1$ mode of the Fierz-Pauli field, we shall show here that such ringings are neutralized in waveforms due to (i) the excitation of the quasibound states of the black hole and (ii) the evanescent nature of the particular partial modes which could excite the concerned quasinormal modes. Despite this, with observational consequences in mind, it is interesting to note that the waveform amplitude is nevertheless rather pronounced and slowly decaying (this effect is now due to the long-lived quasibound states). It is worth noting also that, for very low values of the graviton mass (corresponding to the weak instability regime for the black hole), the waveform is now very clean and dominated by an ordinary ringing which could be used as a signature of massive gravity.

gr-qc↗

arXiv2015

Stueckelberg massive electromagnetism in curved spacetime: Hadamard renormalization of the stress-energy tensor and the Casimir effect

We discuss Stueckelberg massive electromagnetism on an arbitrary four-dimensional curved spacetime (gauge invariance of the classical theory and covariant quantization, wave equations for the massive spin-1 field $A_\mu$, for the auxiliary Stueckelberg scalar field $\Phi$ and for the ghost fields $C$ and $C^\ast$, Ward identities, Hadamard representation of the various Feynman propagators and covariant Taylor series expansions of the corresponding coefficients). This permits us to construct, for a Hadamard quantum state, the expectation value of the renormalized stress-energy tensor associated with the Stueckelberg theory. We provide two alternative but equivalent expressions for this result. The first one is obtained by removing the contribution of the "Stueckelberg ghost" $\Phi$ and only involves state-dependent and geometrical quantities associated with the massive vector field $A_\mu$. The other one involves contributions coming from both the massive vector field and the auxiliary Stueckelberg scalar field, and it has been constructed in such a way that, in the zero-mass limit, the massive vector field contribution reduces smoothly to the result obtained from Maxwell's theory. As an application of our results, we consider the Casimir effect outside a perfectly conducting medium with a plane boundary. We discuss the results obtained using Stueckelberg but also de Broglie-Proca electromagnetism and we consider the zero-mass limit of the vacuum energy in both theories. We finally compare the de Broglie-Proca and Stueckelberg formalisms and highlight the advantages of the Stueckelberg point of view, even if, in our opinion, the de Broglie-Proca and Stueckelberg approaches of massive electromagnetism are two faces of the same field theory.

gr-qc↗

arXiv2015

Waveforms produced by a scalar point particle plunging into a Schwarzschild black hole: Excitation of quasinormal modes and quasibound states

With the possibility of testing massive gravity in the context of black hole physics in mind, we consider the radiation produced by a particle plunging from slightly below the innermost stable circular orbit into a Schwarzschild black hole. In order to circumvent the difficulties associated with black hole perturbation theory in massive gravity, we use a toy model in which we replace the graviton field with a massive scalar field and consider a linear coupling between the particle and this field. We compute the waveform generated by the plunging particle and study its spectral content. This permits us to highlight and interpret some important effects occurring in the plunge regime which are not present for massless fields such as (i) the decreasing and vanishing, as the mass parameter increases, of the signal amplitude generated when the particle moves on quasicircular orbits near the innermost stable circular orbit and (ii) in addition to the excitation of the quasinormal modes, the excitation of the quasibound states of the black hole.

gr-qc↗

arXiv2014

Renormalized stress tensor for massive fields in Kerr-Newman spacetime

In a four-dimensional spacetime, the DeWitt-Schwinger expansion of the effective action associated with a massive quantum field reduces, after renormalization and in the large mass limit, to a single term constructed from the purely geometrical Gilkey-DeWitt coefficient $a_3$ and its metric variation provides a good analytical approximation for the renormalized stress-energy tensor of the quantum field. Here, from the general expression of this tensor, we obtain analytically the renormalized stress-energy tensors of the massive scalar field, the massive Dirac field and the Proca field in Kerr-Newman spacetime. It should be noted that, even if, at first sight, the expressions obtained are complicated, their structure is in fact rather simple, involving naturally spacetime coordinates as well as the mass $M$, the charge $Q$ and the rotation parameter $a$ of the Kerr-Newman black hole and permitting us to recover rapidly the results already existing in the literature for the Schwarzschild, Reissner-Nordström and Kerr black holes (and to correct them in the latter case). In the absence of exact results in Kerr-Newman spacetime, our approximate renormalized stress-energy tensors could be very helpful, in particular to study the backreaction of massive quantum fields on this spacetime or on its quasinormal modes.

