Black hole shadows and Brans-Dicke theory

Abstract

A possible alternative to General Relativity (GR) is Brans-Dicke (BD) theory, a scalar-tensor theory where gravity is mediated both by a symmetric tensor gμν (the metric) and a scalar field ϕ. In this work, we obtain an expression for a black hole shadow angle valid for static and spherically symmetric configurations of the source in GR and beyond. We derive the BD field equations from the action and find solutions for a static, spherically symmetric spacetime in the weak field limit (analytically) and for a strong field (numerically). We show that for finite values of the coupling constant ω the BD field equations allow for naked singularities, whose existence is controversial. We then conclude that no constraints on the theory can be obtained from black hole shadows observations, since static black holes in BD theory are identical to those in GR