Pulsation of Spherically Symmetric Systems in General Relativity

TL;DR

This paper derives a standard form for pulsation equations in spherically symmetric systems within general relativity, applicable to various matter models, and illustrates their use with Einstein-Yang-Mills and Einstein-Skyrme systems.

Contribution

It provides a unified framework for pulsation equations applicable to a broad class of matter models in spherically symmetric spacetimes, linking to the energy principle.

Findings

Unified pulsation equations for black holes and solitons

Application to Einstein-Yang-Mills and Einstein-Skyrme systems

Connection to the energy principle via second variation of Schwarzschild mass

Abstract

The pulsation equations for spherically symmetric black hole and soliton solutions are brought into a standard form. The formulae apply to a large class of field theoretical matter models and can easily be worked out for specific examples. The close relation to the energy principle in terms of the second variation of the Schwarzschild mass is also established. The use of the general expressions is illustrated for the Einstein-Yang-Mills and the Einstein-Skyrme system.