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