A point mass and continuous collapse to a point mass in general relativity

TL;DR

This paper presents a novel formulation of the Schwarzschild black hole as a point mass using Dirac delta functions within a field-theoretical framework of general relativity, including a continuous collapse process.

Contribution

It introduces a generalized, physically consistent description of black holes as point masses in a field-theoretical setting, extending traditional geometric approaches.

Findings

A new representation of Schwarzschild black holes as point masses with delta functions.

A continuous collapse model leading to a point mass in general relativity.

Potential applications for studying black hole singularities and practical calculations.

Abstract

An original way of presentation of the Schwarzschild black hole in the form of a point-like mass with making the use of the Dirac $\delta$-function, including a description of a continuous collapse to such a point mass, is given. A maximally generalized description restricted by physically reasonable requirements is developed. A so-called field-theoretical formulation of general relativity, being equivalent to the standard geometrical presentation of general relativity, is used. All of the dynamical fields, including the gravitational field, are considered as propagating in a background (curved or flat) spacetime. Namely these properties allow us to present a non-contradictive picture of the point mass description. The results can be useful for studying the structure of the black hole true singularities and could be developed for practical calculations in models with black holes.