<p>Various types of inhomogeneous collapse models in general relativity (GR) lead to the formation of spacetime singularities either visible or hidden by a spacetime horizon. Our aim in the present work is to search for nonsingular models in Rastall gravity that arise as the final outcomes of spherically symmetric gravitational collapse of an inhomogeneous matter cloud. We firstly assume linear equations of state (EoS) for radial and tangential pressure profiles, i.e., <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6049_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="TEX">$p_r=w_r\rho $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>p</mi> <mi>r</mi> </msub> <mo>=</mo> <msub> <mi>w</mi> <mi>r</mi> </msub> <mi>ρ</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6049_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="TEX">$p_\theta =w_\theta \rho $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>p</mi> <mi>θ</mi> </msub> <mo>=</mo> <msub> <mi>w</mi> <mi>θ</mi> </msub> <mi>ρ</mi> </mrow> </math></EquationSource> </InlineEquation>, then we set the Rastall parameter in such a way that the effective pressure in radial direction vanishes and examine the conditions under which the spacetime singularity can be avoided. We find exact nonsingular collapse solutions for which the collapsing cloud reaches a minimum physical radius at a finite amount of time and then rebounds to an expanding phase where the matter shells start moving away from each other. The solutions we obtain respect the weak energy condition (WEC) which is important for physical validity of the model.</p>

Singularity Avoidance in Gravitational Collapse of an Inhomogeneous Fluid in Rastall Gravity

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发表日期：

2025年6月30日

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Akbar Jahan,
Halime Miraghaei,
Shayesteh Ghaffari,
Amir Hadi Ziaie

摘要

Various types of inhomogeneous collapse models in general relativity (GR) lead to the formation of spacetime singularities either visible or hidden by a spacetime horizon. Our aim in the present work is to search for nonsingular models in Rastall gravity that arise as the final outcomes of spherically symmetric gravitational collapse of an inhomogeneous matter cloud. We firstly assume linear equations of state (EoS) for radial and tangential pressure profiles, i.e., $p_r=w_r\rho $ $p_{r} = w_{r} ρ$ and $p_\theta =w_\theta \rho $ $p_{θ} = w_{θ} ρ$ , then we set the Rastall parameter in such a way that the effective pressure in radial direction vanishes and examine the conditions under which the spacetime singularity can be avoided. We find exact nonsingular collapse solutions for which the collapsing cloud reaches a minimum physical radius at a finite amount of time and then rebounds to an expanding phase where the matter shells start moving away from each other. The solutions we obtain respect the weak energy condition (WEC) which is important for physical validity of the model.