Light Cone analysis of relativistic first-order in the gradients hydrodynamics

TL;DR

This paper uses light spectrum analysis to test causality in relativistic hydrodynamics, showing that modified Eckart's theory ensures causal solutions while classical Eckart's formalism does not.

Contribution

It introduces a light cone analysis method to assess causality in relativistic hydrodynamic equations, comparing classical and modified Eckart's formalisms.

Findings

Classical Eckart's formalism shows non-causal behavior with solutions outside the light cone.

Modified Eckart's theory produces causal solutions within the light cone.

The technique establishes a new way to verify causality in relativistic fluid models.

Abstract

This work applies a Rayleigh-Brillouin light spectrum analysis in order to establish a causality test by means of a frequency cone. This technique allows to identify forbidden and unforbidden regions in light scattering experiments and establishes if a set of linearized transport equations admits causal solutions. It is shown that, when studying a relativistic fluid with its acoustic modes interacting with light, Eckart's formalism yields a non causal behavior. In this case the solutions describing temperature, density and pressure fluctuations are located outside the frequency cone. In contrast, the set of equations that arises from modified Eckart's theory (based on relativistic kinetic theory) yields solutions that lie within the cone, so that they are causal.