Regular Black Strings and BTZ Black Hole in Unimodular Gravity Supported by Maxwell Fields

TL;DR

This paper derives regular black string and BTZ black hole solutions in unimodular gravity with Maxwell fields, highlighting the role of a radially dependent vacuum term as an integration constant.

Contribution

It introduces a Maxwell source for these solutions within unimodular gravity, where the cosmological constant emerges as a radial function rather than a fixed parameter.

Findings

Maxwell electrodynamics supports the regular black string and BTZ black hole solutions.

The vacuum contribution $ extLambda(r)$ acts as a radial-dependent integration constant.

The solutions are consistent with the unimodular gravity framework and Maxwell sources.

Abstract

In this work, we obtain a Maxwell source for regular black string and BTZ black hole using the framework of unimodular gravity. This type of alternative to general relativity imposes an additional condition on the spacetime volume element, namely that it is constant, $\det(g_{\mu\nu}) = g_0$, and thus restricts diffeomorphism invariance to volume-preserving transformations. In this procedure, the cosmological constant does not appear directly in the action, but rather as an integration constant of the field equations. By using the non-conservation of the energy-momentum tensor, we show that the integration constant becomes a function $\Lambda(x)$, which is interpreted as a vacuum contribution depending on the radial coordinate, in our case. From the definition of the geometric function $H(r)$, we verify the validity of Maxwell electrodynamics as a source for the solutions and compute the vacuum contribution $\Lambda(r)$ that supports the solutions.