Impact of the Rastall parameter on perfect fluid spheres

Abstract

We examine the effects of the Rastall parameter on the behaviour of spherically symmetric static distributions of perfect fluid matter. It was claimed by Visser [Physics Letters B, 782, 83, (2018)] that the Rastall proposition is completely equivalent to the Einstein theory. While many authors have raised contrary arguments, our intention is to analyze the properties of Rastall gravity through variation of the Rastall parameter in the context of perfect fluids spheres that may be used to model neutron stars or cold fluid planets. This analysis also serves to counter the claim that Rastall gravity is equivalent to the standard Einstein theory. It turns out that the condition of pressure isotropy is exactly the same as for Einstein gravity and hence that any known solution of the Einstein equations may be used to study the effects of the Rastall dynamical quantities. Moreover, by choosing the well studied Tolman metrics, we discover that in the majority of cases there is substantial deviation from the Einstein case when the Rastall parameter vanishes and in cases where the Einstein model displays defective behaviour, certain Rastall models obey the well known elementary requirements for physical plausibility. These empirical findings do not support the idea that Rastall theory is equivalent to Einstein theory as several deviations in physical behavior are displayed as counterexamples.

Linear growth index of matter perturbations in Rastall gravity

“…It is worth mentioning that the growth index is determined within the matter dominated epoch which corresponds to Ω x = 0. According to relation (22), this corresponds to Ω m = 2 3−γ . After some algebraic calculations, based, on Eqs.…”

Decoupling gravitational sources by MGD approach in Rastall gravity

“…To illustrate how gravitational decoupling by means of MGD works in the Rastall gravity scenario we apply it to the well known Tolman IV solution. This space-time was already studied in the context of MDG in [61] and in the framework of Rastall theory [49]. So, it allows us to compare the resulting deformed solution immersed in an anisotropic scenario with previous results already obtained and therefore establish if it is plausible the study of the compact structure containing anisotropic matter distributions in the arena of Rastall gravity + gravitational decoupling by MGD approach.…”

“…In addition, to contrast our results we have taken the geometry of the inner space-time to be Tolman IV. This solution which describes a spherically symmetric and static object whose material content respects a perfect fluid distribution has already been extended to anisotropic domains by MGD [61] and has also been studied in the Rastall gravity picture [49]. One of the most notable features of Rastall's theory of gravity is that any perfect fluid solution of Einstein's equations is also a solution of it.…”

Null Fluid Collapse in Rastall Theory of Gravity

“…Moreover, the effects of the Rastall's coupling parameter on modeling the static and spherically symmetric distributions of a perfect fluid have been surveyed in ref. [101], where the properties of a well‐known stellar model proposed by Tolman, [ 102 ] was investigated. Therein, it was shown that, in most of the case studies, Rastall theory remains well consistent with the basic requirements for physical reliability of the model while the GR theory exhibits defective behavior.…”