Solutions of the Einstein and Einstein-Maxwell Equations

Debney, George; Kerr, R. P.; Schild, Alfred

doi:10.1063/1.1664769

Cited by 379 publications

(553 citation statements)

References 4 publications

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“…This was a much better treatment anyway, one that could be extended to Einstein-Maxwell fields. The original derivation was published much later in Debney et al [4].…”

Section: By Roy Patrick Kerrmentioning

confidence: 96%

“…The analysis for this is given in Debney et al [4]. The first stumbling block was that I could not prove that the special null vector was geodesic (and still cannot).…”

Section: By Roy Patrick Kerrmentioning

confidence: 99%

“…4 The Carter paper, and that of Boyer and Lindquist [6], are also good sources of information about geometrical properties of the Kerr metric.…”

mentioning

confidence: 99%

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Editorial note to: R. P. Kerr and A. Schild, A new class of vacuum solutions of the Einstein field equations

2009

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The Kerr solution is today textbook material and a basic element of education in relativity. However, derivations of it are not easy to find in the literature-most textbooks and monographs simply quote it as a given thing. There exist several uniqueness theorems (see part 2 of this note) that refer to physical and geometrical properties of the Kerr solution, but none of them gives a hint on how to derive it starting from the EinsteinThe republication of the original paper can be found in this issue following the editorial note and online via

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“…This was a much better treatment anyway, one that could be extended to Einstein-Maxwell fields. The original derivation was published much later in Debney et al [4].…”

Section: By Roy Patrick Kerrmentioning

confidence: 96%

“…The analysis for this is given in Debney et al [4]. The first stumbling block was that I could not prove that the special null vector was geodesic (and still cannot).…”

Section: By Roy Patrick Kerrmentioning

confidence: 99%

See 1 more Smart Citation

Editorial note to: R. P. Kerr and A. Schild, A new class of vacuum solutions of the Einstein field equations

2009

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“…Two solutions Y ± (x) are determined by the Kerr Theorem [2,3,4,5,6]. Projection of the Kerr PNC on auxiliary background M 4 is depicted on Fig.1 .…”

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confidence: 99%

“…The typical exact electromagnetic solutions on the Kerr background take the form of singular beams propagating along the rays of PNC, contrary to smooth angular dependence of the wave solutions used in perturbative approach! Position of the horizon is determined by function H which has for the exact KS solutions the form, [2],…”

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confidence: 99%

Instability of black hole horizon with respect to electromagnetic excitations

Burinskii

2009

Gen Relativ Gravit

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Analyzing exact solutions of the Einstein-Maxwell equations in the Kerr-Schild formalism we show that black hole horizon is instable with respect to electromagnetic excitations. Contrary to perturbative smooth harmonic solutions, the exact solutions for electromagnetic excitations on the Kerr background are accompanied by singular beams which have very strong back reaction to metric and break the horizon, forming the holes which allow radiation to escape interior of blackhole. As a result, even the weak vacuum fluctuations break the horizon topologically, covering it by a set of fluctuating microholes. We conclude with a series of nontrivial consequences, one of which is that there is no information loss inside of black-hole.

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Spin‐Spacetime Censorship

2021

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Quantum entanglement and relativistic causality are key concepts in theoretical works seeking to unify quantum mechanics and gravity. In this article, a gedanken experiment that couples the spin to spacetime is proposed, and is then analyzed in the context of quantum information by using different approaches to quantum gravity. Both classical gravity theory and certain quantum theories predict that around a spin-half particle, the spherical symmetry of spacetime is broken by its magnetic field or merely by its intrinsic angular momentum. It is asserted that any spin-related deviation from spherical symmetry, upon appropriate measurement, can violate relativistic causality and quantum no-cloning. To avoid these violations, the measurable spacetime around the particle's rest frame shall typically remain spherically symmetric, potentially as a back-action by the act of a covariant measurement, or due to a quantized spin-dependence of the magnetic field. This way, this gedanken experiment suggests a censorship mechanism preventing the possibility of spacetime-based spin detection, which can shed light on the interface between quantum mechanics and gravity. Since this proposed gedanken experiment is independent of any specific theory, it is suitable for testing the coupling of quantum matter and spacetime in present and future candidate theories of quantum gravity.

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Solutions of the Einstein and Einstein-Maxwell Equations

Cited by 379 publications

References 4 publications

Editorial note to: R. P. Kerr and A. Schild, A new class of vacuum solutions of the Einstein field equations

Editorial note to: R. P. Kerr and A. Schild, A new class of vacuum solutions of the Einstein field equations

Instability of black hole horizon with respect to electromagnetic excitations

Spin‐Spacetime Censorship

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