Non-linearity of Vaidya spacetime and forces in the central naked singularity

TL;DR

This paper investigates non-linear Vaidya spacetimes with power-law mass functions, showing that central naked singularities can form but are gravitationally weak, and analyzing the conditions under which forces near these singularities are finite.

Contribution

It demonstrates the formation of gravitationally weak naked singularities in non-linear Vaidya spacetimes and analyzes the finiteness of forces in these scenarios.

Findings

Naked singularities can form for n>1 in non-linear Vaidya spacetime.

Such naked singularities are gravitationally weak.

Forces near the naked singularity are finite only in the weak case.

Abstract

In this paper we consider non-linear Vaidya spacetime i.e. the case when the mass function has the non-linear form $M(v) \equiv \lambda v^n \,, \lambda >0 \,, n>1 $. We prove that the central naked singularity might form for values $n>1$ but they are gravitationally weak. Also we investigate the question about forces in the naked singularity and prove that they might be finite only in the case of the gravitationally weak naked singularity.