Toward an invariant definition of repulsive gravity

TL;DR

This paper introduces an invariant method using the Riemann tensor to identify regions of repulsive gravity near naked singularities, providing a coordinate-independent approach validated on Kerr-Newman spacetimes.

Contribution

It proposes a novel, invariant technique based on the Riemann tensor to define repulsive gravity regions, improving upon coordinate-dependent methods.

Findings

The Riemann tensor method effectively identifies repulsive regions in Kerr-Newman spacetimes.

The approach yields consistent results across different coordinate systems.

It enhances understanding of naked singularities' gravitational properties.

Abstract

A remarkable property of naked singularities in general relativity is their repulsive nature. The effects generated by repulsive gravity are usually investigated by analyzing the trajectories of test particles which move in the effective potential of a naked singularity. This method is, however, coordinate and observer dependent. We propose to use the properties of the Riemann tensor in order to establish in an invariant manner the regions where repulsive gravity plays a dominant role. In particular, we show that in the case of the Kerr-Newman singularity and its special subcases the method delivers plausible results.