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

Eloy Ayón
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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.

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Eloy Ayón. 1996-06-28. On the Equivalence of Brans-Dicke and Einstein Theories with Static Black Holes. https://arxiv.org/abs/gr-qc/9606082

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