On the Distributional Nature of the Energy Momentum Tensor of a Black Hole or What Curves the Schwarzschild Geometry ?

TL;DR

This paper employs distributional techniques to compute the energy-momentum tensor of Schwarzschild geometry, revealing it as a well-defined distribution concentrated at the singularity, thus offering a physical interpretation of the curvature.

Contribution

It introduces a distributional approach to analyze the energy-momentum tensor of black holes, clarifying the nature of curvature at the singularity.

Findings

Energy-momentum tensor is a distribution concentrated at r=0

Provides a physical interpretation of Schwarzschild curvature

Tensor is well-defined as a distribution

Abstract

Using distributional techniques we calculate the energy--momentum tensor of the Schwarzschild geometry. It turns out to be a well--defined tensor--distribution concentrated on the $r=0$ region which is usually excluded from space--time. This provides a physical interpretation for the curvature of this geometry.