arXiv subjects

Carlos Gabarrete

Publications and source records attributed to Carlos Gabarrete.

8 recordsLinked to original sources

arXiv2026

Entropy covector field and macroscopic observables for rotating and non-rotating relativistic kinetic gases around a Schwarzschild black hole

In this article, we derive the components of the entropy covector field for a relativistic kinetic gas composed of collisionless, spinless, massive, and uncharged particles following bound orbits in a curved spacetime background. By assuming a dependence on the inclination angle of the particle orbits, we consider two distinct models that describe a rotating and a non-rotating relativistic kinetic gas around a Schwarzschild black hole. We analyze the behavior of key macroscopic observables (including the anisotropy parameter and the kinetic temperature) which are constructed from the particle density, energy density, and principal pressures. We aim to characterize and compare the morphology of the resulting configurations, thereby extending and complementing a previous work. The results reveal significant differences between the rotating and non-rotating cases, particularly in the asymptotic behavior of the anisotropy parameter, kinetic temperature, and average pressure, highlighting the role of angular momentum in shaping the macroscopic properties of collisionless gases in strong gravitational fields.

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arXiv2026

Rotating Kinetic Gas Disk Morphology Surrounding a Schwarzschild Black Hole

This paper discusses the behavior of a rotating relativistic kinetic gas surrounding a Schwarzschild black hole. We are interested in the description and analysis of the morphology of the resulting configurations for kinetic gas clouds with and without total angular momentum, and we also compare the macroscopic observables with configurations of finite total mass. Considering models for the one-particle distribution function based on a polytropic ansatz and the inclination angle of the orbits of the particles in the kinetic gas, a collisionless gas in the Schwarzschild spacetime background is analyzed. Profiles of the macroscopic observables of the gas configurations are presented, which are derived from the density current vector field and energy-momentum-stress tensor.

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arXiv2025

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 J\"uttner 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.

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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

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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