arXiv subjects

Olivier Sarbach

Publications and source records attributed to Olivier Sarbach.

At least 37 records · Page 2Linked to original sources

arXiv2023

Boson stars and their relatives in semiclassical gravity

We construct boson star configurations in quantum field theory using the semiclassical gravity approximation. Restricting our attention to the static case, we show that the semiclassical Einstein-Klein-Gordon system for a {\it single real quantum} scalar field whose state describes the excitation of $N$ {\it identical particles}, each one corresponding to a given energy level, can be reduced to the Einstein-Klein-Gordon system for $N$ {\it complex classical} scalar fields. Particular consideration is given to the spherically symmetric static scenario, where energy levels are labeled by quantum numbers $n$, $\ell$ and $m$. When all particles are accommodated in the ground state $n=\ell=m=0$, one recovers the standard static boson star solutions, that can be excited if $n\neq 0$. On the other hand, for the case where all particles have fixed radial and total angular momentum numbers $n$ and $\ell$, with $\ell\neq 0$, but are homogeneously distributed with respect to their magnetic number $m$, one obtains the $\ell$-boson stars, whereas when $\ell=m=0$ and $n$ takes multiple values, the multi-state boson star solutions are obtained. Further generalizations of these configurations are presented, including the multi-$\ell$ multi-state boson stars, that constitute the most general solutions to the $N$-particle, static, spherically symmetric, semiclassical real Einstein-Klein-Gordon system, in which the total number of particles is definite. In spite of the fact that the same spacetime configurations also appear in multi-field classical theories, in semiclassical gravity they arise naturally as the quantum fluctuations associated with the state of a single field describing a many-body system. Our results could have potential impact on direct detection experiments in the context of ultralight scalar field/fuzzy dark matter candidates.

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arXiv2023

On the radial linear stability of nonrelativistic $\ell$-boson stars

We study the linear stability of nonrelativistic $\ell$-boson stars, describing static, spherically symmetric configurations of the Schrödinger-Poisson system with multiple wave functions having the same value of the angular momentum $\ell$. In this work we restrict our analysis to time-dependent perturbations of the radial profiles of the $2\ell+1$ wave functions, keeping their angular dependency fixed. Based on a combination of analytic and numerical methods, we find that for each $\ell$, the ground state is linearly stable, whereas the $n$'th excited states possess $2n$ unstable (exponentially in time growing) modes. Our results also indicate that all excited states correspond to saddle points of the conserved energy functional of the theory.

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arXiv2022

Axisymmetric, stationary collisionless gas clouds trapped in a Newtonian potential

The properties of an axisymmetric, stationary gas cloud surrounding a massive central object are discussed. It is assumed that the gravitational field is dominated by the central object which is modeled by a nonrelativistic rotationally-symmetric potential. Further, we assume that the gas consists of collisionless, identical massive particles that follow bound orbits in this potential. Several models for the one-particle distribution function are considered and the essential formulae that describe the relevant macroscopical observables, such as the particle and energy densities, pressure tensor, and the kinetic temperature are derived. The asymptotic decay of the solutions at infinity is discussed and we specify configurations with finite total mass, energy and (zero or non-zero) angular momentum. Finally, our configurations are compared to their hydrodynamic analogs. In an accompanying paper, the equivalent general relativistic problem is discussed, where the central object consists of a Schwarzschild black hole.

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arXiv2022

Axisymmetric, stationary collisionless gas configurations surrounding black holes

The properties of a stationary gas cloud surrounding a black hole are discussed, assuming that the gas consists of collisionless, identical massive particles that follow spatially bound geodesic orbits in the Schwarzschild spacetime. Several models for the one-particle distribution function are considered, and the essential formulae that describe the relevant macroscopic observables, like the current density four-vector and the stress-energy-momentum tensor are derived. This is achieved by rewriting these observables as integrals over the constants of motion and by a careful analysis of the range of integration. In particular, we provide configurations with finite total mass and angular momentum. Differences between these configurations and their nonrelativistic counterparts in a Newtonian potential are analyzed. Finally, our configurations are compared to their hydrodynamic analogues, the "polish doughnuts".

