Radiating jump conditions in General Relativity

TL;DR

This paper provides a unified framework for describing various spherical discontinuity surfaces in General Relativity, deriving exact jump conditions and analyzing quasi-static approximations for different surface types.

Contribution

It introduces a comprehensive description of spherical discontinuity surfaces in General Relativity using two parameters, unifying different surface types and deriving their exact jump conditions.

Findings

Derived exact jump conditions for all surface types

Unified description using mass function and surface permeability

Analyzed quasi-static approximation in hydrodynamic processes

Abstract

We present a unified description of spherical discontinuity surfaces in General Relativity based on two parameters: mass function and surface permeability. The surfaces considered are: \textit{Impulsive fronts}, massive permeable layer; \textit{Surface layers}, massive impermeable layer; \textit{Shock fronts}, massless permeable surface; and \textit{Boundary surfaces}, massless impermeable surface. We derive the exact jump conditions for the physical variables across all these surfaces. Finally, we discuss the quasi-static approximation from studying slow hydrodynamic processes involving discontinuity surfaces.