# Higher order gravities and the Strong Equivalence Principle

## TL;DR

This paper demonstrates that in metric theories of gravity, gravitational energy-momentum couples to gravity similarly to matter energy-momentum, and explores implications for the Strong Equivalence Principle and gauge transformations.

## Contribution

It establishes the universal coupling of gravitational energy-momentum to gravity in all covariant metric theories and analyzes its relation to the Strong Equivalence Principle.

## Key findings

- Gravity couples to gravitational energy-momentum as matter does.
- The coupling holds order by order in weak field approximation.
- The gauge transformation properties of the gravitational energy-momentum tensor are characterized.

## Abstract

We show that, in all metric theories of gravity with a general covariant action, gravity couples to the gravitational energy-momentum tensor in the same way it couples to the matter energy-momentum tensor order by order in the weak field approximation around flat spacetime. We discuss the relation of this property to the Strong Equivalence Principle. We also study the gauge transformation properties of the gravitational energy-momentum tensor.