# Schwarzschild Black Hole Lives to Fight Another Day - Comment on the paper J. Math. Phys. 50, 042502 (2009) by A. Mitra

## TL;DR

This paper critiques a previous claim that the Schwarzschild black hole's mass must be zero, clarifying that the earlier proof was based on a misunderstanding of coordinate volume elements in differential geometry.

## Contribution

It refutes Mitra's incorrect proof regarding the mass of Schwarzschild black holes, emphasizing proper mathematical treatment of coordinate volume elements.

## Key findings

- Mitra's proof is incorrect due to a misunderstanding of coordinate volume elements.
- The Schwarzschild black hole's mass parameter does not necessarily vanish.
- Proper mathematical analysis invalidates the previous claim.

## Abstract

In a comment published several years ago in this Journal [J. Math. Phys. 50, 042502 (2009)] Mitra has claimed to prove that a neutral point particle in general relativity as described by the Schwarzschild metric must have zero gravitational mass, i.e. the mass parameter $M_{0}$ of a Schwarzschild black hole necessarily vanishes. It is shown that the purported proof is incorrect. The error stems from a basic misunderstanding of the mathematical description of coordinate volume element in a differentiable manifold.

---
Source: https://tomesphere.com/paper/1706.07463