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arXiv2022

Extreme $\ell$-boson stars

A new class of complex scalar field objects, which generalize the well known boson stars, was recently found as solutions to the Einstein-Klein-Gordon system. The generalization consists in incorporating some of the effects of angular momentum, while still maintaining the spacetime's spherical symmetry. These new solutions depend on an (integer) angular parameter $\ell$, and hence were named $\ell$-boson stars. Like the standard $\ell=0$ boson stars these configurations admit a stable branch in the solution space; however, contrary to them they have a morphology that presents a shell-like structure with a "hole" in the internal region. In this article we perform a thorough exploration of the parameter space, concentrating particularly on the extreme cases with large values of $\ell$. We show that the shells grow in size with the angular parameter, doing so linearly for large values, with the size growing faster than the thickness. Their mass also increases with $\ell$, but in such a way that their compactness, while also growing monotonically, converges to a finite value corresponding to about one half of the Buchdahl limit for stable configurations. Furthermore, we show that $\ell$-boson stars can be highly anisotropic, with the radial pressure diminishing relative to the tangential pressure for large $\ell$, reducing asymptotically to zero, and with the maximum density also approaching zero. We show that these properties can be understood by analyzing the asymptotic limit $\ell\rightarrow\infty$ of the field equations and their solutions. We also analyze the existence and characteristics of both timelike and null circular orbits, especially for very compact solutions.

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arXiv2022

An introduction to the relativistic kinetic theory on curved spacetimes

This article provides a self-contained pedagogical introduction to the relativistic kinetic theory of a dilute gas propagating on a curved spacetime manifold (M,g) of arbitrary dimension. Special emphasis is made on geometric aspects of the theory in order to achieve a formulation which is manifestly covariant on the relativistic phase space. Whereas most previous work has focussed on the tangent bundle formulation, here we work on the cotangent bundle associated with (M,g) which is more naturally adapted to the Hamiltonian framework of the theory. In the first part of this work we discuss the relevant geometric structures of the cotangent bundle T*M, starting with the natural symplectic form on T*M, the one-particle Hamiltonian and the Liouville vector field, defined as the corresponding Hamiltonian vector field. Next, we discuss the Sasaki metric on T*M and its most important properties, including the role it plays for the physical interpretation of the one-particle distribution function. In the second part of this work we describe the general relativistic theory of a collisionless gas, starting with the derivation of the collisionless Boltzmann equation for a neutral simple gas. Subsequently, the description is generalized to a charged gas consisting of several species of particles and the general relativistic Vlasov-Maxwell equations are derived for this system. The last part of this work is devoted to a transparent derivation of the collision term, leading to the general relativistic Boltzmann equation on (M,g). The meaning of global and local equilibrium and the stringent restrictions for the existence of the former on a curved spacetime are discussed. We close this article with an application of our formalism to the expansion of a homogeneous and isotropic universe filled with a collisional simple gas and its behavior in the early and late epochs. [abbreviated version]

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arXiv2022

Kinetic gas disks surrounding Schwarzschild black holes

We describe stationary and axisymmetric gas configurations surrounding black holes. They consist of a collisionless relativistic kinetic gas of identical massive particles following bound orbits in a Schwarzschild exterior spacetime and are modeled by a one-particle distribution function which is the product of a function of the energy and a function of the orbital inclination associated with the particle's trajectory. The morphology of the resulting configuration is analyzed.

