Black hole solutions of gravity theories with non-minimal coupling between matter and curvature

Abstract

We study black hole solutions in an extension of general relativity (GR) with an explicit non-minimal coupling between matter and curvature. General black hole solutions satisfying the known energy conditions are derived including the ones with anti-de Sitter background. These solutions differ from those of GR by just a coupling function-dependent rescaling of the mass and charge of the black hole and by a ‘dressing’ of the cosmological constant. The existence of black hole solutions of the non-minimally coupled theory as well as the conditions for a suitable weak-field limit are considered as a constraint on the coupling function responsible for the non-minimal coupling between matter and curvature. The ‘dressing’ of the cosmological constant is then used to address the cosmological constant problem.