arXiv subjects

Olivier Sarbach

Publications and source records attributed to Olivier Sarbach.

At least 19 recordsLinked to original sources

arXiv2026

Relaxation of a Vlasov gas to an inhomogeneous state due to phase space mixing in an axisymmetric potential: A Newtonian analogy of the Kerr orbital motion

We explore the dynamics of a Vlasov gas propagating in an external axisymmetric potential consisting of a central potential with an additional quadrupolar component which gives rise to two potential wells along the symmetry axis. Employing independently $N$-particle simulations and statistical methods, we show that an initially homogeneous and isotropic configuration evolves to an inhomogeneous final state with overdensities located at the wells. The quadrupolar component is chosen such that the equations of motion form an integrable Hamiltonian system, which allows one to compute the final state of the gas analytically. On the one hand, this allows one to compare the late-time behaviour of the simulations with an analytic prediction and on the other hand to understand the relaxation process through phase space mixing. Our model constitutes a Newtonian analogue of the particle motion in a Kerr spacetime, and we discuss possible applications to recently observed astrophysical phenomena.

astro-ph.HE↗

arXiv2026

General first-order constitutive equations for a relativistic dissipative multi-component fluid in the presence of a weak background electromagnetic field

In this work we establish general constitutive equations for a relativistic plasma composed of an arbitrary number of classical, charged, and chemically non-reacting species in the presence of a background electromagnetic field. The intensity of the electromagnetic force acting on either species is assumed to be comparable with the gradients of the state variables and is thus considered as a first-order driving force for dissipation within the gradient expansion. Assuming that the species share the same temperature and velocity flow when in equilibrium, we determine the entropy production and establish constitutive equations in terms of first-order frame invariant quantities. Conditions on the corresponding transport coefficients are given in order to comply with Onsager's reciprocal relations and the second law of thermodynamics. In particular, we discuss cross effects for the binary mixture which may be relevant for astrophysical and cosmological applications. Finally, we derive a complete set of evolution equations governing the dynamics of a binary mixture propagating on an arbitrary spacetime background.

gr-qc↗

arXiv2026

Kinetic theory for a relativistic charged gas: mathematical foundations of the hydrodynamic limit and first-order results within the projection method

This work derives first-order constitutive equations for a relativistic charged gas using the Chapman-Enskog expansion of near-equilibrium solutions to the Boltzmann equation, implemented via a novel projection method. The analysis is performed in an arbitrary fixed background spacetime with an external electromagnetic field. Based on a detailed study of the linearized collision operator, we identify the trace-fixed particle frame as the most natural choice for constructing dissipative relativistic fluid theories from kinetic theory. In this frame, the state variables are defined by matching the lowest order moments of the one-particle distribution function with those of the Jüttner equilibrium distribution. The corresponding constitutive relations are obtained, and the associated transport coefficients are shown to be frame-independent when properly defined. We also identify an additional freedom, referred to as representation freedom, and show how both the representation and frame freedoms can be implemented at the microscopic level within the projection method. This allows for a systematic derivation of general first-order constitutive equations starting from the ones obtained in the trace-fixed particle frame. For suitable parameter choices, the resulting fluid theory is strongly hyperbolic, causal, and admits stable global equilibrium states.

gr-qc↗

arXiv2026

Existence of nonrelativistic $\ell$- and multi-$\ell$-boson stars and their radial stability

Using direct methods of the calculus of variations we establish the existence of an infinite class of spherically-symmetric solutions to the multi-field Schrödinger-Poisson system. This is achieved by proving that the energy functional admits a global minimum when restricted to the set of vector-valued wave functions in the Sobolev space $H^1$ which are invariant with respect to a suitable representation of the rotation group and whose components have fixed $L^2$-norms. Additionally, we show that these minima correspond to solutions which are orbital stable with respect to perturbations of the wave function within this set. The generalization to include an external potential and some important properties of the minima are also discussed.

math-ph↗

arXiv2026

Linear stability of nonrelativistic Proca stars

We study the linear stability of nonrelativistic Proca stars under generic perturbations. Using a combination of analytic and numerical methods, we demonstrate that, as expected, the ground state is always mode-stable. Additionally, we identify several mode-stable spherically symmetric excited states, including stationary states of constant and radial polarization, as well as multi-frequency states in case that the spin-spin selfinteraction vanishes. The existence of stable excited states may have implications for spin-$1$ ultralight dark matter models.

