Regular solutions for black strings and torus-like black holes

TL;DR

This paper introduces new regular black hole solutions with torus-like and string topologies in a cosmological setting, extending previous spherical solutions and ensuring regularity at the core, with mass corrections from electromagnetic self-energy.

Contribution

It presents novel regular black hole solutions with different topologies, derived using regularized potentials, and discusses their properties including mass corrections.

Findings

Solutions are regular at the origin.

Total mass includes electromagnetic self-energy correction.

Special limits recover known solutions.

Abstract

In this letter, we extend the recent black hole solution with spherical symmetry [Phys. Lett. B \textbf{835} (2022), 137546], to a new class of black hole solutions with different topology, namely, a torus-like black hole and a black string in the presence of the cosmological constant. We have used the regularized expressions for the gravitational and the electromagnetic potentials, then we derived the corrections to the energy density and, finally, the black hole solutions are obtained which are regular in the limit $r \to 0$. Interestingly, it is found that the total mass of the black hole is corrected due to the regularized self-energy of the electrostatic field. In the special limit, we recover the well-known solutions in the literature.