Black bounces in Cotton gravity

TL;DR

This paper explores black bounce solutions in Cotton gravity coupled with non-linear electrodynamics and scalar fields, aiming to find non-singular, horizon-possessing geometries inspired by black bounce models.

Contribution

It introduces new non-singular solutions in Cotton gravity with matter fields, extending the understanding of regular black hole geometries in this modified gravity theory.

Findings

Identified NLED Lagrangians and scalar potentials producing bouncing solutions.

Analyzed horizon structure and regularity of the solutions.

Extended the class of non-singular geometries in Cotton gravity.

Abstract

Recently, J. Harada proposed a theory relating gravity to the Cotton tensor, dubbed as ''Cotton gravity'' (CG). This is an extension of General Relativity such that every solution of the latter turns out to be a solution of the former (but the converse is not true) and, furthermore, it is possible to derive the cosmological constant as an integration constant within it. In this work we investigate CG by coupling it to both non-linear electrodynamics (NLED) and scalar fields. We study static and spherically symmetric solutions implementing a bouncing behaviour in the radial function so as to avoid the development of singularities, inspired by the Simpson-Visser black bounce and the Bardeen model, both interpreted as magnetic monopoles. We identify the NLED Lagrangian density and the scalar field potential generating such solutions, and investigate the corresponding gravitational configurations in terms of horizons, behaviour of the metric functions, and regularity of the Kretchsman curvature scalar. Our analysis extends the class of non-singular geometries found in the literature and paves the ground for further analysis of black holes in CG.