Static scalar field solutions in symmetric gravity
We study an extension of general relativity with a second metric and an exchange symmetry between the two metrics. Such an extension might help to address some of the outstanding problems with general relativity, for example the smallness of the cosmological constant. We here derive a family of exact solutions for this theory. 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.