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arXiv2021

Accretion of a Vlasov gas on to a black hole from a sphere of finite radius and the role of angular momentum

The accretion of a spherically symmetric, collisionless kinetic gas cloud on to a Schwarzschild black hole is analysed. Whereas previous studies have treated this problem by specifying boundary conditions at infinity, here the properties of the gas are given at a sphere of finite radius. The corresponding steady-state solutions are computed using four different models with an increasing level of sophistication, starting with the purely radial infall of Newtonian particles and culminating with a fully general relativistic calculation in which individual particles have angular momentum. The resulting mass accretion rates are analysed and compared with previous models, including the standard Bondi model for a hydrodynamic flow. We apply our models to the supermassive black holes Sgr A* and M87*, and we discuss how their low luminosity could be partially explained by a kinetic description involving angular momentum. Furthermore, we get results consistent with previous model-dependent bounds for the accretion rate imposed by rotation measures of the polarised light coming from Sgr A* and with estimations of the accretion rate of M87* from the Event Horizon Telescope collaboration. Our methods and results could serve as a first approximation for more realistic black hole accretion models in various astrophysical scenarios in which the accreted material is expected to be nearly collisionless.

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arXiv2021

Spherical accretion: Bondi, Michel and rotating black holes

In this work we revisit the steady state, spherically symmetric gas accretion problem from the non-relativistic regime to the ultra-relativistic one. We first perform a detailed comparison between the Bondi and Michel models, and show how the mass accretion rate in the Michel solution approaches a constant value as the fluid temperature increases, whereas the corresponding Bondi value continually decreases, the difference between these two predicted values becoming arbitrarily large at ultra-relativistic temperatures. Additionally, we extend the Michel solution to the case of a fluid with an equation of state corresponding to a monoatomic, relativistic gas. Finally, using general relativistic hydrodynamic simulations, we study spherical accretion onto a rotating black hole, exploring the influence of the black hole spin on the mass accretion rate, the flow morphology and characteristics, and the sonic surface. The effect of the black hole spin becomes more significant as the gas temperature increases and as the adiabatic index $γ$ stiffens. For an ideal gas in the ultra-relativistic limit ($γ=4/3$), we find a reduction of 10 per cent in the mass accretion rate for a maximally rotating black hole as compared to a non-rotating one, while this reduction is of up to 50 per cent for a stiff fluid ($γ=2$).

astro-ph.HE↗

arXiv2021

Static spherical perfect fluid stars with finite radius in general relativity: a review

In this article, we provide a pedagogical review of the Tolman-Oppenheimer-Volkoff (TOV) equation and its solutions which describe static, spherically symmetric gaseous stars in general relativity. Our discussion starts with a systematic derivation of the TOV equation from the Einstein field equations and the relativistic Euler equations. Next, we give a proof for the existence and uniqueness of solutions of the TOV equation describing a star of finite radius, assuming suitable conditions on the equation of state characterizing the gas. We also prove that the compactness of the gas contained inside a sphere centered at the origin satisfies the well-known Buchdahl bound, independent of the radius of the sphere. Further, we derive the equation of state for an ideal, classical monoatomic relativistic gas from statistical mechanics considerations and show that it satisfies our assumptions for the existence of a unique solution describing a finite radius star. Although none of the results discussed in this article are new, they are usually scattered in different articles and books in the literature; hence it is our hope that this article will provide a self-contained and useful introduction to the topic of relativistic stellar models.

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arXiv2021

On the linear stability of $\ell$-boson stars with respect to radial perturbations

In previous work we constructed new boson star solutions consisting of a family of massive complex scalar fields minimally coupled to gravity in which the individual fields have angular momentum, yet the configuration as a whole is static and spherically symmetric. In the present article we study the linear stability of these $\ell$-boson stars with respect to time-dependent, radial perturbations. The pulsation equations, governing the dynamics of such perturbations are derived, generalizing previous work initiated by M. Gleiser, and shown to give rise to a two-channel Schrödinger operator. Using standard tools from the literature, we show that for each fixed value $\ell$ of the angular momentum number, there exists a family of $\ell$-boson stars which are linearly stable with respect to radial fluctuations; in this case the perturbations oscillate in time with given characteristic frequencies which are computed and compared with the results from a nonlinear numerical simulation. Further, there is also a family of $\ell$-boson stars which are linearly unstable. The two families are separated by the configuration with maximum mass. These results are qualitatively similar to the corresponding stability results of the standard boson stars with $\ell=0$, and they imply the existence of new stable configurations that are more massive and compact than usual boson stars.

