The strong equivalence principle from gravitational gauge structure

TL;DR

This paper explores how gravitational gauge structures enforce the strong equivalence principle in metric theories, extending mass equality to complex bodies and identifying specific tensor and scalar theories within generalized Brans-Dicke models.

Contribution

It introduces a gauge-theoretic approach to gravitational self-interactions, providing a framework to derive the strong equivalence principle and identify compatible theories.

Findings

Extends mass equality to bodies with gravitational binding energy.

Identifies specific tensor and scalar theories consistent with the gauge constraint.

Suggests a method for minimal violation of the strong equivalence principle.

Abstract

Gravitational self-interactions are assumed to be determined by the covariant derivative acting on the Riemann-Christoffel field strength. Once imposed on a metric theory, this Yang-Mills gauge constraint extends the equality of gravitational mass and inertial mass to compact bodies with non-negligible gravitational binding energy. Applied to generalized Brans-Dicke theories, it singles out one tensor theory and one scalar theory for gravity but also suggests a way to implement a minimal violation of the strong equivalence principle.