Preserving the Energy-Momentum Tensor in f(R, Matter) Theories

TL;DR

This paper introduces a class of f(R, Matter) gravity theories using the Herglotz variational principle to restore energy-momentum conservation in models with matter-geometry coupling.

Contribution

It formulates a novel Herglotz extension of f(R, Matter) gravity that preserves the covariant conservation of the energy-momentum tensor.

Findings

Herglotz extension restores energy-momentum conservation.

The approach interprets nonconservation as an effective dissipative process.

Provides a variational framework for dissipative modified gravity theories.

Abstract

In certain modified theories of gravity, non-minimal couplings between matter and geometry lead to the nonconservation of the energy-momentum tensor. By interpreting this as an effective dissipative process, we formulate a general class of f(R, Matter) theories with the Herglotz variational principle, a variational approach designed for dissipative systems. We demonstrate that, for an appropriate choice of the Herglotz contribution, the resulting Herglotz extension of f(R, Matter) gravity restores the covariant conservation of the energy-momentum tensor.