arXiv subjects

Eric Gourgoulhon

Publications and source records attributed to Eric Gourgoulhon.

At least 19 recordsLinked to original sources

arXiv2026

Horizon Multipole Moments of a Kerr Black Hole

The horizon multipole moments of a Kerr black hole are computed from two distinct definitions that have been proposed in the literature. The first one [Ashtekar et al., Class. Quantum Grav. 21, 2549 (2004)] regards axisymmetric isolated horizons, while the second one [Ashtekar et al., J. High Energ. Phys. 2022, 28 (2022)] applies to generic (i.e., not necessarily axisymmetric) non-expanding horizons. We review these definitions in a common frame and perform a detailed study of the resulting multipole moments for the Kerr event horizon. The horizon multipoles are found to share several properties with the (Hansen) field multipoles, including parity constraints and the leading scaling behavior with respect to the Kerr spin parameter a in the regime of small a. For the axisymmetry-based definition, we have obtained a closed-form expression of the multipole moments in terms of a and the spherical harmonic degree l. For the generic definition, we have established closed-form expressions for the conformal unit round metric, the `electric' and `magnetic' potentials related to the multipoles, and the values of the multipoles in the small a limit. We show that the two definitions lead to different values of the Kerr horizon multipoles as soon as l >= 1 (generic nonzero value of a) or l >= 2 (small a limit).

gr-qc↗

arXiv2026

Jet launching from the Kerr black hole magnetosphere: An electrogeodesic approach

The launch of relativistic jets of plasma on astrophysical to cosmological scales is observed in a variety of astrophysical sources, from active galactic nuclei to X-ray binaries. While these jets can be reproduced by general relativistic magneto-hydrodynamics (GRMHD) and particle-in-cells (GRPIC) simulations of the dynamical Kerr magnetosphere, the development of analytic models to describe the physics of the jets has remained limited. A key challenge is to analytically describe the individual trajectories of accelerated charged particles, which ultimately build up the jet and emit radiation. In this work, we provide a first simple but fully analytical model of jet launching from the Kerr magnetosphere based on the motion of charged particles. To that end, we use the integrability of electrogeodesic motion in the Kerr monopole magnetosphere to study the ejection of charged particles near the poles. This enables us to derive (i) a criterion for the rotation axis to constitute a stable latitudinal equilibrium position, thereby representing an idealized jet, (ii) the expression for the magnetic frame-dragging effect, and (iii) the condition for an asymptotic observer to measure blueshifted particles emanating from the black hole surroundings. Our study reveals that particles can be accelerated only in a specific region whose maximal radius depends on the spin and magnetization of the black hole. Alongside these results, we provide a detailed review of the construction of test magnetospheres from (explicit and hidden) symmetries of the Kerr geometry and the condition for the separability of the electrogeodesic motion in a test magnetosphere, which serves as a basis for the model studied in this work.

astro-ph.HE↗

arXiv2025

Magnetically supramassive and hypermassive compact stars

It is known that the mass of magnetized relativistic compact star is larger than that of non-magnetized one for the same equation of state and central density, albeit the excess of mass is sizable only if the magnetic fields are strong enough B~10^17-10^18G. Using our recently developed numerical code COCAL, we systematically compute such compact star solutions in equilibrium associated with mixed poloidal and toroidal magnetic fields, and show the magnetically supramassive solutions whose masses exceed by more than 10% of the maximum mass of the static and spherically symmetric solutions. For some extremely strong magnetic field configurations, we also obtain solutions more massive than the maximum mass of the uniformly rotating solutions at the Kepler (mass-shedding) limit, namely magnetically hypermassive solutions.

gr-qc↗

arXiv2025

Black hole photon ring beyond General Relativity: an integrable parametrization

In recent years, the shape of the photon ring in black holes images has been argued to provide a sharp test of the Kerr hypothesis for future black hole imaging missions. In this work, we confront this proposal to beyond Kerr geometries and investigate the degeneracy in the estimations of the black hole parameters using the circlipse shape proposed by Gralla and Lupsasca. To that end, we consider a model-independent parametrization of the deviations to the Kerr black hole geometry, dubbed Kerr off shell (KOS), which preserves the fundamental symmetry structure of Kerr known as the Killing tower. Besides exhibiting a Killing tensor and thus a Carter-like constant, all the representants of this family also possess a Killing-Yano tensor and are of Petrov type D. The allowed deviations to Kerr, selected by the symmetry, are encoded in two free functions which depend respectively on the radial and polar angle coordinates. Using the symmetries, we provide an analytic study of the radial and polar motion of photon trajectories generating the critical curve, to which the subrings composing the photon ring converge. This allows us to derive a ready-to-use closed formula for the parametric critical curve in term of the free functions parametrizing the deviations to Kerr. Using this result, we confront the circlipse fitting function to four examples of Kerr-like objects and we show that it admits a high degree of degeneracy. At a given inclination, the same circlipse can fit both a Kerr black hole of a given mass and spin $(M,a)$ or a modified rotating black hole with different mass and spin parameters $(M,a)$ and a new parameter $α$. Therefore, future tests of the Kerr hypothesis could be achieved only provided one can measure independently the mass and spin of the black hole to break this degeneracy.

