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

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’s 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 Bohmian formalism.