Geometrodynamics: the nonlinear dynamics of curved spacetime

Scheel, Mark A.; Thorne, Kip S.

doi:10.3367/ufnr.0184.201404b.0367

Cited by 16 publications

(5 citation statements)

References 42 publications

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“…The BKL conjecture is one of the guiding principles in the studies of spacetime singularities. According to the BKL conjecture, the behaviors of the spacetime and the matter field are described by the Kasner solution [43][44][45][46][47][48][49][50][51]. The four-dimensional homogeneous but anisotropic Kasner solution with a massless scalar field ψ minimally coupled to gravity can be written as follows [45,49,50]:…”

Section: A Bh Formation By Spherical Scalar Collapsementioning

confidence: 99%

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Dynamics of critical collapse

Guo

Zhang

2019

Eur. Phys. J. C

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Critical collapse of a massless scalar field in spherical symmetry is systematically studied. We combine numerical simulations and asymptotic analysis, and synthesize critical collapse, spacetime singularities, and complex science. First set of approximate analytic expressions near the center are obtained. We observe that, near the center, the spacetime is nearly conformally flat, the dynamics is not described by the Kasner solution, and the Kreschmann scalar is proportional to r −5.30 , where r is the areal radius. These features are significantly different from those in black hole singularities. It is speculated that the scalar field in critical collapse may be a special standing wave. arXiv:1808.09826v3 [gr-qc]

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Section: A Bh Formation By Spherical Scalar Collapsementioning

confidence: 99%

“…For reviews on the BKL conjecture, see Refs. [49][50][51]. In BH formation by spherical scalar collapse, the dynamics near the central singularity is described by the Kasner solution [34].…”

Section: A Bh Formation By Spherical Scalar Collapsementioning

confidence: 99%

Dynamics of critical collapse

Guo

Zhang

2019

Eur. Phys. J. C

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“…The similarity to (169) is impressive. The GEM analogy quite apparently applies to the full nonlinear theory.…”

Section: Quadratic Invariantsmentioning

confidence: 95%

“…[80,138]. 20 Alternatively, we could generalize the Newtonian tidal force matrix of (9) to the gravitoelectric and gravitomagnetic tidal force matrices, E ij = R i0j0 and B ij = ikl R klj0 , respectively, see Scheel & Thorne [169]. Both matrices are symmetric and trace-free.…”

Section: Gravitoelectromagnetic Field Strengthmentioning

confidence: 99%

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

Heinicke

Hehl

2015

Int. J. Mod. Phys. D

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Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(-Droste) solution, and into one specific stationary axially symmetric solution, the Kerr solution. The Schwarzschild solution is unique and its metric can be interpreted as the exterior gravitational field of a spherically symmetric mass. The Kerr solution is only unique if the multipole moments of its mass and its angular momentum take on prescribed values. Its metric can be interpreted as the exterior gravitational field of a suitably rotating mass distribution. Both solutions describe objects exhibiting an event horizon, a frontier of no return. The corresponding notion of a black hole is explained to some extent. Eventually, we present some generalizations of the Kerr solution.

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“…[18]. In critical collapse, the scalar field carries away its energy and an infinitesimal naked singularity is left behind [19], which is a counterexample to the original censorship conjecture. Due to this discovery, the cosmic censorship was restated such that it only applies to collapse with generic initial data.…”

Section: Introductionmentioning

confidence: 97%

Strength of the naked singularity in critical collapse

et al. 2020

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The critical collapse of a scalar field is a threshold solution of black hole formation, in which a naked singularity arises. We study here the curvature strength of this singularity using a numerical ansatz. The behavior of the Jacobi volume forms is examined along a non-spacelike geodesic in the limit of approach to the singularity. These are seen to be vanishing, thus showing that all physical objects will be crushed to zero size near the singularity. Consequently, although the critical collapse is considered to be a fine-tuning problem, the naked singularity forming is gravitationally strong. This implies that the spacetime cannot be extended beyond the singularity, thus making the singularity genuine and physically interesting. These results imply that the nature of critical collapse may need to be examined and explored further.

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Geometrodynamics: the nonlinear dynamics of curved spacetime

Cited by 16 publications

References 42 publications

Dynamics of critical collapse

Dynamics of critical collapse

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

Strength of the naked singularity in critical collapse

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