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arXiv2020

Choked accretion onto a Kerr black hole

The choked accretion model consists of a purely hydrodynamical mechanism in which, by setting an equatorial to polar density contrast, a spherically symmetric accretion flow transitions to an inflow-outflow configuration. This scenario has been studied in the case of a (non-rotating) Schwarzschild black hole as central accretor, as well as in the non-relativistic limit. In this article, we generalize these previous works by studying the accretion of a perfect fluid onto a (rotating) Kerr black hole. We first describe the mechanism by using a steady-state, irrotational analytic solution of an ultrarelativistic perfect fluid, obeying a stiff equation of state. We then use hydrodynamical numerical simulations in order to explore a more general equation of state. Analyzing the effects of the black hole's rotation on the flow, we find in particular that the choked accretion inflow-outflow morphology prevails for all possible values of the black hole's spin parameter, showing the robustness of the model.

astro-ph.HE↗

arXiv2020

Phase space mixing in an external gravitational central potential

This article is devoted to the study of the dynamical behavior of a collisionless kinetic gas in d=1,2,3 space dimensions which is trapped in a rotationally symmetric potential well. Although at the microscopic level the trajectories of individual gas particles are quasi-periodic and characterized by their d fundamental frequencies, at the macroscopic level the gas relaxes in time to a stationary state, provided the potential satisfies a certain non-degeneracy condition. In this article, we provide a mathematically precise formulation for this relaxation process which is due to phase space mixing. In particular, we prove that a physically relevant class of macroscopic observables computed from the one-particle distribution function, such as particle and energy densities, pressure and stress tensors, converge in time to the corresponding observables associated with an averaged distribution function. The latter can be determined from the initial datum and depends only on integrals of motion. Thus, the final state of the gas is described by an effective distribution function depending only on integrals of motion, which considerably reduces the degrees of freedom of the gas configuration. We discuss some applications to gravitational physics, including the propagation of a collisionless gas in typical potentials arising in stellar dynamics and the modeling of dark matter halos, and we also generalize our results to a relativistic gas whose individual particles follow bound timelike trajectories in the exterior region of a static, spherically symmetric black hole spacetime.

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arXiv2020

Gauge-invariant spherical linear perturbations of wormholes in Einstein gravity minimally coupled to a self-interacting phantom scalar field

Recently, there has been quite a lot of interest in static, spherical wormhole spacetimes and the question of their stability with respect to time-dependent perturbations. The consideration of linearized perturbations usually leads to a master wave equation with effective potential which can then be analyzed using standard tools from quantum mechanics. However, in the wormhole case, particular care must be taken with the gauge conditions when formulating the master equation. A poor coordinate choice, based for example on fixing the areal radial coordinate, may lead to singularities at the throat which complicate the stability analysis or might even lead to erroneous conclusions regarding the stability of the underlying wormhole configuration. In this work, we present a general method for deriving a gauge-invariant wave system of linearized perturbation equations in the spherically symmetric case, assuming that the matter supporting the wormhole is a phantom scalar field, that is, a self-interacting scalar field whose kinetic energy has the reversed sign. We show how this system can be decoupled and reduced to a single master wave equation with a regular potential, with no intermediate steps involving singularities at the throat. Two applications of our formalism are given. First, we rederive the master equation for the linearly perturbed Ellis-Bronnikov wormhole using our new, singularity-free method. Second, we derive the master equation describing the linear perturbations of a certain Anti de Sitter wormhole, provide a detailed analysis of the spectral properties of the underlying operator and prove that this wormhole is linearly unstable. In the final part of the paper, we consider a wormhole with de Sitter-type ends, whose spacetime presents horizons and admits a nonstatic extension beyond them; for this system we derive partial results of linear instability.

