The possibility of modifications on general relativity is investigated. We propose an alternative theory of gravity constructed with the combination of Rastall and rainbow theories. The hydrostatic equilibrium equations are obtained in order to test the new theory in neutron stars, whose mass-radius diagrams are obtained using modern equations of state of nuclear matter derived from relativistic mean field models and compared with the ones computed by the Tolman-Oppenheimer-Volkoff equations. Different sets of parameters are used and the obtained results confronted with accepted masses and radii values, including important astrophysical objects as the quiescent LMXB NGC 6397 and the double neutron system J0737. We conclude that substantial modifications are obtained even for very small alterations on the two free parameters, making the reproduction of astrophysical observations an easier task.

In this work, we investigate anisotropic effects on the equations of state (EoS) used to describe neutron and quark stars in the framework of Rastall–Rainbow gravity. All our calculations are computed using two different EoS to describe the matter contained within the star: the MIT bag model for quark stars and the IU-FSU parameterisation for the standard hadronic matter. From the values of masses and radii obtained, we can conclude that anisotropic pressure has significant consequences on the structure of compact objects. Specifically, when anisotropy is considered within general relativity, it significantly modifies the maximum stellar mass. On the other hand, when Rastall–Rainbow gravity and anisotropy are simultaneously considered, they provide the best results for the masses and radii of some important astrophysical objects such as the low-mass x-ray binary (LMXB) NGC 6397 and the extremely massive millisecond pulsating source of radio (PSR) J0740 + 6620, for instance. Radii results inferred from the Lead Radius EXperiment (PREX-2) and the compact object in the mass-gap of GW190814 event can also be described for certain values of the Rastall–Rainbow and anisotropy parameters.

In this work, we study the influence of f(R, T) gravity on rapidly rotating neutron stars. First we discuss the main aspects of this modified theory of gravity where the gravitational Lagrangian is an arbitrary function of the Ricci scalar R and of the trace of the energy–momentum tensor T. Then we present the basic equations for neutron stars including the equations of state used in the present work to describe the hadronic matter. Some physical quantities of interest are calculated such as mass–radius relations, moments of inertia, angular momentum, and compactness. By considering four different rotation regimes, we obtain results that indicate substantial modifications in the physical properties of neutron stars in f(R, T) gravity when compared to those in the context of general relativity. In particular, the mass–radius relation for sequences of stars indicates that f(R, T) gravity increases the mass and the equatorial radius of the neutron stars for stars rotating with an angular velocity smaller than Kepler limit.

In this paper, we investigate the evolution of strange quark stars (SQS) from birth as proto-strange quark stars to maturity as stable SQSs at a zero temperature. We assume that self-bound free quarks form entirely the compact star and study its evolution through a series of snapshots using a density-dependent quark mass model. We consider $$\beta $$β -equilibrated stellar matter at two major stages of the star’s evolution: neutrino trapped regime and neutrino transparent regime during the deleptonization and cooling processes of the star. We fix the entropy density per baryon and the lepton fraction to investigate the nuclear equation of state (EoS), particle distribution, temperature profile inside the star, sound velocity, polytropic index, and the structure of the star. Our results show that stars with higher neutrino concentrations are slightly more massive than the neutrino-poor ones along the evolution lines of the SQS. We obtain EoSs in agreement with the conformal boundary set through sound velocity, and also the 2 M $$_\odot $$⊙ mass constraint for NSs was satisfied at all stages of the star’s evolution.

In this work we study rapidly rotating stars by considering the Rastall theory of gravity. We obtain and solve the equations by numerical methods for two usual parametrization of polytropic stars. Then the mass–radius relations, moments of inertia and other results of interest are obtained and compared with the ones for non-rotating stars.