Black Hole Solutions in Rastall Theory

TL;DR

This paper derives black hole solutions within Rastall gravity, showing the cosmological constant emerges naturally from the theory's field equations, and explores various known black hole solutions as special cases.

Contribution

It presents the first derivation of Reissner-Nordström black holes in Rastall gravity with a natural cosmological constant.

Findings

Reissner-Nordström solution in Rastall gravity obtained

Cosmological constant arises naturally from field equations

Includes Schwarzschild and (anti-)de Sitter solutions as special cases

Abstract

The Reissner-Nordstr\"om black hole solution in a generic cosmological constant background in the the context of Rastall gravity is obtained. It is shown that the cosmological constant arises naturally from the consistency of the non-vacuum field equations of the Rastall theory for a spherical symmetric spacetime, rather than its {\it ad-hoc} introduction in the usual Einstein and Einstein-Maxwell field equations. The usual Reissner-Nordstr\"om, Schwarzschild and Schwarzschild-(anti)de Sitter black hole solutions in the framework of this theory are also addressed as the special independent subclasses of the obtained general solution.