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11 pages, 317 KiB

Open AccessArticle

Phenomenological Charged Extensions of the Quantum Oppenheimer–Snyder Collapse Model

by S. Habib Mazharimousavi

Universe 2025, 11(8), 257; https://doi.org/10.3390/universe11080257 - 4 Aug 2025

Viewed by 115

This work presents a semi-classical, quantum-corrected model of gravitational collapse for a charged, spherically symmetric dust cloud, extending the classical Oppenheimer–Snyder (OS) framework through loop quantum gravity effects. Our goal is to study phenomenological quantum modifications to geometry, without necessarily embedding them within full loop quantum gravity (LQG). Building upon the quantum Oppenheimer–Snyder (qOS) model, which replaces the classical singularity with a nonsingular bounce via a modified Friedmann equation, we introduce electric and magnetic charges concentrated on a massive thin shell at the boundary of the dust ball. The resulting exterior spacetime generalizes the Schwarzschild solution to a charged, regular black hole geometry akin to a quantum-corrected Reissner–Nordström metric. The Israel junction conditions are applied to match the interior APS (Ashtekar–Pawlowski–Singh) cosmological solution to the charged exterior, yielding constraints on the shell’s mass, pressure, and energy. Stability conditions are derived, including a minimum radius preventing full collapse and ensuring positivity of energy density. This study also examines the geodesic structure around the black hole, focusing on null circular orbits and effective potentials, with implications for the observational signatures of such quantum-corrected compact objects. Full article

(This article belongs to the Special Issue Loop Quantum Gravity and Non-Perturbative Approaches to Quantum Cosmology, Second Edition)

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18 pages, 251 KiB

Open AccessArticle

Complex Riemannian Spacetime: Removal of Black Hole Singularities and Black Hole Paradoxes

by John W. Moffat

Axioms 2025, 14(6), 440; https://doi.org/10.3390/axioms14060440 - 4 Jun 2025

Viewed by 351

Abstract

An approach is presented to resolve key paradoxes in black hole physics through the application of complex Riemannian spacetime. We extend the Schwarzschild metric into the complex domain, employing contour integration techniques to remove singularities while preserving the essential features of the original solution. A new regularized radial coordinate is introduced, leading to a singularity-free description of black hole interiors. Crucially, we demonstrate how this complex extension resolves the long-standing paradox of event horizon formation occurring only in the infinite future of distant observers. By analyzing trajectories in complex spacetime, we show that the horizon can form in finite complex time, reconciling the apparent contradiction between proper and coordinate time descriptions. This approach also provides a framework for the analytic continuation of information across event horizons, resolving the Hawking information paradox. We explore the physical interpretation of the complex extension versus its projection onto real spacetime. The gravitational collapse of a dust sphere with negligible dust is explored in the complex spacetime extension. The approach offers a mathematically rigorous framework for exploring quantum gravity effects within the context of classical general relativity. Full article

(This article belongs to the Special Issue Complex Variables in Quantum Gravity)

17 pages, 325 KiB

Open AccessArticle

An Interior Solution for the Kerr Metric: A Novel Approach

by Yu-Ching Chou

Universe 2025, 11(1), 23; https://doi.org/10.3390/universe11010023 - 15 Jan 2025

Cited by 1 | Viewed by 2269

Abstract

We present a novel approach for the construction of interior solutions for the Kerr metric, extending J. Ovalle’s foundational work through ellipsoidal coordinate transformations. By deriving a physically plausible interior solution that smoothly matches the Kerr exterior metric, we analyze the energy conditions across various rotation parameters. Our findings reveal anisotropic fluid properties and energy condition behaviors in specific space-time regions, providing insights into the strong-field regime of rotating black holes. The proposed solution offers a more realistic description of rotating black hole interiors, with implications for understanding compact astrophysical objects. Full article

(This article belongs to the Collection Open Questions in Black Hole Physics)

13 pages, 2464 KiB

Open AccessEditor’s ChoiceArticle

Anisotropy Induced by Electric Charge: A Computational Analytical Approach

by Franyelit Suárez-Carreño and Luis Rosales-Romero

Physics 2024, 6(2), 780-792; https://doi.org/10.3390/physics6020048 - 16 May 2024

Viewed by 1108

Abstract

This paper presents a novel class of interior solutions for anisotropic stars under the imposition of a self-similar symmetry. This means proposing exact solutions to the Einstein field equations to describe charged matter distribution with radiation flow. The Einstein–Maxwell system by employing specific choices of mass function is formulated to describe the gravitational collapse of charged, anisotropic, spherically symmetric distributions using the Schwarzschild metric. Two ordinary differential equations governing the dynamics are derived by matching a straightforward solution of the symmetry equations to the charged exterior (Reissner–Nordström–Vaidya). Models with satisfactory physical behavior are constructed by extensively exploring self-similar solutions for a set of parameters and initial conditions. Finally, the paper presents the evolution of physical variables and the collapsing radius, demonstrating the inevitable collapse of the matter distribution. Full article

