The Generalised Raychaudhuri Equations : Examples

TL;DR

This paper explores the generalized Raychaudhuri equations through specific examples involving the evolution and focusing of deformations of embedded surfaces in various spacetime backgrounds.

Contribution

It provides explicit examples of the generalized Raychaudhuri equations for different embedded surfaces, illustrating their application in diverse spacetime geometries.

Findings

Examples of surface deformation evolution in curved spacetimes

Analysis of focusing phenomena for families of surfaces

Insights into the behavior of embedded surfaces in general relativity

Abstract

Specific examples of the generalized Raychaudhuri Equations for the evolution of deformations along families of $D$ dimensional surfaces embedded in a background $N$ dimensional spacetime are discussed. These include string worldsheets embedded in four dimensional spacetimes and two dimensional timelike hypersurfaces in a three dimensional curved background. The issue of focussing of families of surfaces is introduced and analysed in some detail.