Metric-affine f(R,T) theories of gravity and their applications

TL;DR

This paper investigates metric-affine f(R,T) gravity theories, revealing they have second-order field equations similar to f(R) theories, lack new propagating degrees of freedom, and exhibit non-conservation of energy-momentum, with potential applications in various fields.

Contribution

It demonstrates that metric-affine f(R,T) theories have second-order equations and no additional propagating degrees of freedom compared to GR, differing from metric formulations.

Findings

Field equations resemble metric-affine f(R) theories with an effective energy-momentum tensor.

No new propagating degrees of freedom are introduced.

Weak field limit yields a modified Poisson equation similar to Eddington-inspired Born-Infeld gravity.

Abstract

We study f(R,T) theories of gravity, where T is the trace of the energy-momentum tensor T_{\mu\nu}, with independent metric and affine connection (metric-affine theories). We find that the resulting field equations share a close resemblance with their metric-affine f(R) relatives once an effective energy-momentum tensor is introduced. As a result, the metric field equations are second-order and no new propagating degrees of freedom arise as compared to GR, which contrasts with the metric formulation of these theories, where a dynamical scalar degree of freedom is present. Analogously to its metric counterpart, the field equations impose the non-conservation of the energy-momentum tensor, which implies non-geodesic motion and consequently leads to the appearance of an extra force. The weak field limit leads to a modified Poisson equation formally identical to that found in Eddington-inspired Born-Infeld gravity. Furthermore, the coupling of these gravity theories to perfect fluids, electromagnetic, and scalar fields, and their potential applications are discussed.