arXiv subjects

Ana Laura García-Perciante

Publications and source records attributed to Ana Laura García-Perciante.

6 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↗

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↗

arXiv2002

A six dimensional analysis of Maxwell's Field Equations

A framework based on an extension of Kaluza's original idea of using a five dimensional space to unify gravity with electromagnetism is used to analyze Maxwell\'{}s field equations. The extension consists in the use of a six dimensional space in which all equations of electromagnetism may be obtained using only Einstein's field equation. Two major advantages of this approach to electromagnetism are discussed, a full symmetric derivation for the wave equations for the potentials and a natural inclusion of magnetic monopoles without using any argument based on singularities.

gr-qc↗