Analysis of relativistic hydrodynamics in conservation form

TL;DR

This paper thoroughly analyzes the formulation of relativistic hydrodynamics in conservation form, focusing on geometric source terms, equivalence transformations, and computational efficiencies for numerical simulations in various spacetimes.

Contribution

It introduces transformations to simplify source terms, extends analysis to general equations of state, and proposes a comprehensive approach for numerical relativistic hydrodynamics.

Findings

Reduction of source term complexity in generic spacetimes

Extension of characteristic analysis to general EOS

Explicit inversion formulas for specific EOS classes

Abstract

Formulations of Eulerian general relativistic ideal hydrodynamics in conservation form are analyzed in some detail, with particular emphasis to geometric source terms. Simple linear transformations of the equations are introduced and the associated equivalence class is exploited for the optimization of such sources. A significant reduction of their complexity is readily possible in generic spacetimes. The local characteristic structure of the standard member of the equivalence class is analyzed for a general equation of state (EOS). This extends previous results restricted to the polytropic case. The properties of all other members of the class, in particular specialized forms employing Killing symmetries, are derivable from the standard form. Special classes of EOS are identified for both spacelike and null foliations, which lead to explicit inversion of the state vector and computational savings. The entire approach is equally applicable to spacelike or lightlike foliations and presents a complete proposal for numerical relativistic hydrodynamics on stationary or dynamic geometries.