<p>We present an exact interior solution to Einstein’s field equations describing a static, spherically symmetric compact object with isotropic pressure. While inspired by gravastar models, our configuration does not attain the ultracompactness <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6163_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">\(M/R \sim 0.5\)</EquationSource> </InlineEquation> typically required for black hole mimickers&#xa0;[<CitationRef CitationID="CR1">1</CitationRef>, <CitationRef CitationID="CR2">2</CitationRef>]. Instead, we interpret it as a gravastar-inspired model for neutron star–scale objects. The solution is regular, stable, and consistent with neutron star observables within classical general relativity. Unlike earlier models relying on thin shells or exotic matter, our approach employs a single monotonic gravitational potential and provides exact, closed-form expressions for pressure, density, mass, and redshift. Although smooth interior solutions exist in the literature, our model is a rare case where such profiles are derived analytically from the isotropic Einstein equations, yielding a continuous solution that satisfies all energy and stability conditions and remains dynamically stable only within specific parameter ranges, as confirmed by eigenvalue analysis, without invoking anisotropy, numerical integration, or exotic components. The model satisfies the Buchdahl compactness limit, energy conditions, and causality. Dynamical stability is further examined by solving the Sturm–Liouville eigenvalue problem, confirming stability in some parameter regimes while identifying instabilities in others. Our results align closely with neutron star observables such as mass, radius, and surface redshift. Comparison with NICER data for PSR J0030+0451 and PSR J0740+6620 shows observational consistency. Phase diagrams, redshift surfaces, and mass–radius curves reveal smooth transitions between stable and unstable regimes. Overall, this study demonstrates that exact isotropic gravastar interiors can reproduce neutron star observables while satisfying all theoretical requirements.</p>

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A Stable Gravastar-inspired Interior from Exact Einstein Solutions: Compactness, Redshift Surfaces, and Observational Matching with NICER Data

  • M. I. H. Sakib,
  • M. A. Kauser,
  • M. G. Hafez

摘要

We present an exact interior solution to Einstein’s field equations describing a static, spherically symmetric compact object with isotropic pressure. While inspired by gravastar models, our configuration does not attain the ultracompactness \(M/R \sim 0.5\) typically required for black hole mimickers [1, 2]. Instead, we interpret it as a gravastar-inspired model for neutron star–scale objects. The solution is regular, stable, and consistent with neutron star observables within classical general relativity. Unlike earlier models relying on thin shells or exotic matter, our approach employs a single monotonic gravitational potential and provides exact, closed-form expressions for pressure, density, mass, and redshift. Although smooth interior solutions exist in the literature, our model is a rare case where such profiles are derived analytically from the isotropic Einstein equations, yielding a continuous solution that satisfies all energy and stability conditions and remains dynamically stable only within specific parameter ranges, as confirmed by eigenvalue analysis, without invoking anisotropy, numerical integration, or exotic components. The model satisfies the Buchdahl compactness limit, energy conditions, and causality. Dynamical stability is further examined by solving the Sturm–Liouville eigenvalue problem, confirming stability in some parameter regimes while identifying instabilities in others. Our results align closely with neutron star observables such as mass, radius, and surface redshift. Comparison with NICER data for PSR J0030+0451 and PSR J0740+6620 shows observational consistency. Phase diagrams, redshift surfaces, and mass–radius curves reveal smooth transitions between stable and unstable regimes. Overall, this study demonstrates that exact isotropic gravastar interiors can reproduce neutron star observables while satisfying all theoretical requirements.