gr-qc↗

arXiv2026

Noble gravitational atoms: Self-gravitating black hole scalar wigs with angular momentum number

We present new spherically symmetric solutions of the Einstein-Klein-Gordon equations in a quasi-stationary approximation that describe self-gravitating scalar field configurations around a black hole, including angular momentum number $\ell$. An approach analogous to the one which gives rise to $\ell$-boson stars is used here to construct self-gravitating ``gravitational atoms" with $\ell\ge0$. We refer to these new solutions as {\it noble gravitational atoms}, by analogy with noble atoms, which are characterized by closed electron shells. We show that, in the proper limit, noble gravitational atoms approach $\ell$-boson stars globally, displaying noticeable differences only in a region very close to the event horizon. Noble gravitational atoms with $\ell>0$ sometimes present density maxima located at relatively large radii, with small density close to the horizon for $\ell>1$. Furthermore, they do not always present the typical density spike at the event horizon if $\ell > 0$; on the contrary, they sometimes exhibit a small dip there. When $\ell=0$, a spike can appear, but its contribution to the total mass density is always negligible. The size, density, and lifetime of these objects vary significantly depending on the parameters, being in some cases as large as galaxies, as dilute as dark matter, and as long-lived as the Universe itself.

gr-qc↗

arXiv2026

Bondi-type accretion onto a Kerr black hole in the kinetic regime

We derive an exact solution representing a Bondi-type stationary accretion of a kinetic (Vlasov) gas onto the Kerr black hole. The solution is exact in the sense that relevant physical quantities, such as the particle current density or the accretion rates, are expressed as explicit integrals, which can be evaluated numerically. We provide an analytic approximation which allows us to obtain simple formulas for the mass, energy, and angular momentum accretion rates. These formulas are used to derive characteristic time scales of the black hole mass growth and the associated spin-down in two different scenarios: assuming that the ambient energy density is either constant or decreases on a cosmological scale.

gr-qc↗

arXiv2026

Accretion of a Vlasov gas by a Kerr black hole

We investigate the accretion of a collisionless, relativistic kinetic gas by a rotating Kerr black hole, assuming that at infinity the state of the gas is described by a distribution function depending only on the energy of the particles. Neglecting the self-gravity of the gas, we show that relevant physical observables, including the particle current density and the accretion rates associated with the mass, the energy, and the angular momentum, can be expressed in the form of closed integrals that can be evaluated numerically or approximated analytically in the slow-rotation limit. The accretion rates are computed in this manner for both monoenergetic particles and the Maxwell-Jüttner distribution and compared with the corresponding results in the non-rotating case. We show that the angular momentum accretion rate decreases the absolute value of the black hole spin parameter. It is also found that the rotation of the black hole has a small but non-vanishing effect on the mass and the energy accretion rates, which is remarkably well described by an analytic calculation in the slow-rotation approximation to quadratic order in the rotation parameter. The effects of rotation on the morphology of the accretion flow are also analyzed.

gr-qc↗

arXiv2026

Cosmological evolution of collisionless relativistic gases as dark matter

We study a phenomenological dark matter model described as a collisionless relativistic kinetic gas in a spatially flat Friedmann-Lemaître-Robertson-Walker universe. After normalization to the observed present-day dark matter abundance, the model is fully specified by a single dimensionless parameter $β$, interpreted as the present particle velocity in units of the speed of light. The resulting energy density, pressure, and sound speed admit closed analytic expressions, interpolating between a radiation-like regime at early times and cold dark matter at late times. We implement the model in a modified version of the Boltzmann code CLASS and confront it with Planck 2018 CMB data. We find that sufficiently small values of $β$ are observationally indistinguishable from $Λ$CDM, while larger values inducing relativistic effects at early times are constrained. These results establish the consistency of the relativistic kinetic gas scenario with current cosmological observations.

physics.gen-ph↗

arXiv2025

Gravitational atoms beyond the test field limit: The case of Sgr A* and ultralight dark matter

We construct gravitational atoms including self-gravity, obtaining solutions of the Einstein-Klein-Gordon equations for a scalar field surrounding a non-rotating black hole in a quasi-stationary approximation. We resolve the region near the horizon as well as the far field region. Our results are relevant in a wide range of masses, from ultralight to MeV scalar fields and for black holes ranging from primordial to supermassive. For instance, a system with a scalar field consistent with ultralight dark matter and a black hole mass comparable to that of Sagittarius A* can be modeled. A density spike near the event horizon, although present, is negligible, contrasting with the prediction in [P. Gondolo and Silk, Phys. Rev. Lett., 83:1719-1722, 1999] for cold dark matter.

