Classification of minimum global embeddings for nonrotating black holes

Sheykin, A. A.; Paston, S. A.

doi:10.1007/s11232-015-0364-1

Cited by 10 publications

(15 citation statements)

References 36 publications

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“…In Section 3 we construct new explicit global embedding of static BTZ black hole in 6D spacetime. In section 4 we finish the proof of the absence of global 6-dimensional embeddings for AdS black holes which was started in [16]. Then we construct global 7dimensional embedding for Schwarzschild-AdS black hole, as well as its generalization: the global embedding of d-dimensional Schwarzschild-AdS black hole in (d + 3)D flat spacetime.…”

Section: Introductionmentioning

confidence: 91%

“…The construction and classification of embeddings for RN [15], Schwarzschild-de Sitter [31] and RN-dS [16] black holes was already done in our previous papers. The only remaining metric which has to be globally embedded in an ambient space with minimal possible number of dimensions is an embedding of the black hole (with or without an electric charge) with negative cosmological constant, i.e.…”

Section: The Embedding Of Static Black Holesmentioning

confidence: 99%

“…Unfortunately, it turned out that it is impossible to embed these metrics in 6-dimensional flat ambient space. For S-AdS we had proven it earlier [16]. RN-AdS case is more complicated one, so it took us a little time to realize that global embedding of RN-AdS black hole in 6-dimensional Minkowski space also does not exist.…”

Section: The Embedding Of Static Black Holesmentioning

confidence: 99%

“…Let us turn to the consideration of the 3+1-dimensional black holes. As we mentioned earlier, the non-existence of 6-dimensional Schwarzschild-AdS black hole embedding was proven in [16], so we only need to analyse the remaining case of RN-AdS black hole which has the following metric:…”

Section: The Absence Of 6-dimensional Embeddingsmentioning

confidence: 99%

“…The non-globality of spiral embedding can be proved in similar way. In this case the system (1) gives us the conditions (see [16]):…”

Section: The Absence Of 6-dimensional Embeddingsmentioning

confidence: 99%

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Global Embeddings of BTZ and Schwarzschild-ADS Type Black Holes in a Flat Space

2019

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We study the problem of construction of global isometric embedding for spherically symmetric black holes with negative cosmological constant in various dimensions. Firstly, we show that there is no such embedding for 4D RN-AdS black hole in 6D flat ambient space, completing the classification which we started earlier. Then we construct an explicit embedding of non-spinning BTZ black hole in 6D flat ambient space. Using this embedding as an anzats, we then construct a global explicit embedding of (d)-dimensional Schwarzschild-AdS black hole in a flat (d + 3)-dimensional ambient space. *

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Section: Introductionmentioning

confidence: 91%

Section: The Embedding Of Static Black Holesmentioning

confidence: 99%

Section: The Embedding Of Static Black Holesmentioning

confidence: 99%

Section: The Absence Of 6-dimensional Embeddingsmentioning

confidence: 99%

“…The non-globality of spiral embedding can be proved in similar way. In this case the system (1) gives us the conditions (see [16]):…”

Section: The Absence Of 6-dimensional Embeddingsmentioning

confidence: 99%

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Global Embeddings of BTZ and Schwarzschild-ADS Type Black Holes in a Flat Space

2019

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Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction

Sheykin

Markov

Paston

2021

Journal of Mathematical Physics

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It is often easier to study pseudo-Riemannian manifolds by presenting them as surfaces in some ambient space. We propose an algorithm for construction of explicit isometric embeddings of pseudo-Riemannian manifolds with symmetries into an ambient space of higher dimension. While most of the existing methods are based on Gauss–Codazzi–Mainardi–Peterson equations, we do not use them and instead concentrate on a system of equations that connects the metric on the manifold and the embedding function of the surface. Our algorithm is based on the group theoretical method of separation of variables that we developed earlier. The algorithm makes this method more convenient and simple to use. It allowed us to simplify the construction of many known embeddings as well as obtain some new ones. In particular, we obtain explicit global (i.e., smooth at all values of radius) embeddings of spinning the BTZ black hole in seven-dimensional flat space.

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Explicit isometric embeddings of collapsing dust ball

Kapustin

Ioffe

Paston

2020

Class. Quantum Grav.

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The work is devoted to the search for explicit isometric embeddings of a metric corresponding to the collapse of spherically symmetric matter with the formation of a black hole. Two approaches are considered: in the first, the embedding is constructed for the whole manifold at once; in the second, the idea of a junction of solutions, obtained separately for areas inside and outside the dust ball, is used. In the framework of the first approach, a global smooth embedding in 7D space with a signature (2 + 5) was constructed. It corresponds to the formation of the horizon as a result of matter falling from infinity. The second approach generally leads to an embedding in 7D space with the signature (1 + 6). This embedding corresponds to the case when matter flies out of a white hole with the disappearance of its horizon, after which the radius of the dust ball reaches its maximum, and then a collapse occurs with the formation of the horizon of a black hole. The embedding obtained is not smooth everywhere—it contains a kink on the edge of the dust ball, and also, it is not quite global. In the particular case, when the maximum radius of the dust ball coincides with the radius of the horizon, it is possible to construct a global smooth embedding in a flat 6D space with a signature (1 + 5).

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Classification of minimum global embeddings for nonrotating black holes

Cited by 10 publications

References 36 publications

Global Embeddings of BTZ and Schwarzschild-ADS Type Black Holes in a Flat Space

Global Embeddings of BTZ and Schwarzschild-ADS Type Black Holes in a Flat Space

Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction

Explicit isometric embeddings of collapsing dust ball

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