Maxwell-Juttner distribution for rigidly-rotating flows in spherically symmetric spacetimes using the tetrad formalism

TL;DR

This paper derives the Maxwell-Juttner distribution for rigidly rotating thermal states in spherically symmetric spacetimes, analyzing particle flow, stress-energy, and transport coefficients using tetrad formalism, with applications to black hole spacetimes.

Contribution

It introduces a method to compute equilibrium distributions and related physical quantities in rotating relativistic fluids within curved spacetimes using tetrad formalism.

Findings

Distribution functions are explicitly constructed for various spacetimes.

Transport coefficients are computed within the Marle model.

Properties of rotating thermal states are analyzed in different spacetime topologies.

Abstract

We consider rigidly rotating states in thermal equilibrium on static spherically symmetric spacetimes. Using the Maxwell-Juttner equilibrium distribution function, onstructed as a solution of the relativistic Boltzmann equation, the equilibrium particle flow four-vector, stress-energy tensor and the transport coefficients in the Marle model are computed. Their properties are discussed in view of the topology of the speed-of-light surface induced by the rotation for two classes of spacetimes: maximally symmetric (Minkowski, de Sitter and anti-de Sitter) and charged (Reissner-Nordstrom) black-hole spacetimes. To facilitate our analysis, we employ a non-holonomic comoving tetrad field, obtained unambiguously by applying a Lorentz boost on a fixed background tetrad.