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arXiv2019

Traversable $\ell$-wormholes supported by ghost scalar fields

We present new, asymptotically flat, static, spherically symmetric and traversable wormhole solutions in General Relativity which are supported by a family of ghost scalar fields with quartic potential. This family consists of a particular composition of the scalar field modes, in which each mode is characterized by the same value of the angular momentum number $\ell$, yet the composition yields a spherically symmetric stress-energy-momentum and metric tensor. For $\ell = 0$ our solutions reduce to wormhole configurations which had been reported previously in the literature. We discuss the effects of the new parameter $\ell$ on the wormhole geometry including the motion of free-falling test particles.

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arXiv2019

Dynamical evolutions of $\ell$-boson stars in spherical symmetry

In previous work, we have found new static, spherically symmetric boson star solutions which generalize the standard boson stars by allowing a particular superposition of scalar fields in which each of the fields is characterized by a fixed value of its non-vanishing angular momentum number $\ell$. We call such solutions "$\ell$-boson stars". Here, we perform a series of fully non-linear dynamical simulations of perturbed $\ell$-boson stars in order to study their stability, and the final fate of unstable configurations. We show that for each value of $\ell$, the configuration of maximum mass separates the parameter space into stable and unstable regions. Stable configurations, when perturbed, oscillate around the unperturbed solution and very slowly return to a stationary configuration. Unstable configurations, in contrast, can have three different final states: collapse to a black hole, migration to the stable branch, or explosion (dissipation) to infinity. Just as it happens with $\ell=0$ boson stars, migration to the stable branch or dissipation to infinity depends on the sign of the total binding energy of the star: bound unstable stars collapse to black holes or migrate to the stable branch, whereas unbound unstable stars either collapse to a black hole or explode to infinity. Thus, the parameter $\ell$ allows us to construct a new set of stable configurations. All our simulations are performed in spherical symmetry, leaving a more detailed stability analysis including non-spherical perturbations for future work.

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arXiv2019

Well-posed Cauchy formulation for Einstein-æther theory

We study the well-posedness of the initial value (Cauchy) problem of vacuum Einstein-aether theory. The latter is a Lorentz-violating gravitational theory consisting of General Relativity with a dynamical timelike 'aether' vector field, which selects a 'preferred time' direction at each spacetime event. The Einstein-aether action is quadratic in the aether, and thus yields second order field equations for the metric and the aether. However, the well-posedness of the Cauchy problem is not easy to prove away from the simple case of perturbations over flat space. This is particularly problematic because well-posedness is a necessary requirement to ensure stability of numerical evolutions of the initial value problem. Here, we employ a first-order formulation of Einstein-aether theory in terms of projections on a tetrad frame. We show that under suitable conditions on the coupling constants of the theory, the resulting evolution equations can be cast into strongly or even symmetric hyperbolic form, and therefore they define a well-posed Cauchy problem.

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arXiv2018

Phase space mixing in the equatorial plane of a Kerr black hole

It is shown that a collisionless, relativistic kinetic gas configuration propagating in the equatorial plane of a Kerr black hole undergoes a relaxation process and eventually settles down to a stationary, axisymmetric configuration surrounding the black hole. The underlying mechanism for this relaxation process is due to phase space mixing, which implies that although the one-particle distribution function $f$ satisfying the collisionless Boltzmann equation which describes the microscopic state of the gas is quasi-periodic in time, the associated macroscopic observables computed from averages over $f$ possess well-defined limits as time goes to infinity. The final state of the gas is described by an effective distribution function depending only on constants of motion which can be predicted from the initial distribution function.

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