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Certain exact solutions of the Einstein field equations over nonsimply-connected manifolds are reviewed. These solutions are spherically symmetric and have no curvature singularity. They provide a regularization of the standard…

General Relativity and Quantum Cosmology · Physics 2015-06-17 F. R. Klinkhamer

We demonstrate that the Schwarzschild black hole can be ``resolved'' into bound states of Reissner-Nordstr\"om black holes in four dimensions. These bound states closely resemble the Schwarzschild geometry from the asymptotic region up to…

High Energy Physics - Theory · Physics 2024-08-01 Raphaël Dulac , Pierre Heidmann

We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…

General Relativity and Quantum Cosmology · Physics 2021-04-16 Jorge L. deLyra , Rodrigo de A. Orselli , C. E. I. Carneiro

We introduce a two-parameter static, nonspherically-symmetric black hole solution in the Einstein theory of gravity coupled with a massless scalar field. The scalar field depends only on the polar coordinate $\theta$ in the spherical…

General Relativity and Quantum Cosmology · Physics 2025-02-21 S. Habib Mazharimousavi

We address the question of the uniqueness of the Schwarzschild black hole by considering the following question: How many meaningful solutions of the Einstein equations exist that agree with the Schwarzschild solution (with a fixed mass m)…

High Energy Physics - Theory · Physics 2016-11-15 Matthias Blau , Martin O'Loughlin

The Schwarzschild and Reissner-Nordstrom solutions to Einstein's equations describe space- times which contain spherically symmetric black holes. We consider solutions to the linear wave equation in the exterior of a fixed black hole space-…

Analysis of PDEs · Mathematics 2015-06-26 P. Blue , A. Soffer

We present a generalization of the black hole solution with spherical symmetry already known in the literature for $N$-dimensional $F(R)$ gravity with a conformally invariant Maxwell field and constant scalar curvature $R$. This solution…

General Relativity and Quantum Cosmology · Physics 2022-04-21 Ernesto F. Eiroa , Griselda Figueroa-Aguirre

By utilizing non-standard slicings of 5-dimensional Schwarzschild and Schwarzschild-AdS manifolds based on isotropic coordinates, we generate static and spherically symmetric braneworld spacetimes containing shell-like naked null…

General Relativity and Quantum Cosmology · Physics 2009-11-11 Sanjeev S. Seahra

There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…

General Relativity and Quantum Cosmology · Physics 2024-08-27 O. S. Stashko , V. I. Zhdanov

An exact solution of the vacuum Einstein field equations over a nonsimply-connected manifold is presented. This solution is spherically symmetric and has no curvature singularity. It can be considered to be a regularization of the…

General Relativity and Quantum Cosmology · Physics 2013-09-06 F. R. Klinkhamer

We find static spherically symmetric solutions of scale invariant $R^2$ gravity. The latter has been shown to be equivalent to General Relativity with a positive cosmological constant and a scalar mode. Therefore, one expects that solutions…

High Energy Physics - Theory · Physics 2015-02-23 Alex Kehagias , Costas Kounnas , Dieter Lust , Antonio Riotto

With the back reaction of the vacuum energy-momentum tensor consistently taken into account, we study static spherically symmetric black-hole-like solutions to the semi-classical Einstein equation. The vacuum energy is assumed to be given…

High Energy Physics - Theory · Physics 2018-04-18 Pei-Ming Ho , Yoshinori Matsuo

Regular and spherically symmetric black holes that solve the singularity problems of the Schwarzschild solution are phenomenologically viable at large distance but usually suffer from the Cauchy horizon instability. To overcome this…

General Relativity and Quantum Cosmology · Physics 2025-07-10 Marco Calzá , Massimiliano Rinaldi , Sergio Zerbini

We study static, spherically symmetric solutions with an electric field in an extension of general relativity (GR) containing a Ricci-squared term and formulated in the Palatini formalism. We find that all the solutions present a central…

General Relativity and Quantum Cosmology · Physics 2015-06-05 Gonzalo J. Olmo , D. Rubiera-Garcia

This paper explores ``black hole'' solutions of various Einstein-wave matter systems admitting an isometry of their domain of outer communications taking every point to its future. In the first two parts, it is shown that such solutions,…

General Relativity and Quantum Cosmology · Physics 2010-11-19 Mihalis Dafermos

The static black hole solutions to the Einstein-Maxwell equations are all spherically symmetric, as are many of the recently discovered black hole solutions in theories of gravity coupled to other forms of matter. However, counterexamples…

General Relativity and Quantum Cosmology · Physics 2010-11-19 S. Alexander Ridgway , Erick J. Weinberg

We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semi-classical theory. The singularity is eliminated but…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Rodolfo Gambini , Jorge Pullin

The Reissner-Nordstr\"om black hole solution in a generic cosmological constant background in the the context of Rastall gravity is obtained. It is shown that the cosmological constant arises naturally from the consistency of the non-vacuum…

General Relativity and Quantum Cosmology · Physics 2017-12-05 Y. Heydarzade , H. Moradpour , F. Darabi

We show via an explicit construction how an infinite tower of higher-curvature corrections generically leads to a resolution of the Schwarzschild singularity in any spacetime dimension $D \ge 5$. The theories we consider have two key…

General Relativity and Quantum Cosmology · Physics 2024-03-20 Pablo Bueno , Pablo A. Cano , Robie A. Hennigar

The definition of well-behaved coordinate charts for black hole spacetimes can be tricky, as they can lead for example to either unphysical coordinate singularities in the metric (e.g. $r=2M$ in the Schwarzschild black hole) or to an…

General Relativity and Quantum Cosmology · Physics 2021-10-20 Emanuel Gallo , Carlos Kozameh , Thomas Mädler , Osvaldo M. Moreschi , Alejandro Pérez
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