gr-qc↗

arXiv2024

More on thermal holographic RG flows in a 3D gauged supergravity

We continue our studies of holographic renormalization group (RG) flows for a 3d truncated supergravity model, the scalar potential of which can have either one or three extrema depending on the radius of the target manifold. We construct numerically and analytically thermal holographic RG flows, which are described by asymptotically AdS$_3$ black holes (non-rotating BTZ) characterized by the value of the scalar field on the horizon. We find two classes of RG flows with monotonic and non-monotonic behavior of the scalar field. The first one exists for both types of the potential, while the second one appears only for the potential with three extrema. For the slowly changing scalar field we find a special class of RG flows, which are described by the scalar field in the BTZ black hole geometry. For such flows we present an analytic solution for the scalar field from the horizon to the boundary. We discuss thermodynamical properties of the constructed holographic RG flows.

hep-th↗

arXiv2023

Equilibriums of extremely magnetized compact stars with force-free magnetotunnels

We present numerical solutions for stationary and axisymmetric equilibriums of compact stars associated with extremely strong magnetic fields. The interior of the compact stars is assumed to satisfy ideal magnetohydrodynamic (MHD) conditions, while in the region of negligible mass density the force-free conditions or electromagnetic vacuum are assumed. Solving all components of Einstein's equations, Maxwell's equations, ideal MHD equations, and force-free conditions, equilibriums of rotating compact stars associated with mixed poloidal and toroidal magnetic fields are obtained. It is found that in the extreme cases the strong mixed magnetic fields concentrating in a toroidal region near the equatorial surface expel the matter and form a force-free toroidal magnetotunnel. We also introduce a new differential rotation law for computing solutions associated with force-free magnetosphere, and present other extreme models without the magnetotunnel.

gr-qc↗

arXiv2023

Peeling at extreme black hole horizons

The starting point of this work was an intriguing similarity between the behaviour of fields near a degenerate horizon and near the infinity of an asymptotically flat spacetime, as revealed by the scattering theory for Dirac fields in the ``exterior'' region of the extreme Kerr - de Sitter black hole, developed by one of the authors (JB). However, in that situation, the comparison was somewhat clouded by some of the analytical techniques used in intermediate steps of the proof. The aim of the present work is to clarify the comparison further by studying instead the peeling behaviour of solutions to the wave equation at an extremal horizon. We focus first on the extreme Reissner-Nordström black hole, for which the Couch-Torrence inversion (a global conformal isometry that exchanges the horizon and infinity) makes the analogy explicit. Then, we explore more general spherically symmetric situations using the Couch-Torrence inversion outside of its natural context.

gr-qc↗

arXiv2023

High precision numerical sequences of rotating hairy black holes

We analyze numerically the existence of regular stationary rotating hairy black holes within the framework of general relativity, which are the result of solving the Einstein-Klein-Gordon system for a complex-valued scalar field under suitable boundary (regularity and asymptotically flat) conditions. To that aim we solve the corresponding system of elliptic partial differential equations using spectral methods which are specially suited for such a numerical task. In order to obtain such system of equations we employ a parametrization for the metric that corresponds to quasi-isotropic coordinates (QIC) that have been used in the past for analyzing different kinds of stationary rotating relativistic systems. Our findings are in agreement with those reported originally by Herdeiro \& Radu ite{Herdeiro2014,Herdeiro2015}. The method is submitted to several analytic and numerical tests, which include the recovery of the Kerr solution in QIC and the cloud solutions in the Kerr background. We report different global quantities that allow us to determine the contribution of the boson hair to the spacetime, as well as relevant quantities at the horizon, like the surface gravity. The latter indicates to what extent the hairy solutions approach the extremal limit, noting that for this kind of solutions the ratio of the angular momentum per squared mass $J_\infty/M^2_{\rm ADM}$ can be larger than unity due to the contribution of the scalar hair, a situation which differs from the Kerr metric where this parameter is bounded according to $0\leq |J/M^2| \leq 1$ with the upper bound corresponding to the extremal case.

