Causal Feature of Central Singularity and Gravitational Mass

TL;DR

This paper defines the mass of singularities in spherically symmetric spacetimes and explores how its sign influences the causal nature of the singularity, linking mass to spacetime geometry and particle dynamics.

Contribution

It introduces a definition for the mass of singularities and analyzes its relation to the causal character of singularities in spherical symmetry.

Findings

Positive mass implies non-timelike singularities

Negative mass implies non-spacelike singularities

Connection established between mass sign and particle force

Abstract

Mass of singularity is defined, and its relation to whether the singularity is spacelike, timelike or null is discussed for spherically symmetric spacetimes. It is shown that if the mass of singularity is positive (negative) the singularity is non-timelike (non-spacelike). The connection between the sign of the mass and the force on a particle is also discussed.