Dynamics of spherically symmetric spacetimes: hydrodynamics and radiation

TL;DR

This paper derives equations for the evolution of spherically symmetric spacetimes with matter and radiation, using various coordinate systems, to better understand their dynamics in general relativity.

Contribution

It provides a unified framework for modeling spherically symmetric spacetimes with hydrodynamics and radiation in different coordinate gauges.

Findings

Derived equations for spacetime dynamics with matter and radiation.

Analyzed three coordinate systems for modeling these spacetimes.

Facilitated future numerical simulations of astrophysical phenomena.

Abstract

Using the 3+1 formalism of general relativity we obtain the equations governing the dynamics of spherically symmetric spacetimes with arbitrary sources. We then specialize for the case of perfect fluids accompanied by a flow of interacting massless or massive particles (e.g. neutrinos) which are described in terms of relativistic transport theory. We focus in three types of coordinates: 1) isotropic gauge and maximal slicing, 2) radial gauge and polar slicing, and 3) isotropic gauge and polar slicing.