gr-qc↗

arXiv2022

Heavy quarks in rotating plasma via holography

We continue to explore the dynamics of a heavy quark in a strongly coupled rotating quark-gluon plasma within the holographic framework. We use the 5d Kerr-AdS black hole with two arbitrary rotating parameters to describe the rotating quark-gluon plasma. We present the relations for the drag force acting on the heavy quark both in the rotating- and static-at-infinity frames for arbitrary choice of the rotational parameters. We also calculate the thermal mass of a static quark in different frames and show that at high-$T$ limit the dependence on rotation is suppressed.

hep-th↗

arXiv2022

Equatorial orbits and imaging of hairy cubic Galileon black holes

Null and timelike equatorial orbits are investigated in a family of hairy black holes in the cubic Galileon theory. These include rotating generalizations of static black hole metrics supporting a time-dependent scalar field. Depending on the coupling and rotation, the properties of the geodesics expectedly deviate from general relativity. In particular, it is found that stable circular geodesics only exist below a critical coupling, which is related to the existence of an outermost stable circular orbit. Focusing on the strong-field region, images of an accretion disk are also produced to highlight tendencies that would constrain the model given further accurate observations of supermassive black holes.

gr-qc↗

arXiv2021

Holographic drag force in 5d Kerr-AdS black hole

We consider the 5d Kerr-AdS black hole as a gravity dual to rotating quark-gluon plasma. In the holographic prescription we calculate the drag force acting on a heavy quark. According to the holographic approach a heavy quark can be considered through the string in the gravity dual. We study the dynamics of the string for the Kerr-AdS backgrounds with one non-zero rotational parameter and two non-zero rotational parameters that are equal in magnitude. For the case of one non-zero rotational parameter we find good agreement with the prediction from the 4d case considered by arXiv:1012.3800).

hep-th↗

arXiv2020

A Galactic centre gravitational-wave Messenger

Our existence in the Universe resulted from a rare combination of circumstances. The same must hold for any highly developed extraterrestrial civilisation, and if they have ever existed in the Milky Way, they would likely be scattered over large distances in space and time. However, all technologically advanced species must be aware of the unique property of the galactic centre: it hosts Sagittarius A* (Sgr A*), the closest supermassive black hole to anyone in the Galaxy. A civilisation with sufficient technical know-how may have placed material in orbit around Sgr A* for research, energy extraction, and communication purposes. In either case, its orbital motion will necessarily be a source of gravitational waves. We show that a Jupiter-mass probe on the retrograde innermost stable circular orbit around Sgr A* emits, depending on the black hole spin, at a frequency of $f_{GW} = 0.63 - 1.07$ mHz and with a power of $P_{GW}=2.7 \times\, 10^{36} - 2.0 \times\, 10^{37}$ erg/s. We discuss that the energy output of a single star is sufficient to stabilise the location of an orbiting probe for a billion years against gravitational wave induced orbital decay. Placing and sustaining a device near Sgr A* is therefore astrophysically possible. Such a probe will emit an unambiguously artificial continuous gravitational wave signal that is observable with LISA-type detectors.

astro-ph.HE↗

arXiv2020

Hairy rotating black holes in cubic Galileon theory

Numerical solutions for asymptotically flat rotating black holes in the cubic Galileon theory are presented. These black holes are endowed with a nontrivial scalar field and exhibit a non-Schwarzschild behaviour: faster than $1/r$ convergence to Minkowski spacetime at spatial infinity and hence vanishing of the Komar mass. The metrics are compared with the Kerr metric for various couplings and angular velocities. Their physical properties are extracted and show significant deviations from the Kerr case.

gr-qc↗

arXiv2019

New code for equilibriums and quasiequilibrium initial data of compact objects. IV. Rotating relativistic stars with mixed poloidal and toroidal magnetic fields

A new code for computing fully general relativistic solutions of strongly magnetized rapidly rotating compact stars is developed as a part of the COCAL (Compact Object CALculator) code. The full set of Einstein's equations, Maxwell's equations and magnetohydrodynamic equations are consistently solved assuming perfect conductivity, stationarity, and axisymmetry, and strongly magnetized solutions associated with mixed poloidal and toroidal components of magnetic fields are successfully obtained in generic (non-circular) spacetimes. We introduce the formulation of the problem and the numerical method in detail, then present examples of extremely magnetized compact star solutions and their convergence tests. It is found that, in extremely magnetized stars, the stellar matter can be expelled from the region of strongest toroidal fields. Hence we conjecture that a toroidal electro-vacuum region may appear inside of the extremely magnetized compact stars, which may seem like the neutron star becoming the strongest toroidal solenoid coil in the universe.