gr-qc↗

arXiv2025

Spherical accretion of a collisionless kinetic gas into a generic static black hole

We present a nontrivial extension of the problem of spherical accretion of a collisionless kinetic gas into the standard Schwarzschild black hole. This extension consists of replacing the Schwarzschild black hole by generic static and spherically symmetric black hole spacetimes with the aim of studying the effects of either modified gravitational theories beyond Einstein gravity or matter sources coupled to general relativity on the accretion process. This generalization also allows us to investigate the accretion into other types of black hole spacetimes, such as ones inspired by loop quantum gravity and string theory. To do so, we take into account a large class of static and spherically symmetric black holes whose spacetime is asymptotically flat with a positive total mass, has a regular Killing horizon, and satisfies appropriate monotonicity conditions of the metric functions. We provide the most general solution of the collisionless Boltzmann equation on such spacetimes by expressing the one-particle distribution function in terms of suitable symplectic coordinates on the cotangent bundle, and we calculate the relevant observables, such as particle current density and energy-momentum-stress tensor. Specializing to the case where the gas is described by an isotropic ideal fluid at rest at infinity, we compute the mass accretion rate and compression ratio, and we show that the tangential pressure is larger than the radial one at the horizon, indicating that the behavior of a collisionless gas is different from the one of an isotropic perfect fluid. As an example, we apply our generic formulae to two special black hole spacetimes, namely the Reissner-Nordström black hole and a loop quantum corrected black hole. We explore the effects of the free parameters on the observables and accretion rate, and we compare the results with those corresponding to the Schwarzschild black hole.

gr-qc↗

arXiv2025

Relativistic dissipative fluids in the trace-fixed particle frame: Hyperbolicity, causality, and stability

We propose a first-order theory of relativistic dissipative fluids in the trace-fixed particle frame, which is similar to Eckart's frame except that the temperature is determined by fixing the trace of the stress-energy tensor. Our theory is hyperbolic and causal provided a single inequality holds. For low wave numbers, the expected damped modes in the shear, acoustic, and heat diffusion channels are recovered. Stability of global equilibria with respect to all wave numbers is also analyzed. The conditions for hyperbolicity, causality and stability are satisfied for a simple gas of hard spheres or disks.

gr-qc↗

arXiv2025

Relativistic dissipative fluids in the trace-fixed particle frame: Strongly hyperbolic quasi-linear first-order evolution equations

In this paper we derive a new first-order theory of relativistic dissipative fluids by adopting the trace-fixed particle frame. Whereas in a companion letter we show that this theory is hyperbolic, causal and stable at global equilibrium states, here we prove that the full nonlinear system of equations can be cast into a first-order quasilinear system which is strongly hyperbolic. By rewriting the system in first-order form, auxiliary constraints are introduced. However, we show that these constraints propagate, and thus our theory leads to a well-posed Cauchy problem.

gr-qc↗

arXiv2025

Nonrelativistic Proca stars: Spherical stationary and multi-frequency states

In this paper we follow an effective theory approach to study the nonrelativistic limit of a selfgravitating and selfinteracting massive vector field. Our effective theory is characterized by three parameters: the field's mass $m_0$ and the selfinteraction constants $λ_n$ and $λ_s$. For definiteness, we focus on a systematic study of the equilibrium configurations, commonly referred to as Proca stars when they have finite energy. We identify two different types of Proca stars, depending on the specific sector of the effective theory that we are exploring. In the generic sector, defined by $λ_s\neq 0$, all equilibrium configurations are stationary states described by wave functions that evolve harmonically in time. However, in the symmetry-enhanced sector, for which $λ_s=0$, there exist multi-frequency states whose wave functions oscillate with two or three distinct frequencies in addition to the stationary states. We determine the conditions under which a ground state configuration with fixed particle number exists. When these conditions are met, we prove that the lowest energy is reached by a stationary spherically symmetric configuration of constant polarization that is linear or circular depending on the sign of $λ_s$. We numerically construct some illustrative examples of spherical stationary and multi-frequency solutions, analyze their properties, and compare them with our analytical predictions. Unlike stationary states and other soliton configurations, which form a discrete set in the solution space associated with fixed particle number, the symmetry-enhanced sector exhibits a continuum of solutions with multi-frequency states connecting stationary states of constant polarization.

gr-qc↗

arXiv2024

Are nonrelativistic ground state $\ell$-boson stars only stable for $\ell=0$ and $\ell=1$?

