On the Equivalence of Brans-Dicke and Einstein Theories with Static Black Holes

TL;DR

This paper proves that under certain conditions, Brans-Dicke theory with matter of definite-sign trace is equivalent to Einstein gravity with a zero-trace energy-momentum tensor, especially in the context of static black holes.

Contribution

It establishes a no-hair theorem for the Brans-Dicke field, showing equivalence to Einstein gravity under specific conditions for static black holes.

Findings

Brans-Dicke theory reduces to Einstein gravity with T=0 for matter with definite-sign trace.

A no-hair theorem for the Brans-Dicke field in static black hole spacetimes is proven.

Equivalence holds when the trace of the energy-momentum tensor has a definite sign.

Abstract

A `no-hair' theorem for the Brans-Dicke field, in the domain of outer communications of a static black hole, is established, when the trace of the energy-momentum tensor, T, is a definite-sign scalar. This implies that Brans-Dicke theory of gravitation, for matter with T of definite sign, is equivalent to Einstein gravity with the constraint T=0.