Bianchi - Euler system for relativistice fluids and Bel - Robinson type energy

TL;DR

This paper develops a first-order symmetric hyperbolic system linking the Riemann tensor with the fluid's acceleration in relativistic fluids, and analyzes the associated Bel-Robinson energy and its integral properties.

Contribution

It introduces a new coupled hyperbolic system for relativistic fluids and derives the Bel-Robinson energy's integral equality, advancing the mathematical understanding of relativistic fluid dynamics.

Findings

Established a symmetric hyperbolic system coupling Riemann and acceleration.

Derived the Bel-Robinson energy and its integral equality.

Provided a framework for analyzing energy in relativistic fluids.

Abstract

We write a first order symmetric hyperbolic system coupling the Riemann with the dynamical acceleration of a relativistic fluid. W determine the associated, coupled, Bel - Robinson energy, and the integral equality that it satisfies.