In previous work we analyzed the linear stability of non-relativistic $\ell$-boson stars with respect to radial modes and showed that ground state configurations are stable with respect to these modes, whereas excited states are unstable. In this work we extend the analysis to non-spherical linear mode perturbations. To this purpose, we expand the wave function in terms of tensor spherical harmonics which allows us to decouple the perturbation equations into a family of radial problems. By using a combination of analytic and numerical methods, we show that ground state configurations with $\ell > 1$ possess exponentially in time growing non-radial modes, whereas only oscillating modes are found for $\ell=0$ and $\ell=1$. This leads us to conjecture that nonrelativistic $\ell$-boson stars in their ground state are stable for $\ell=1$ as well as $\ell=0$, while ground state and excited configurations with $\ell > 1$ are unstable.

gr-qc↗

arXiv2024

Wave propagation through a spacetime containing thin concentric shells of matter

We investigate the transmission of scalar, electromagnetic, and linearized odd-parity gravitational waves in a static spacetime characterized by a spherical distribution of matter in the form of thin concentric equidistant shells of equal mass. These shells connect Schwarzschild spacetimes of different masses between themselves, and they satisfy the Israel junction conditions with a polytropic-type equation of state for the surface energy-momentum tensor. We assume that the central region has zero mass, and we verify that the resulting spacetime is stable with respect to small perturbations of the shell radii as long as the gravitational field is sufficiently weak. We focus on the transmission of monochromatic waves emitted from the center and propagating through a succession of $N$ shells. To this purpose, we neglect the self-gravity of the waves and solve the Regge-Wheeler equation in the weak field limit of the background field. Analytical expressions for the transmission and reflection coefficients are obtained and their dependency on the frequency, the number of shells and their mutual distance is analyzed. In particular, in the high-frequency limit, we observe that the reflection coefficient decays with the fourth power of the frequency. Increasing the number of shells initially produces oscillations in the transmission coefficient; however, as $N$ grows, this coefficient rapidly stabilizes at a constant positive value. We attribute this property to the fact that reflections are mainly determined by the surface density of the shells, which decreases as the inverse square of their radii.

gr-qc↗

arXiv2024

On the linear stability of nonrelativistic selfinteracting boson stars

In this paper we study the linear stability of selfinteracting boson stars in the nonrelativistic limit of the Einstein-Klein-Gordon theory. For this purpose, based on a combination of analytic and numerical methods, we determine the behavior of general linear perturbations around the stationary and spherically symmetric solutions of the Gross-Pitaevskii-Poisson system. In particular, we conclude that ground state configurations are linearly stable if the selfinteraction is repulsive, whereas there exist a state of maximum mass that divides the stable and the unstable branches in case the selfinteraction is attractive. Regarding the excited states, they are in general unstable under generic perturbations, although we identify a stability band in the first excited states of the repulsive theory. This result is independent of the mass of the scalar field and the details of the selfinteraction potential, and it is in contrast to the situation of vanishing selfinteraction, in which excited states are always unstable.

gr-qc↗

arXiv2023

Phase space mixing of a Vlasov gas in the exterior of a Kerr black hole

We study the dynamics of a collisionless kinetic gas whose particles follow future-directed timelike and spatially bound geodesics in the exterior of a sub-extremal Kerr black hole spacetime. Based on the use of generalized action-angle variables, we analyze the large time asymptotic behavior of macroscopic observables associated with the gas. We show that, as long as the fundamental frequencies of the system satisfy a suitable non-degeneracy condition, these macroscopic observables converge in time to the corresponding observables determined from an averaged distribution function. In particular, this implies that the final state is characterized by a distribution function which is invariant with respect to the full symmetry group of the system, that is, it is stationary, axisymmetric and Poisson-commutes with the integral of motion associated with the Carter constant. As a corollary of our result, we demonstrate the validity of the strong Jeans theorem in our setting, stating that the distribution function belonging to a stationary state must be a function which is independent of the generalized angle variables. An analogous theorem in which the assumption of stationarity is replaced with the requirement of invariance with respect to the Carter flow is also proven. Finally, we prove that the aforementioned non-degeneracy condition holds. This is achieved by providing suitable asymptotic expansions for the energy and Carter constant in terms of action variables for orbits having sufficiently large radii, and by exploiting the analytic dependency of the fundamental frequencies on the integrals of motion.

gr-qc↗