gr-qc↗

arXiv2019

Gravitational waves from bodies orbiting the Galactic Center black hole and their detectability by LISA

We present the first fully relativistic study of gravitational radiation from bodies in circular equatorial orbits around the massive black hole at the Galactic Center, Sgr A* and we assess the detectability of various kinds of objects by the gravitational wave detector LISA. Our computations are based on the theory of perturbations of the Kerr spacetime and take into account the Roche limit induced by tidal forces in the Kerr metric. The signal-to-noise ratio in the LISA detector, as well as the time spent in LISA band, are evaluated. We have implemented all the computational tools in an open-source SageMath package, within the Black Hole Perturbation Toolkit framework. We find that white dwarfs, neutrons stars, stellar black holes, primordial black holes of mass larger than $10^{-4} M_\odot$, main-sequence stars of mass lower than $\sim 2.5\, M_\odot$ and brown dwarfs orbiting Sgr A* are all detectable in one year of LISA data with a signal-to-noise ratio above 10 during at least $10^5$ years in the slow inspiral towards either the innermost stable circular orbit (compact objects) or the Roche limit (main-sequence stars and brown dwarfs). The longest times in-band, of the order of $10^6$ years, are achieved for primordial black holes of mass $\sim 10^{-3} M_\odot$ down to $10^{-5} M_\odot$, depending on the spin of Sgr A*, as well as for brown dwarfs, just followed by white dwarfs and low mass main-sequence stars. The long time in-band of these objects makes Sgr A* a valuable target for LISA. We also consider bodies on close circular orbits around the massive black hole in the nucleus of the nearby galaxy M32 and find that, among them, compact objects and brown dwarfs stay for $10^3$ to $10^4$ years in LISA band with a 1-year signal-to-noise ratio above 10.

gr-qc↗

arXiv2018

Symbolic tensor calculus on manifolds: a SageMath implementation

These lecture notes present a method for symbolic tensor calculus that (i) runs on fully specified smooth manifolds (described by an atlas), (ii) is not limited to a single coordinate chart or vector frame, (iii) runs even on non-parallelizable manifolds and (iv) is independent of the symbolic backend used to perform calculus at the level of coordinate expressions. In addition to the main ideas, we discuss some details of the implementation in the open-source mathematics software system SageMath, which has been performed via the SageManifolds project.

gr-qc↗

arXiv2018

Thermalization of holographic Wilson loops in spacetimes with spatial anisotropy

In this paper, we study behaviour of Wilson loops in the boost-invariant nonequilibrium anisotropic quark-gluon plasma produced in heavy-ion collisions within the holographic approach. We describe the thermalization studying the evolution of the Vaidya metric in the boost-invariant and spatially anisotropic background. To probe the system during this process we calculate rectangular Wilson loops oriented in different spatial directions. We find that anisotropic effects are more visible for the Wilson loops lying in the transversal plane unlike the Wilson loops with partially longitudinal orientation. In particular, we observe that the Wilson loops can thermalizes first unlike to the order of the isotropic model. We see that Wilson loops on transversal contours have the shortest thermalization time. We also calculate the string tension and the pseudopotential at different temperatures for the static quark-gluon plasma. We show that the pseudopotential related to the configuration on the transversal plane has the screened Cornell form. We also show that the jet-quenching parameter related with the average of the light-like Wilson loop exhibits the dependence on orientations.

hep-th↗

arXiv2018

Imaging a non-singular rotating black hole at the center of the Galaxy

We show that the rotating generalization of Hayward's non-singular black hole previously studied in the literature is geodesically incomplete, and that its straightforward extension leads to a singular spacetime. We present another extension, which is devoid of any curvature singularity. The obtained metric depends on three parameters and, depending on their values, yields an event horizon or not. These two regimes, named respectively regular rotating Hayward black hole and naked rotating wormhole, are studied both numerically and analytically. In preparation for the upcoming results of the Event Horizon Telescope, the images of an accretion torus around Sgr A*, the supermassive object at the center of the Galaxy, are computed. These images contain, even in the absence of a horizon, a central faint region which bears a resemblance to the shadow of Kerr black holes and emphasizes the difficulty of claiming the existence of an event horizon from the analysis of strong-field images. The frequencies of the co- and contra-rotating orbits at the innermost stable circular orbit (ISCO) in this geometry are also computed, in the hope that quasi-periodic oscillations may permit to compare this model with Kerr's black hole on observational grounds.

gr-qc↗