gr-qc↗

arXiv2014

Resonant excitation of black holes by massive bosonic fields and giant ringings

We consider the massive scalar field, the Proca field and the Fierz-Pauli field in the Schwarzschild spacetime and we focus more particularly on their long-lived quasinormal modes. We show numerically that the associated excitation factors have a strong resonant behavior and we confirm this result analytically from semiclassical considerations based on the properties of the unstable circular geodesics on which a massive particle can orbit the black hole. The conspiracy of (i) the long-lived behavior of the quasinormal modes and (ii) the resonant behavior of their excitation factors induces intrinsic giant ringings, i.e., ringings of a huge amplitude. Such ringings, which are moreover slowly decaying, are directly constructed from the retarded Green function. If we describe the source of the black hole perturbation by an initial value problem with Gaussian initial data, i.e., if we consider the excitation of the black hole from an extrinsic point of view, we can show that these extraordinary ringings are still present. This suggests that physically realistic sources of perturbations should generate giant and slowly decaying ringings and that their existence could be used to constrain ultralight bosonic field theory interacting with black holes.

gr-qc↗

arXiv2014

Giant black hole ringings induced by massive gravity

A distorted black hole radiates gravitational waves in order to settle down in one of the geometries permitted by the no-hair theorem. During that relaxation phase, a characteristic damped ringing is generated. It can be theoretically constructed from the black hole quasinormal frequencies (which govern its oscillating behavior and its decay) and from the associated excitation factors (which determine intrinsically its amplitude) by carefully taking into account the source of the distortion. Here, by considering the Schwarzschild black hole in the framework of massive gravity, we show that the excitation factors have an unexpected strong resonant behavior leading to giant ringings which are, moreover, slowly decaying. Such extraordinary black hole ringings could be observed by the next generations of gravitational wave detectors and allow us to test the various massive gravity theories or their absence could be used to impose strong constraints on the graviton mass.

gr-qc↗

arXiv2011

Resonance and absorption spectra of the Schwarzschild black hole for massive scalar perturbations: a complex angular momentum analysis

We reexamine some aspects of scattering by a Schwarzschild black hole in the framework of complex angular momentum techniques. More precisely, we consider, for massive scalar perturbations, the high-energy behavior of the resonance spectrum and of the absorption cross section by emphasizing analytically the role of the mass. This is achieved (i) by deriving asymptotic expansions for the Regge poles of the $S$-matrix and then for the associated weakly damped quasinormal frequencies and (ii) by taking into account the analytic structure of the greybody factors which allows us to extract by resummation the physical information encoded in the absorption cross section.

gr-qc↗

arXiv2011

Fine structure of high-energy absorption cross sections for black holes

The high-energy absorption cross section of the Schwarzschild black hole is well approximated, in the eikonal regime, by the sum of two terms: the geometrical cross section of the black hole photon sphere and the contribution of a sinc function involving the geometrical characteristics (orbital period and Lyapunov exponent) of the null unstable geodesics lying on this photon sphere. From a numerical analysis, we show that, beyond the eikonal description, this absorption cross section presents a simple fine structure. We then describe it analytically by using Regge pole techniques and interpret it in geometrical terms. We naturally extend our analysis to arbitrary static spherically symmetric black holes endowed with a photon sphere and we then apply our formalism to Schwarzschild-Tangherlini and Reissner-Nordström black holes. Finally, on the example of the Schwarzschild black hole, we show numerically that a complicated hyperfine structure lying beyond the fine structure can also be observed.

gr-qc↗

arXiv2011

Universality of high-energy absorption cross sections for black holes

We consider the absorption problem for a massless scalar field propagating in static and spherically symmetric black holes of arbitrary dimension endowed with a photon sphere. For this wide class of black holes, we show that the fluctuations of the high-energy absorption cross section are totally and very simply described from the properties (dispersion relation and damping) of the waves trapped near the photon sphere and therefore, in the eikonal regime, from the characteristics (orbital period and Lyapunov exponent) of the null unstable geodesics lying on the photon sphere. This is achieved by using Regge pole techniques. They permit us to make an elegant and powerful resummation of the absorption cross section and to extract then all the physical information encoded in the sum over the partial wave contributions. Our analysis induces moreover some consequences concerning Hawking radiation which we briefly report.

gr-qc↗

arXiv2010

Surface polaritons of a left-handed curved slab

We study the propagation of surface polaritons in a left-handed curved slab, i.e. a curved slab made of a negative-refractive-index material. We consider the effects of the slab curvature on their dispersion relations and attenuations. We show more particularly that surface polaritons with a "left-handed behavior" (i.e. with opposite group and phase velocities) propagate without any attenuation.

physics.optics↗