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.

This study explores the behavior of compact stars within the framework of $$f(R,L_m,T)$$f ( R , L m , T ) gravity, focusing on the functional form $$f(R,L_m,T) = R + \alpha TL_m$$f ( R , L m , T ) = R + α T L m . The modified Tolman–Oppenheimer–Volkoff (TOV) equations are derived and numerically solved for several values of the free parameter $$\alpha $$α by considering both quark and hadronic matter—described by realistic equations of state (EoSs). Furthermore, the stellar structure equations are adapted for two different choices of the matter Lagrangian density (namely, $$L_m= p$$L m = p and $$L_m= -\rho $$L m = - ρ ), laying the groundwork for our numerical analysis. As expected, we recover the traditional TOV equations in General Relativity (GR) when $$\alpha \rightarrow 0$$α → 0 . Remarkably, we found that the two choices for $$L_m$$L m have appreciably different effects on the mass-radius diagrams. Results showcase the impact of $$\alpha $$α on compact star properties, while final remarks summarize key findings and discuss implications, including compatibility with observational data from NGC 6397’s neutron star. Overall, this research enhances comprehension of $$f(R,L_m,T)$$f ( R , L m , T ) gravity’s effects on compact star internal structures, offering insights for future investigations.

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.