Conical Space-times: a Distributional Theory Approach

TL;DR

This paper develops a distributional approach to compute the Gaussian and Riemannian curvatures of conical spaces and extends the method to more general space-times with conical singularities.

Contribution

It introduces a novel distributional method for curvature calculation in conical geometries and extends this approach to complex space-times with singularities.

Findings

Successfully computes curvature using distribution theory

Extends method to general conical space-times

Provides a framework for analyzing singular space-time geometries

Abstract

We consider the problem of calculating the Gaussian curvature of a conical 2-dimensional space by using concepts and techniques of distribution theory. We apply the results obtained to calculate the Riemannian curvature of the 4-dimensional conical space-time. We show that the method can be extended for calculating the curvature of a special class of more general space-times with conical singularity.