A no-hair theorem for black holes in f(R) gravity

Abstract

In this work we present a no-hair theorem which discards the existence of four-dimensional asymptotically flat, static and spherically symmetric or stationary axisymmetric, non-trivial black holes in the frame of f (R) gravity under metric formalism. Here we show that our no-hair theorem also can discard asymptotic de Sitter stationary and axisymmetric non-trivial black holes. The novelty is that this no-hair theorem is built without resorting to known mapping between f (R) gravity and scalar-tensor theory. Thus, an advantage will be that our no-hair theorem applies as well to metric f (R) models that cannot be mapped to scalar-tensor theory. © 2017 IOP Publishing Ltd.