Gravitational repulsive effects in 3D regular black holes

TL;DR

This paper investigates the presence and effects of repulsive gravity in 3D regular black holes, analyzing curvature eigenvalues and energy conditions to identify regions where gravity switches from attractive to repulsive.

Contribution

It introduces an invariant method to detect repulsive gravity in 3D regular black holes and relates this to violations of the strong energy condition.

Findings

Repulsive gravity regions are identified near the black hole core.

Reversal of gravity sign correlates with violation of strong energy condition.

Repulsive effects depend on parameters like electric charge and AdS length.

Abstract

In this work, we consider the effects of repulsive gravity in an invariant way for four static 3D regular black holes, using the eigenvalues of the Riemann curvature tensor, the Ricci scalar, and the strong energy conditions. The eigenvalues of the solutions are non-vanishing asymptotically (in asymptotically AdS) and increase as the source of gravity is approached, providing a radius at which the passage from attractive to repulsive gravity might occur. We compute the onsets and the regions of repulsive gravity and conclude that the regular behavior of the solutions at the origin of coordinates can be interpreted as due to the presence of repulsive gravity, which also turns out to be related with the violation of the strong energy condition. We showed that in all of the solutions for the allowed region of parameters, gravity changes its sign, but the repulsive regions only for the non-logarithmic solution are affected by the mass that generates the regular black hole. The repulsive regions for the logarithmic solutions are dependent on electric charge and the AdS$_{3}$ length. The implications and physical consequences of these results are discussed in detail.