Characteristic decomposition for relativistic numerical simulations. I. Hydrodynamics
Phys. Rev. D 113, 124015 – Published 8 June, 2026
DOI: https://doi.org/10.1103/d41l-8kvd
Abstract
The characteristic decomposition for general relativistic magnetohydrodynamics (GRMHD) is not known in a form useful for current numerical simulations. This prevents us from using the most accurate known computational methods, such as full-wave Riemann solvers. In this paper, we present a new method of finding decompositions. The method is based on transformations from the comoving frame, where the fluid flow is simplest and the decomposition has been known for a long time. The key innovation we introduce is that of quasi-invertible transformations. In this first paper, we introduce these transformations using the simpler example of relativistic hydrodynamics. We recover the known decomposition for relativistic hydrodynamics in somewhat simpler form than previously derived, and without the need for computer algebra. A new result in this paper is the characteristic decomposition when the evolution tracks the composition of a fluid in nuclear statistical equilibrium. In Paper II of this series, we apply a quasi-invertible transformation to derive the complete characteristic decomposition for GRMHD in the conserved variables used in simulations.
