Schwarzschild limit of conformal gravity in the presence of macroscopic scalar fields

Abstract

In their original study of conformal gravity, a candidate alternate gravitational theory, Mannheim and Kazanas showed that in any empty vacuum region exterior to a localized static spherically symmetric gravitational source, the geometry would reduce to the standard attractive gravity Schwarzschild geometry on solar system distance scales. In a recent paper Flanagan has argued that this would not be the case if the source has associated with it a macroscopic scalar field which makes a non-zero contribution to the energy-momentum tensor in the otherwise empty exterior region. In this paper we examine Flanagan's analysis and show that even with such long range scalar fields, the standard Schwarzschild phenomenology is still recovered.