Impact of the Rastall parameter on perfect fluid spheres

TL;DR

This paper investigates how the Rastall parameter influences perfect fluid spheres, revealing deviations from Einstein gravity and challenging the claim that Rastall theory is equivalent to Einstein's theory.

Contribution

It demonstrates that Rastall gravity exhibits distinct physical behaviors from Einstein gravity, especially in modeling astrophysical objects, and refutes the claim of their equivalence.

Findings

Rastall parameter significantly affects fluid sphere properties.

Many Rastall models differ from Einstein solutions, especially when the parameter vanishes.

Some Rastall models satisfy physical plausibility where Einstein models fail.

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 counter-examples.