Tidal Forces in Naked Singularity Backgrounds

TL;DR

This paper compares tidal forces near naked singularities and black holes, revealing significant differences that could help identify the nature of singularities at galactic centers through observations.

Contribution

It provides the first numerical analysis of Roche limits in naked singularity backgrounds, highlighting potential observational signatures distinguishing them from black holes.

Findings

Naked singularities exhibit larger tidal forces than black holes.

Significant deviations in Roche limits suggest observational differences.

Potential for using tidal force measurements to identify singularity types.

Abstract

The end stage of a gravitational collapse process can generically result in a black hole or a naked singularity. Here we undertake a comparative analysis of the nature of tidal forces in these backgrounds. The effect of such forces is generically exemplified by the Roche limit, which predicts the distance within which a celestial object disintegrates due to the tidal effects of a second more massive object. In this paper, using Fermi normal coordinates, we numerically compute the Roche limit for a class of non-rotating naked singularity backgrounds, and compare them with known results for Schwarzschild black holes. Our analysis indicates that there might be substantially large deviations in the magnitudes of tidal forces in naked singularity backgrounds, compared to the black hole cases. If observationally established, these can prove to be an effective indicator of the nature of the singularity at a galactic centre.