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 nonconservation of the energy-momentum tensor, which implies nongeodesic 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.

We construct a steady analytic accretion flow model for a finite rotating gas cloud that accretes material to a central gravitational object. The pre

Aims. We investigate in detail two physical properties of the metric \( f(R) \) theory developed by Sobouti (2007, A&A, 464, 921). We first look for the possibility of producing gravitational waves which travel at the speed of light. We then check the possibility of producing extra bending in the lenses produced by the theory. Methods. We do this by using standard weak field approximations to the gravitational field equations that appear in Sobouti's theory. Results. We show that the metric theory of gravitation proposed by Sobouti (2007) predicts the existence of gravitational waves travelling at the speed of light in vacuum. In fact, this is proved in general terms for all metric theories of gravity which can be expressed as powers of Ricci's scalar. We also show that an extra additional lensing as compared to that predicted by standard general relativity is produced. Conclusions. These two points are generally considered to be of crucial importance in the development of relativistic theories of gravity that could provide an alternative description to the dark matter paradigm.

Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics