Numerical Approaches to Spacetime Singularities

Berger, B. K.

doi:10.12942/lrr-1998-7

Cited by 69 publications

(129 citation statements)

References 179 publications

(382 reference statements)

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“…Every spatial point of spacetime will then become disconnected from the others, and will evolve following ordinary differential equations that present chaotic behavior. Numerical studies have shown evidence in favor of this behavior; see [25,26] for modern discussions.…”

Section: B Singularitiesmentioning

confidence: 99%

Where Does the Physics of Extreme Gravitational Collapse Reside?

2016

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Abstract:The gravitational collapse of massive stars serves to manifest the most severe deviations of general relativity with respect to Newtonian gravity: the formation of horizons and spacetime singularities. Both features have proven to be catalysts of deep physical developments, especially when combined with the principles of quantum mechanics. Nonetheless, it is seldom remarked that it is hardly possible to combine all these developments into a unified theoretical model, while maintaining reasonable prospects for the independent experimental corroboration of its different parts. In this paper we review the current theoretical understanding of the physics of gravitational collapse in order to highlight this tension, stating the position that the standard view on evaporating black holes stands for. This serves as the motivation for the discussion of a recent proposal that offers the opposite perspective, represented by a set of geometries that regularize the classical singular behavior and present modifications of the near-horizon Schwarzschild geometry as the result of the propagation of non-perturbative ultraviolet effects originated in regions of high curvature. We present an extensive exploration of the necessary steps on the explicit construction of these geometries, and discuss how this proposal could change our present understanding of astrophysical black holes and even offer the possibility of detecting genuine ultraviolet effects in gravitational-wave experiments.

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Section: B Singularitiesmentioning

confidence: 99%

Where Does the Physics of Extreme Gravitational Collapse Reside?

2016

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“…Concerning the dynamics of Bianchi space-times with non-vanishing spatial curvature in the effective theory coming from self-dual LQC, it is likely that numerical simulations like the ones recently performed in standard LQC for the Bianchi II and Bianchi IX space-times [72,73] will be necessary in order to understand the selfdual LQC dynamics of these space-times in all regimes. Nonetheless, it is known from general relativity that as a big-bang or big-crunch singularity is approached in the Bianchi models with a massless scalar field (the case considered here) in a fashion where theȧ j all have the same sign (i.e., in general relativity this would lead to what is called an isotropic or 'point-like' singularity in the terminology of [74]), the space-times become asymptotically velocity-term dominated (AVTD) in which case the spatial curvature is negligible [37]. When the spatial curvature becomes negligible, then the Hamiltonian constraint is essentially that of the Bianchi I space-time, and all of the results obtained for Bianchi I, described in the paragraph above, hold for AVTD Bianchi space-times also.…”

Section: The Effective Theorymentioning

confidence: 99%

Anisotropic loop quantum cosmology with self-dual variables

Wilson-Ewing

2016

Phys. Rev. D

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A loop quantization of the diagonal class A Bianchi models starting from the complex-valued self-dual connection variables is presented in this paper. The basic operators in the quantum theory correspond to areas and generalized holonomies of the Ashtekar connection, and the reality conditions are implemented via the choice of the inner product on the kinematical Hilbert space. The action of the Hamiltonian constraint operator is given explicitly for the case when the matter content is a massless scalar field (in which case the scalar field can be used as a relational clock), and it is shown that the big bang and big crunch singularities are resolved in the sense that singular and nonsingular states decouple under the action of the Hamiltonian constraint operator.

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“…Among the various open questions posed by BH investigations, understanding whether spacetime singularities [13][14][15][16] are real or an artifact of our mathematical theories is one of the most challenging problems, from both technical and philosophical perspectives. Though the BH event horizon is taken by some authors as a possibility to minimize this issue, adopting an out of sight, out of mind attitude, a lot of effort has been devoted to the construction of nonsingular alternatives for BH interiors.…”

Section: Introductionmentioning

confidence: 99%

Absorption by black hole remnants in metric-affine gravity

et al. 2019

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Using numerical methods, we investigate the absorption properties of a family of nonsingular solutions which arise in different metric-affine theories, such as quadratic and Born-Infeld gravity. These solutions continuously interpolate between Schwarzschild black holes and naked solitons with wormhole topology. The resulting spectrum is characterized by a series of quasibound states excitations, associated with the existence of a stable photonsphere.

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Numerical Approaches to Spacetime Singularities

Cited by 69 publications

References 179 publications

Where Does the Physics of Extreme Gravitational Collapse Reside?

Where Does the Physics of Extreme Gravitational Collapse Reside?

Anisotropic loop quantum cosmology with self-dual variables

Absorption by black hole remnants in metric-affine gravity

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