Loop quantum dynamics of the Schwarzschild interior

Böhmer, Christian G.; Vandersloot, Kevin

doi:10.1103/physrevd.76.104030

Cited by 196 publications

(325 citation statements)

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“…For an exactly solvable model in LQC 4 , the properties of the spacetime across the bounce are almost identical 5 . Extension of these results on singularity resolution has been investigated for the black hole spacetimes [6][7][8][9][10] . It has been generally expected that as in the case of isotropic model in LQC, the spacetime after the bounce in the black hole interior shares very similar properties as the one before the bounce.…”

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confidence: 99%

Emergence of product of constant curvature spaces in loop quantum cosmology

Dadhich

Joe

Singh

2017

The Fourteenth Marcel Grossmann Meeting

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The loop quantum dynamics of Kantowski-Sachs and Bianchi-III LRS spacetimes with cosmological constant is studied in the effective spacetime description. We show that classical singularity is avoided, and replaced by bounces of the triads. Unlike the singularity resolution in other loop quantum spacetimes, evolution results in a spacetime which retains quantum curvature after the bounce on one side of the temporal evolution. In the asymptotic limit, a spacetime which is a direct product of two constant curvature spaces emerges. Interestingly, despite high curvature, the effective spacetime metric is a solution of Einstein field's equations albeit with a different stress energy tensor. For the Kantowski-Sachs case, the resulting spacetime is a 'charged' Nariai spacetime, and for the Bianchi-III LRS spacetime, one obtains anti-Bertotti-Robinson spacetime with an emergent cosmological constant. The emergent 'charge' and cosmological constant are purely quantum geometric in origin.Keywords: Loop quantum cosmology; black hole interiors.Using techniques of loop quantum gravity, quantization of various homogenous spacetimes has been performed recently in loop quantum cosmology (LQC) 2 . One of the main results is the resolution of big bang singularity and occurrence of bounce at the Planck scale 3 . For the cosmological models, such as the isotropic homogeneous spacetime or Bianchi models, at small curvatures, far from the bounce, dynamics can be approximated extremely well by the classical Hamiltonian evolution of the respective spacetimes. Quantum gravitational effects are important only in a small regime near the bounce. For an exactly solvable model in LQC 4 , the properties of the spacetime across the bounce are almost identical 5 . Extension of these results on singularity resolution has been investigated for the black hole spacetimes 6-10 . It has been generally expected that as in the case of isotropic model in LQC, the spacetime after the bounce in the black hole interior shares very similar properties as the one before the bounce. Recent studies 1,10 , show that this expectation does not hold. For the Kantowski-Sachs spacetime which captures the interior of Schwarzschild black hole and the Bianchi-III LRS spacetime which is isomorphic to higher genus black hole interior, the central singularity is resolved, but the spacetime on one side of the temporal evolution is drastically different from the initial classical spacetime. It turns out that quantum geometric effects do not die, and remain significant even asymptotically, leading to an emergent spacetime metric * Anton Joe passed away before results in this manuscript and its earlier expanded version 1 were communicated. ND and PS dedicate this article to Anton Joe.

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confidence: 99%

Emergence of product of constant curvature spaces in loop quantum cosmology

Dadhich

Joe

Singh

2017

The Fourteenth Marcel Grossmann Meeting

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“…Regarding the fact that the Planck densities and curvatures are the gates of the quantum gravity realm [38,39], These values of the density and curvature in the stable static phase imply that on the cusp of quantum gravity the pure semi-classical effects would become extremely important. As a matter of fact, in this paper we have shown that the resolution of singularity, which is a task relegated to appropriate quantum gravity theories [40][41][42], can also be attained by semi-classical methods like considering quantum vacuum effects on a curved background. In the following, we put a few remarks concerning some aspects and extensions of our considerations in order.…”

Section: Final Remarksmentioning

confidence: 99%

Quantum vacuum effects on the final fate of a collapsing ball of dust

Arfaei

Noorikuhani

2017

J. High Energ. Phys.

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Abstract:We consider the quantum vacuum effects of the massless scalar fields that are non-minimally coupled to the background geometry of a collapsing homogeneous ball of dust. It is shown that for a definite range of coupling constants, there are repulsive quantum vacuum effects, capable of stopping the collapse process inside the black hole and precluding the formation of singularity. The final fate of the collapse will be a black hole with no singularity, inside which the matter stays balanced. The density of the final static matter will be close to the Planck density. We show that the largest possible radius of the stable static ball inside a black hole with Schwarzschild mass M is given by 1 90π M mp 1 3 p . If the black hole undergoes Hawking radiation, the final state will be an extremal quantumcorrected black hole, with zero temperature, with a remnant of matter inside. We show that the resolution of singularity is not disrupted under Hawking radiation.

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“…Efforts in order to find out black holes solutions in the context of LQG have been made by several authors [43][44][45][46][47][48][49][50][51][52][53][54][55][56]. In this work, we shall investigate the thermodynamics of a particular solution called the self-dual solution which was obtained by the use of loop quantum cosmology quantization techniques to the Schwarzschild scenario [39].…”

Section: Loop Quantum Black Holesmentioning

confidence: 99%