Schwarzschild and Kerr solutions of Einstein's field equation: An Introduction

Heinicke, Christian; Hehl, Friedrich W.

doi:10.1142/s0218271815300062

Cited by 37 publications

(11 citation statements)

References 179 publications

(292 reference statements)

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“…As is well known [9], the radial coordinate here can be both positive or negative, r ∈ (−∞, ∞), and there are two asymptotic regions corresponding to r → ±∞ (see [10][11][12] for recent reviews of the Kerr metric). The black hole mass has opposite signs when viewed from these two regions.…”

Section: Zero Mass Limit Of Kerr Spacetimementioning

confidence: 99%

Zero mass limit of Kerr spacetime is a wormhole

Gibbons

Volkov

2017

Phys. Rev. D

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We show that, contrary to what is usually claimed in the literature, the zero mass limit of Kerr spacetime is not flat Minkowski space but a spacetime whose geometry is only locally flat. This limiting spacetime, as the Kerr spacetime itself, contains two asymptotic regions and hence cannot be topologically trivial. It also contains a curvature singularity, because the power-law singularity of the Weyl tensor vanishes in the limit but there remains a distributional contribution of the Ricci tensor. This spacetime can be interpreted as a wormhole sourced by a negative tension ring. We also extend the discussion to similarly interpret the zero mass limit of the Kerr-(anti)-de Sitter

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Section: Zero Mass Limit Of Kerr Spacetimementioning

confidence: 99%

Zero mass limit of Kerr spacetime is a wormhole

Gibbons

Volkov

2017

Phys. Rev. D

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“…Worm-holes can be described as the Lorentzian continuation of the Euclidean cigar. The Schwarzschild metric, shown in Figure 1 , is the most famous wormhole model ( 25 ). It is a two-sided eternal black hole.…”

Section: Methodsmentioning

confidence: 99%

A Brain Tumor Image Segmentation Method Based on Quantum Entanglement and Wormhole Behaved Particle Swarm Optimization

Zhang

Xue

et al. 2022

Front. Med.

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PurposeAlthough classical techniques for image segmentation may work well for some images, they may perform poorly or not work at all for others. It often depends on the properties of the particular image segmentation task under study. The reliable segmentation of brain tumors in medical images represents a particularly challenging and essential task. For example, some brain tumors may exhibit complex so-called “bottle-neck” shapes which are essentially circles with long indistinct tapering tails, known as a “dual tail.” Such challenging conditions may not be readily segmented, particularly in the extended tail region or around the so-called “bottle-neck” area. In those cases, existing image segmentation techniques often fail to work well.MethodsExisting research on image segmentation using wormhole and entangle theory is first analyzed. Next, a random positioning search method that uses a quantum-behaved particle swarm optimization (QPSO) approach is improved by using a hyperbolic wormhole path measure for seeding and linking particles. Finally, our novel quantum and wormhole-behaved particle swarm optimization (QWPSO) is proposed.ResultsExperimental results show that our QWPSO algorithm can better cluster complex “dual tail” regions into groupings with greater adaptability than conventional QPSO. Experimental work also improves operational efficiency and segmentation accuracy compared with current competing reference methods.ConclusionOur QWPSO method appears extremely promising for isolating smeared/indistinct regions of complex shape typical of medical image segmentation tasks. The technique is especially advantageous for segmentation in the so-called “bottle-neck” and “dual tail”-shaped regions appearing in brain tumor images.

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“…In this section, we outline the most widely used black hole solutions and discuss their basic geometric properties [5][6][7].…”

Section: Black Hole Solutionsmentioning

confidence: 99%

Aspects of Semiclassical Black Holes: Development and Open Problems

Yosifov

2021

Advances in High Energy Physics

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The current work is a review, dedicated to the study of semiclassical aspects of black holes. We begin by briefly looking at the main statements of general relativity. We then consider the Schwarzschild, Kerr, and Reissner-Nordstrom black hole solutions and discuss their geometrical properties. Later, the thermodynamic nature of black holes is established. In light of this, we formulate the information loss problem and present the most promising approaches for addressing it with emphasis on introducing low-energy quantum corrections to the classical general relativity picture. Finally, in the context of multimessenger astronomy, we look at naked singularities as possible gravitational collapse endstates and their role in the unitarity of quantum mechanics and discuss their observational prospects.

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Schwarzschild and Kerr solutions of Einstein's field equation: An Introduction

Cited by 37 publications

References 179 publications

Zero mass limit of Kerr spacetime is a wormhole

Zero mass limit of Kerr spacetime is a wormhole

A Brain Tumor Image Segmentation Method Based on Quantum Entanglement and Wormhole Behaved Particle Swarm Optimization

Aspects of Semiclassical Black Holes: Development and Open Problems

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