Insights on the Stability of Compact Stars under Durgapal-Lake Metric Potentials in the Framework of Non-Conservative Theory of Gravity

Insights on the Stability of Compact Stars under Durgapal-Lake Metric Potentials in the Framework of Non-Conservative Theory of Gravity

ELSEVIER Article: https://www.sciencedirect.com/science/article/abs/pii/S2212686424001912

Abstract

This research deals with the impacts of non-conserved gravitational theory on the physical behavior of three anisotropic compact stars. For this purpose, the metric of static spherically symmetric comprising the anisotropic matter composition is taken into account. To examine the various aspects of some particular compact star models, the Durgapal-Lake metric functions are considered. The unknown parameters involved in Durgapal-Lake metric functions are computed via matching constraints with observed data of masses and radii of three particular stellar objects. The obtained results are noted to be as accurate as possible in terms of physical viability. All the physical crucial parameters and characteristics are displayed graphically and these visuals depict the evaluated solutions that are consistent for three distinct stellar models. It is observed that the parameters occurring in the set of solutions have some valuable insights for these solutions. It is determined that the stars under consideration manifest stable structures corresponding to Durgapal-Lake metric potentials in this framework while they exhibit instability in the case of conservative theory, i.e., general relativity. Further, it is exhibited that for the theory factor equals to zero, the results of general relativity can also be observed graphically.

Introduction

General relativity (GR) undoubtedly has made remarkable discoveries but there are few scenarios at the basic level, which cannot be well discussed in this framework. The most important issue for GR to resolve is the presence of dark energy (DE), which is acknowledged as a possible cause for the present conjecture involving accelerated cosmic expansion. One could suppose that the cosmological factor, which appears in the Einstein field equations of GR, explains why our cosmos is expanding faster than before. There are several problems with how GR illustrates the universe’s rapid expansion. Developing a feasible gravitational theory in curved geometries is another notable challenge for scientists working in the framework of quantum gravity. Various efforts have been undertaken, but none of them have been completely successful in developing a convincing theory of quantum gravity. Different gravitational modified theories other than GR have been designed to elaborate these problems of DE and quantum gravity.

These speculations are dubbed as the alternative or modified gravitational theories.

The whole mass (energy) of a gravitational system is retained in GR, but appropriate evidence for this is lacking. To address this issue, Rastall introduced the Rastall theory of gravity (RG) as an extension to GR. Rastall gravity is a type of gravitational field theory that modifies GR, the established theory of relativity, to describe the evolution of non-conservative astrophysical models. Extracted from Newtonian theory, energy conservation in gravity is defined as the departing covariant divergence of the energy–momentum tensor (EMT). The fact that energy and momentum are not conserved is one of the arguments against RG. The net energy production and curvature of spacetime in particular systems can both be used to justify the violation of energy conservation. It has been argued by Rastall that the EMT needs not to vanish for the Einstein tensor to disappear. As an alternative, Rastall proposed that the derivative of the Ricci curvature scalar might affect the divergence of the EMT in a suitable manner.

Theories of gravitational fields that do not maintain energy conservation are not new. Numerous non-conservative theories have been put out in the literature. Einstein’s trace-free theory, also known as unimodular gravity, is one of the oldest. Rearranging the field equations in the form of the energy–momentum trace implies no energy conservation because the metric tensor’s determinant is maintained at −1. Thankfully, there is now only one independent field equation, making it possible to include energy conservation by choice. The more complex theory presented by Harko et al. does not permit this. Here, the form of the Ricci scalar and the EMT’s trace takes the role of the Lagrangian dependency on the Ricci scalar in standard GR. The RG cannot be corrected since it is inherently non-conservative. Another criticism of RG is that, despite producing physically appealing outcomes in cosmology and astrophysics, no Lagrangian for this theory has been discovered so far.