(This article belongs to the Section Astrophysics, Astronomy and Planetology)

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12 pages, 276 KiB

Open AccessArticle

Spherically Symmetric C³ Matching in General Relativity

by Hernando Quevedo

Universe 2023, 9(9), 419; https://doi.org/10.3390/universe9090419 - 14 Sep 2023

Viewed by 1443

Abstract

We study the problem of matching interior and exterior solutions to Einstein’s equations along a particular hypersurface. We present the main aspects of the

C^{3}

matching approach that involve third-order derivatives of the corresponding metric tensors in contrast to the standard [...] Read more.

We study the problem of matching interior and exterior solutions to Einstein’s equations along a particular hypersurface. We present the main aspects of the

C^{3}

matching approach that involve third-order derivatives of the corresponding metric tensors in contrast to the standard

C^{2}

matching procedures known in general relativity, which impose conditions on the second-order derivatives only. The

C^{3}

alternative approach does not depend on coordinates and allows us to determine the matching surface by using the invariant properties of the eigenvalues of the Riemann curvature tensor. As a particular example, we apply the

C^{3}

procedure to match the exterior Schwarzschild metric with a general spherically symmetric interior spacetime with a perfect fluid source and obtain that on the matching hypersurface, the density and pressure should vanish, which is in accordance with the intuitive physical expectation. Full article

(This article belongs to the Special Issue Remo Ruffini Festschrift)

22 pages, 1447 KiB

Open AccessFeature PaperArticle

The Black Hole Universe, Part I

by Enrique Gaztanaga

Symmetry 2022, 14(9), 1849; https://doi.org/10.3390/sym14091849 - 5 Sep 2022

Cited by 15 | Viewed by 7892

Abstract

The original Friedmann (1922) and Lemaitre (1927) cosmological model corresponds to a classical solution of General Relativity (GR), with the same uniform (FLRW) metric as the standard cosmology, but bounded to a sphere of radius R and empty space outside. We study the junction conditions for R to show that a co-moving observer, like us, located anywhere inside R, measures the same background and has the same past light-cone as an observer in an infinite FLRW with the same density. We also estimate the mass M inside R and show that in the observed universe

R < r_{S} \equiv 2

GM, which corresponds to a Black Hole Universe (BHU). We argue that this original Friedmann–Lemaitre model can explain the observed cosmic acceleration without the need of Dark Energy, because

r_{S}

acts like a cosmological constant

Λ = 3 / r_{S}^{2}

. The same solution can describe the interior of a stellar or galactic BHs. In co-moving coordinates the BHU is expanding while in physical or proper coordinates it is asymptotically static. Such frame duality corresponds to a simple Lorentz transformation. The BHU therefore provides a physical BH solution with an asymptotically deSitter metric interior that merges into a Schwarzschild metric exterior without discontinuities. Full article

(This article belongs to the Special Issue Nature and Origin of Dark Matter and Dark Energy)

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12 pages, 391 KiB

Open AccessArticle

Gravastars with Kuchowicz Metric in Energy-Momentum Squared Gravity

by Saba Naz and Muhammad Sharif

Universe 2022, 8(3), 142; https://doi.org/10.3390/universe8030142 - 22 Feb 2022

Cited by 16 | Viewed by 2186

Abstract

This paper investigates the geometry of a gravitational vacuum star (also known as a gravastar) from the perspective of

f (R, T^{2})

gravity. The gravastar can be treated as a black hole substitute with three domains: (i) the inner [...] Read more.

This paper investigates the geometry of a gravitational vacuum star (also known as a gravastar) from the perspective of

f (R, T^{2})

gravity. The gravastar can be treated as a black hole substitute with three domains: (i) the inner domain, (ii) the intrinsic shell, and (iii) the outer domain. We examine these geometries using Kuchowicz ansatz for temporal metric function corresponding to a specific

f (R, T^{2})

model. We compute a nonsingular radial metric potential for both the interior and intermediate domains. The matching of these domains with exterior Schwarzschild vacuum results in boundary conditions that assist in the evaluation of unknown constants. Finally, we examine various attributes of gravastar domains, such as the equation of state parameter, proper length, energy, and surface redshift. We conclude that the gravastar model is a viable alternative to the black hole in the background of this gravity. Full article

(This article belongs to the Special Issue Alternative Gravities and Fundamental Cosmology)

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