Generalized Rastall's gravity and its effects on compact objects

TL;DR

This paper introduces a generalized Rastall's gravity theory that modifies energy-momentum conservation, explores its spherically symmetric solutions, and investigates its impact on neutron star structures using realistic equations of state.

Contribution

It presents a new formulation of Rastall's gravity with a variable gravitational parameter and analyzes its solutions and effects on neutron stars.

Findings

Two classes of vacuum solutions with spherical symmetry are identified.

The gravitational parameter depends on the Rastall constant, differing from general relativity.

Neutron star profiles are significantly affected by the generalized theory.

Abstract

We present a generalization of Rastall's gravity in which the conservation law of the energy-momentum tensor is altered, and as a result, the trace of the energy-momentum tensor is taken into account together with the Ricci scalar in the expression for the covariant derivative. Afterwards, we obtain the field equations in this theory and solve them by considering a spherically symmetric space-time. We show that the external solution has two possible classes of solutions with spherical symmetry in the vacuum in generalized Rastall's gravity, and we analyse one of them explicitly. The generalization, in contrast to constant value $k=8\pi G$ in general relativity, has a gravitational parameter $k$ that depends on the Rastall constant $\alpha$. As an application, we perform a careful analysis of the effects of the theory on neutron stars using realistic equations of state (EoS) as input. Our results show that important differences on the profile of neutron stars are obtained within two representatives EoS.