Black Hole Solutions in Rastall Theory

The Reissner-Nordstr¨om black hole solution in a generic cosmological constant background in 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 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.

Reissner-Nordstr¨om black hole, Rastall theory of gravity.