The present work deals with the study of the gravitational collapsing phenomenon of spherically symmetric massive stars with a <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\Lambda $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation> parametrization. A collapsing model with a cosmological constant of the form <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\Lambda =\beta \left( \frac{\dot{\Theta }}{3} + \frac{\Theta ^2}{9}\right) $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Λ</mi> <mo>=</mo> <mi>β</mi> <mfenced close=")" open="("> <mfrac> <mover accent="true"> <mi mathvariant="normal">Θ</mi> <mo>˙</mo> </mover> <mn>3</mn> </mfrac> <mo>+</mo> <mfrac> <msup> <mi mathvariant="normal">Θ</mi> <mn>2</mn> </msup> <mn>9</mn> </mfrac> </mfenced> </mrow> </math></EquationSource> </InlineEquation> has been considered. In this model, exact solutions of the Einstein field equations (EFEs) are obtained using the <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\Lambda $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation> parametrization and the junction conditions. All the physical and geometrical quantities are calculated in terms of the Schwarzschild mass M and areal radius R of spherically symmetric stars. Consequently, we have approximated the masses and radii of different stars to estimate the value of the model parameter <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\beta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>. We discuss the collapsing process and singularity formation for these stars and observe that all the physical and geometrical parameters of the model heavily depend on the model parameter <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\beta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>. We further discuss spacetime singularity through the development of an apparent horizon.

Impact of $\Lambda $–Parametrization on Stellar Collapse and Spacetime Singularities

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2026年2月16日

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Anjali Pandey,
Anurag Awasthi,
Sudhir Kumar Srivastava

摘要

The present work deals with the study of the gravitational collapsing phenomenon of spherically symmetric massive stars with a $\Lambda $ $Λ$ parametrization. A collapsing model with a cosmological constant of the form $\Lambda =\beta \left( \frac{\dot{\Theta }}{3} + \frac{\Theta ^2}{9}\right) $ $Λ = β (\frac{\dot{Θ}}{3} + \frac{Θ^{2}}{9})$ has been considered. In this model, exact solutions of the Einstein field equations (EFEs) are obtained using the $\Lambda $ $Λ$ parametrization and the junction conditions. All the physical and geometrical quantities are calculated in terms of the Schwarzschild mass M and areal radius R of spherically symmetric stars. Consequently, we have approximated the masses and radii of different stars to estimate the value of the model parameter $\beta $ $β$ . We discuss the collapsing process and singularity formation for these stars and observe that all the physical and geometrical parameters of the model heavily depend on the model parameter $\beta $ $β$ . We further discuss spacetime singularity through the development of an apparent horizon.

Impact of \(\Lambda \)–Parametrization on Stellar Collapse and Spacetime Singularities

摘要