Embeddings of the Black Holes in a flat space

Sheykin, A. A.; Grad, D. A.; Paston, S. A.

doi:10.22323/1.183.0091

Cited by 9 publications

(15 citation statements)

References 33 publications

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“…Hence, for all three new six-dimensional embeddings of the Schwarzschild metric, there is no Hawking into Unruh mapping. An analogous case also occurs for three new embeddings of the Reissner-Nordstrom metric found in [47] and for two new embeddings of the Schwarzschild-de Sitter metrics found in [51] because their structures are completely analogous to embeddings (13)- (15).…”

Section: Examples Of the Absence Of The Mappingmentioning

confidence: 61%

“…In particular, relatively recently constructed embeddings of the Schwarzschild metric [49,50] (including its dS generalization [51]) and the Reissner-Nordstrom metric [47] are such counterexamples. These new embeddings are of three types, and all of them are not hyperbolic, i. e., their time lines are not hyperbolas.…”

Section: Examples Of the Absence Of The Mappingmentioning

confidence: 99%

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Relation between quantum effects in general relativity and embedding theory

Paston

2015

Theor Math Phys

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We present results relevant to the relation between quantum effects in a Riemannian space and on the surface appearing as a result of its isometric embedding in a flat space of a higher dimension. We discuss the mapping between the Hawking effect fixed by an observer in the Riemannian space with a horizon and the Unruh effect related to an accelerated motion of this observer in the ambient space. We present examples for which this mapping holds and examples for which there is no mapping. We describe the general form of the hyperbolic embedding of the metric with a horizon smoothly covering the horizon and prove that there is a Hawking into Unruh mapping for this embedding. We also discuss the possibility of relating two-point functions in a Riemannian space and the ambient space in which it is embedded. We obtain restrictions on the geometric parameters of the embedding for which such a relation is known. *

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Section: Examples Of the Absence Of The Mappingmentioning

confidence: 61%

Section: Examples Of the Absence Of The Mappingmentioning

confidence: 99%

Relation between quantum effects in general relativity and embedding theory

Paston

2015

Theor Math Phys

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“…The S-AdS and RN-dS black holes have no such property; therefore, a global embedding cannot be constructed for them. The minimal global embeddings for the S, S-dS, and RN black holes were respectively constructed in [23], [28] and [26]. It only remains for us to analyze the possibility of constructing such an embedding in the RN-AdS case, which we now do.…”

Section: Spiral Embeddingsmentioning

confidence: 99%

“…For example, seven-dimensional (consequently, not minimal) global embeddings for S-AdS and RN-AdS black holes were proposed in [27]. Minimal global embeddings for the S-dS black hole were found in [28]. Embeddings for axisymmetric black holes, i. e., rotating Kerr and Kerr-Newman black holes, are hardly studied.…”

Section: Introductionmentioning

confidence: 99%

Classification of minimum global embeddings for nonrotating black holes

Sheykin

Paston

2015

Theor Math Phys

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We consider the problem of the existence of global embeddings of metrics of spherically symmetric black holes into an ambient space with the minimal possible dimension. We classify the possible types of embeddings by the type of realization of the metric symmetry by ambient space symmetries. For the Schwarzschild, Schwarzschild-de Sitter, and Reissner-Nordström black holes, we prove that the known global embeddings are the only ones. We obtain a new global embedding for the Reissner-Nordström-de Sitter metrics and prove that constructing such embeddings is impossible for the Schwarzschild-anti-de Sitter metric. We also discuss the possibility of constructing global embeddings of the Reissner-Nordström-anti-de Sitter

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“…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%

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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Embeddings of the Black Holes in a flat space

Cited by 9 publications

References 33 publications

Relation between quantum effects in general relativity and embedding theory

Relation between quantum effects in general relativity and embedding theory

Classification of minimum global embeddings for nonrotating black holes

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

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