Regular solutions for black strings and torus-like black holes

In this letter, we extend the recent black hole solution with spherical symmetry [Phys. Lett. B 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-+ 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.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this letter, 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, are extended based on the recent black hole solution with spherical symmetry. Regularized expressions for the gravitational and electromagnetic potentials are used, and the corrections to the energy density are derived. The obtained black hole solutions are regular in the limit r-+0, and it is found that the total mass of the black hole is corrected due to the regularized self-energy of the electrostatic field. Well-known solutions in the literature are recovered in the special limit.