Black Hole singularity and its possible mitigations: Reformulation of Penrose Singularity theorem using null Raychaudhuri matrix

TL;DR

This paper introduces a matrix-based reformulation of the Penrose singularity theorem using null Raychaudhuri matrices, and explores potential mitigations for black hole singularities through quantum and alternative formalisms.

Contribution

It presents a novel matrix approach to the Raychaudhuri equation and reformulates the Penrose theorem, proposing new methods to address black hole singularities.

Findings

Reformulated Penrose theorem using null Raychaudhuri matrix

Identified characteristics of the Raychaudhuri matrix at singularities

Suggested two possible approaches to mitigate black hole singularities

Abstract

In this paper, we introduce a notion of null Raychaudhuri matrix motivated by the matrix representation of tensor fields. The evolution of this matrix gives the matrix form of null Raychaudhuri equation. Using this distinct geometric approach, we have reformulated the original Penrose singularity theorem on Black-Hole and have commented on the characteristic of the Raychaudhuri matrix at the singularity. The paper also suggests two possible mitigations for the physical singularity of Schwarzschild black hole via the Wheeler-DeWitt formalism and Bohemian formalism.