Static Scalar Field Solutions in Symmetric Gravity

TL;DR

This paper derives exact solutions in symmetric bi-metric gravity with a massless scalar field, revealing that flat space is the only scalar-free solution and that Schwarzschild solutions contain hidden scalar fields.

Contribution

It introduces a new family of exact solutions in bi-metric gravity with exchange symmetry, highlighting the role of scalar fields in these solutions.

Findings

Scalar field solutions form a two-parameter family

Flat space occurs only when scalar field vanishes

Schwarzschild solutions contain hidden scalar fields

Abstract

We derive a family of exact solutions for bi-metric gravity with an exchange symmetry between the two metrics. In this two-parameter family of solutions the gravitational field is sourced by a time-independent massless scalar field. We find that the only limit in which the scalar field entirely vanishes is flat space. The regular Schwarzschild-solution is left with a scalar field hidden in the second metric's sector.