Role of symmetries in the Kerr-Schild derivation of the Kerr black hole

Ayón–Beato, Eloy; Higuita-Borja, Daniel F.

doi:10.1103/physrevd.94.064073

Cited by 7 publications

(4 citation statements)

References 13 publications

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“…Another route, via the complex distance function r c , is perhaps more elegant, but if anything even more mysterious. See equation (25). Overall, on balance we still feel that the Newman-Janis procedure is a trick rather than an algorithm.…”

Section: Discussionmentioning

confidence: 99%

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Cartesian Kerr–Schild variation on the Newman–Janis trick

Rajan

Visser

2017

Int. J. Mod. Phys. D

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Abstract. The Newman-Janis trick is a procedure, (not even really an ansatz), for obtaining the Kerr spacetime from the Schwarzschild spacetime. This 50 year old trick continues to generate heated discussion and debate even to this day. Most of the debate focusses on whether the Newman-Janis procedure can be upgraded to the status of an algorithm, or even an inspired ansatz, or is it just a random trick of no deep physical significance. (That the Newman-Janis procedure very quickly led to the discovery of the Kerr-Newman spacetime is a point very much in its favour.) In the current article we will not answer these deeper questions, we shall instead present a much simpler alternative variation on the theme of the Newman-Janis trick that might be easier to work with. We shall present a 2-step version of the Newman-Janis trick that works directly with the Kerr-Schild "Cartesian" metric presentation of the Kerr spacetime. That is, we show how the original 4-step Newman-Janis procedure can, (using the interplay between oblate spheroidal and Cartesian coordinates), be reduced to a considerably cleaner 2-step process.

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Section: Discussionmentioning

confidence: 99%

“…That can only be checked a posteriori. (See for instance reference [25].) If, instead of the covariant vector a , we choose to work with the contravariant null vector a = η ab b , we obtain closely related results.…”

Section: Why Does the Newman-janis Trick Work?mentioning

confidence: 91%

Cartesian Kerr–Schild variation on the Newman–Janis trick

Rajan

Visser

2017

Int. J. Mod. Phys. D

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“…The Kerr-Schild (KS) ansatz has been a very fruitful arena for the construction of rotating black holes in General Relativity in arbitrary dimensions. The whole family of rotating black holes with horizons of hyperspherical topology can be casts in this form [39][40][41][42][43][44], both in the asymptotically flat case as well as in the presence of a cosmological constant. The Kerr-Schild ansatz is defined by…”

Section: Beyond Slowly Rotating Solutions: Kerr-schild Ansatzmentioning

confidence: 99%

Slowly rotating black holes in Quasi-topological gravity

Fierro,

Mora,

Oliva

2020

Preprint

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While cubic Quasi-topological gravity is unique, there is a family of quartic Quasi-topological gravities in five dimensions. These theories are defined by leading to a first order equation on spherically symmetric spacetimes, resembling the structure of the equations of Lovelock theories in higher-dimensions, and are also ghost free around AdS. Here we construct slowly rotating black holes in these theories, and show that the equations for the off-diagonal components of the metric in the cubic theory are automatically of second order, while imposing this as a restriction on the quartic theories allows to partially remove the degeneracy of these theories, leading to a threeparameter family of Lagrangians of order four in the Riemann tensor. This shows that the parallel with Lovelock theory observed on spherical symmetry, extends to the realm of slowly rotating solutions. In the quartic case, the equations for the slowly rotating black hole are obtained from a consistent, reduced action principle. These functions admit a simple integration in terms of quadratures. We also prove that beyond the slowly-rotating approximation, for generic values of the couplings, it is impossible to embed the rotating solution in a Kerr-Schild ansatz.

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“…[24] where the Kerr-Newman-(A)dS black hole was derived for bigravity following this approach, inspired by the results of Ref. [49] for General Relativity].…”

Section: Appendix B: Most General Vector Potential Supporting Ads Wavesmentioning

confidence: 99%

Exact ghost-free bigravitational waves

et al. 2018

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We study the propagation of exact gravitational waves in the ghost-free bimetric theory. Our focus is on type-N spacetimes compatible with the cosmological constants provided by the bigravity interaction potential, and particularly in the single class known by allowing at least a Killing symmetry: the AdS waves. They have the advantage of being represented by a generalized Kerr-Schild transformation from AdS spacetime. This entails a notorious simplification in bigravity by allowing to straightforwardly compute any power of its interaction square root matrix, opening the door to explore physically meaningful exact configurations. For these exact gravitational waves the complex dynamical structure of bigravity decomposes into elementary exact massless or massive excitations propagating on AdS. We use a complexified formulation of the Euler-Darboux equations to provide for the first time the general solutions to the massive version of the Siklos equation which rules the resulting AdS-wave dynamics, using an integral representation originally due to Poisson. Inspired by this progress, we tackle the subtle problem of how matter couples to bigravity and, more concretely, if this occurs through a composite metric, which is hard to handle in a general setting. Surprisingly, the Kerr-Schild ansatz brings again a huge simplification in how the related energy-momentum tensors are calculated. This allows us to explicitly characterize AdS waves supported by either a massless free scalar field or a wavefront-homogeneous Maxwell field. Considering the most general allowed Maxwell source instead is a highly nontrivial task, which we accomplish by again exploiting the complexified Euler-Darboux description and taking advantage of the classical Riemann method. In fact, this eventually allows us to find the most general configurations for any matter source.

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Role of symmetries in the Kerr-Schild derivation of the Kerr black hole

Cited by 7 publications

References 13 publications

Cartesian Kerr–Schild variation on the Newman–Janis trick

Cartesian Kerr–Schild variation on the Newman–Janis trick

Slowly rotating black holes in Quasi-topological gravity

Exact ghost-free bigravitational waves

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