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On Quantum Deformation of the Schwarzschild Solution
High Energy Physics - Theory · Submitted 19 Oct 1993
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We have found that the Schwarzschild singularity at $r=0$ is shifted to the finite radius $r_{min} \sim r_{Pl}$, where the scalar curvature is finite, so that the space-time looks regular and consists of two asymptotically flat sheets glued at the hypersurface of constant radius.
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The abstract, sentence by sentence
We consider the deformation of the Schwarzschild solution in general relativity due to spherically symmetric quantum fluctuations of the metric and the matter fields. In this case, the 4D theory of gravity with Einstein action reduces to the effective two-dimensional dilaton gravity. We have found that the Schwarzschild singularity at $r=0$ is shifted to the finite radius $r_{min} \sim r_{Pl}$, where the scalar curvature is finite, so that the space-time looks regular and consists of two asymptotically flat sheets glued at the hypersurface of constant radius.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider the deformation of the Schwarzschild solution in general relativity due to spherically symmetric quantum fluctuations of the metric and the matter fields. | contribution 0.85 | 0.48 | 0.05 | asserted 0.70 |
| s1 | In this case, the 4D theory of gravity with Einstein action reduces to the effective two-dimensional dilaton gravity. | method 0.82 | 0.30 | 0.05 | asserted 1.00 |
| s2 | We have found that the Schwarzschild singularity at $r=0$ is shifted to the finite radius $r_{min} \sim r_{Pl}$, where the scalar curvature is finite, so that the space-time looks regular and consists of two asymptotically flat sheets glued at the hypersurface of constant radius. | result 1.00 | 0.95 | 0.90 | asserted 1.00 |
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The paper
Original abstract
We consider the deformation of the Schwarzschild solution in general relativity due to spherically symmetric quantum fluctuations of the metric and the matter fields. In this case, the 4D theory of gravity with Einstein action reduces to the effective two-dimensional dilaton gravity. We have found that the Schwarzschild singularity at $r=0$ is shifted to the finite radius $r_{min} \sim r_{Pl}$, where the scalar curvature is finite, so that the space-time looks regular and consists of two asymptotically flat sheets glued at the hypersurface of constant radius.
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References
How the literature uses it
25 arXiv papers cite this in 68 sentences
Papers citing it · 39 sentences without a confident label
Builds on it 2 papers
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We have generalized the original Kazakov–Solodukhin spacetime to a two-parameter class compatible with the ideas mooted in reference [ref] .
General class of "quantum deformed" regular black holes · Discussion and conclusions · 0.99
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We have generalized the original Kazakov–Solodukhin spacetime to a two-parameter class compatible with the ideas mooted in reference [ref] .
Mimicking Black Holes in General Relativity · Discussion and conclusions · 0.99
Uses its method or tool 2 papers
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Following the method developed in [ref] and considering $r$ as a space-like coordinate, the Ansatz to be studied in the previous theory is that of a spherically symmetric line-element expressed as
Quasinormal modes of a quantum inspired black hole in four dimensions with cosmological constant · Background · 1.00
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To find such approximate solutions we follow Ref. [ref] and consider a general spherically symmetric metric: [equation] Here the four-dimensional spacetime is covered by the coordinates $(z^+, z^-, θ, ϕ)$.
Non-Schwarzschild Primordial Black Holes as Dark Matter in Quadratic Gravity · Static spherically symmetric solutions in quadratic gravity · 0.98
Compares with it 5 papers
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The original Kazakov–Solodukhin “quantum deformed Schwarzschild spacetime” [ref] is slightly more “regular” than Schwarzschild spacetime, but it is not “regular” in the sense normally intended in the general relativity community.
General class of "quantum deformed" regular black holes · Discussion and conclusions · 0.84
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The original Kazakov–Solodukhin “quantum deformed Schwarzschild spacetime” [ref] is slightly more “regular” than Schwarzschild spacetime, but it is not “regular” in the sense normally intended in the general relativity community.
Mimicking Black Holes in General Relativity · Discussion and conclusions · 0.83
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We also note that the form of the solution ([ref]) is similar to the one obtained in general relativity by quantising the corresponding effective 2D dilaton gravity [ref] .
Non-Schwarzschild Primordial Black Holes as Dark Matter in Quadratic Gravity · Static spherically symmetric solutions in quadratic gravity · 0.96
Cites it as support 1 paper
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Indeed, the backreaction of the energy fluctuations in the geometry has been shown to break local symmetries of the solution, such as the spherical symmetry of the Schwarzschild black hole [ref] .
Thermal fluctuations of black holes with non-linear electrodynamics and charged Renyi entropy · Summary and Discussion · 1.00
Cites it as background 12 papers
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The deformation of the Schwarzschild black hole due to spherically symmetric quantum fluctuations was discussed by Kazakov and Solodukhin [ref] .
Influence of Quantum Correction on the Black Hole Shadows, Photon Rings and Lensing Rings · Null geodesic in quantum corrected Schwarzschild black hole · 0.84
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In this regard, Kazakov and Solodukhin originally presented a modified version of the Schwarzschild black hole corrected by terms of quantum nature (see [ref] for further details).
Quasinormal modes of a quantum inspired black hole in four dimensions with cosmological constant · Background · 0.97
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The quantum deformed BH introduced here is mainly related to the theory of the two-dimensional dilaton gravity [ref] .
Effect of quantum deformed black hole on BH shadow in two-dimensional Dilaton gravity · Spherically symmetric quantum deformed BH · 0.88
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