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

TL;DR

This paper demonstrates that the Schwarzschild limit of conformal gravity remains valid even when macroscopic scalar fields are present, countering recent claims that such fields would alter the exterior vacuum geometry.

Contribution

The study refutes Flanagan's argument by showing that conformal gravity's Schwarzschild limit persists despite long-range scalar fields.

Findings

Schwarzschild geometry is recovered in conformal gravity with scalar fields.

Long-range scalar fields do not alter the exterior vacuum solution.

The standard gravitational phenomenology remains valid in the presence of 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.