Singular limits of spacetimes and their isometries

TL;DR

This paper investigates how spacetime symmetries and isometry groups behave under singular limits of metrics, with applications to anti-de Sitter and pp-wave spacetimes, revealing the structure of symmetries in these limits.

Contribution

It provides a general framework for analyzing the isometry groups and symmetries of singular limits of spacetime metrics, including methods to find Killing vectors and Lie algebras.

Findings

Derived general formulas for isometry groups in singular limits.

Applied results to anti-de Sitter and pp-wave spacetimes.

Identified how symmetries evolve in the limits of the metrics.

Abstract

We consider spacetime metrics with a given (but quite generic) dependence on a dimensionful parameter such that in the 0 and infinity limits of that parameter the metric becomes singular. We study the isometry groups of the original spacetime metrics and of the singular metrics that arise in the limits and the corresponding symmetries of the motion of p-branes evolving in them, showing how the Killing vectors and their Lie algebras can be found in general. We illustrate our general results with several examples which include limits of anti-de Sitter spacetime in which the holographic screen is one of the singular metrics and of pp-waves.