Field Sources for $f(R,R_{\mu\nu})$ Black-Bounce Solutions: The Case of K-Gravity

TL;DR

This paper constructs regularized black-bounce solutions in 2+1 dimensional K-gravity, identifying scalar fields as the sources and analyzing their causal and geodesic structures.

Contribution

It introduces a novel regularization method for black-bounce solutions in K-gravity and identifies scalar fields as their sources, expanding understanding of lower-dimensional black hole models.

Findings

Curvature singularities are eliminated within the event horizon.

Scalar fields are necessary to source the regularized solutions.

Stable circular orbits exist for particles in the spacetime.

Abstract

In the framework of Simpson-Visser, the search for field sources that produce black-bounces in alternative gravity theories has remained unresolved. In this paper, the first in a series exploring sources for alternative theories of gravity, we identify such a source for the $2+1$ dimensional K-gravity black-bounce. The K-gravity black hole is notable for allowing asymptotically locally flat solutions in lower-dimensional spacetime, yet it possesses curvature singularities concealed within the event horizon. Using the Simpson-Visser regularization technique, we eliminate this singularity, constructing asymptotically locally flat black-bounce solutions in $2+1$ dimensions. We explore the causal structure of these solutions, identifying the conditions under which they describe regular black holes or wormholes. By calculating curvature invariants, we confirm the absence of singularities within the event horizon. Additionally, we demonstrate that, beyond non-linear electrodynamics, a non-linear scalar field is required to source the solution. Finally, we investigate the geodesic structure of this spacetime, analyzing the trajectories of both massive and massless particles. We also confirm the existence of circular orbits and assess their stability.