Reduction of a family of metric gravities

Abstract

A recent proposal by Shuler regarding a postulate-based derivation of a family of metrics describing the gravitational field outside a static spherically symmetric mass distribution is reviewed. All of Shuler's gravities agree with the Schwarzschild solution in the weak-field limit, but they differ in the strong-field domain, i.e., close enough to a sufficiently compact source of the field. It is found that the evoked postulates of i) momentum conservation and ii) consistency of field strength measurement are satisfied in all metric theories of gravity compatible with the Einstein equivalence principle, no matter what the form of the metric. Therefore, they cannot be used, within any correct deduction, to derive a particular metric. Shuler's derivations are based on an inconsistent set of correspondences between local and distant quantities. Furthermore, it is shown here that out of the family of possible metrics given by Shuler only one member, the Schwarzschild metric, satisfies a standard relativistic generalization of Newton's law of gravitation, suggesting the others to be unphysical.

3 figures. Submitted to European Physical Journal Plus on 16/04/19, accepted on 02/05/2019. This version corresponds to the preprint with some grammatical corrections added. In the journal version, titles have been removed from references, so the arXiv version gives more complete references. Otherwise, there are essentially only style differences (bracket references vs. superscript ones)

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