On static spherically symmetric solutions of the vacuum Brans-Dicke theory

TL;DR

This paper analyzes static spherically symmetric solutions in vacuum Brans-Dicke gravity, showing only two independent classes exist, and concludes that no non-Schwarzschild black hole solutions are physically viable within the theory.

Contribution

It demonstrates that only two classes of solutions are independent and identifies conditions under which solutions can represent realistic massive objects.

Findings

Only two independent classes of solutions exist.

Brans class I solution can model exterior fields of massive objects.

No physically viable non-Schwarzschild black hole solutions are found.

Abstract

It is shown that among the four classes of the static spherically symmetric solution of the vacuum Brans-Dicke theory of gravity only two are really independent. Further by matching exterior and interior (due to physically reasonable spherically symmetric matter source) scalar fields it is found that only Brans class I solution with certain restriction on solution parameters may represent exterior metric for a nonsingular massive object. The physical viability of the black hole nature of the solution is investigated. It is concluded that no physical black hole solution different from the Schwarzschild black hole is available in the Brans-Dicke theory.