On the imbedding of the Schwarzschild space-time I.

Fujitani, Tamehiro; Ikeda, Mineo; Matsumoto, Makoto

doi:10.1215/kjm/1250525103

Cited by 19 publications

(28 citation statements)

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“…When investigating possible embedding functions, it was noticed that line elements in both Kasner embedding signature (++----) and Fronsdal embedding signature (+-----) there are compound dz elements, not just simple dx [69]. This is analogous to presence of nonradial components [27], indicating that abstract higher-dimensional quasi-geometric spatial structures can comprise several overlapped/superimposed 3D single spaces.…”

Section: Embeddings Of Higher-dimensional Spatial Structuresmentioning

confidence: 99%

Operational Restrictions on Morphing of Quasi-Geometric 4D Physical Spaces

Czajko

2014

ILCPA

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Since a hierarchical notion of dimension is needed to ensure that a virtual, indirect orthogonality of dimensions is maintained in higher-dimensional spatial structures, a generic function for furling and unfurling of the fourth dimension in four-dimensional (4D) spatial structures is proposed. The furling allows three extra dimensions (above the regular three) in a 6D algebraic structure to be represented as a single fourth dimension and thus effectively facilitates morphing of the 4D spacetime into its dual 4D timespace. The effect of the furling of the extra three dimensions resembles that of compactification proposed by Kaluza-Klein theory yet without curling of the furled dimension. The furling supports reexpansion of stringy space into yet another dimension and so enables mapping of radius R (of a closed string being squeezed beyond its minimal radius) into an inverse radius 1/R, which was attributed to string duality, but is shown as due to duality of the 4D spatial structures of spacetime and timespace. Mathematically, it may appear as if further squeezing of the minimal string morphs it into an expanding pointletlike energy bubble so that the stringy spacetime reexpands in a new direction/dimension located within the bubbly dual timespace. So vibrating string is a mirror image of an energy bubblet, both of which do represent the same stringlet. By analogy, particle cast in spacetime could appear mathematically as having a mirror image (or its superpartner) cast in the dual timespace.

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Section: Embeddings Of Higher-dimensional Spatial Structuresmentioning

confidence: 99%

Operational Restrictions on Morphing of Quasi-Geometric 4D Physical Spaces

Czajko

2014

ILCPA

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“…which is the combination of (8.58) with two translations in the X-direction. The resulting metricR −2 (dX 2 + dR 2 − dT 2 ) is still isometric to r −2 (−V dt 2 + V −1 dr 2 ), but now the 9 The term (4r − 9m) is reminiscent of the Misner-Sharp mass of the Schwarzschild metric conformally rescaled to the ultra-static form.…”

Section: Time Dependent Embeddingsmentioning

confidence: 99%

“…We note a couple of consequences of (2.6). We may decompose the derivative of σ ABA B into irreducible parts as 9) and by taking the trace on AB and A B we find…”

Section: The Theory Of Conformal Embedding Classmentioning

confidence: 99%

Conformally isometric embeddings and Hawking temperature

Dunajski¹,

Paul²

2019

Class. Quantum Grav.

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We find necessary and sufficient conditions for existence of a locally isometric embedding of a vacuum space-time into a conformally-flat 5-space. We explicitly construct such embeddings for any spherically symmetric Lorentzian metric in 3 + 1 dimensions as a hypersurface in R 4,1 . For the Schwarzschild metric the embedding is global, and extends through the horizon all the way to the r = 0 singularity. We discuss the asymptotic properties of the embedding in the context of Penrose's theorem on Schwarzschild causality. We finally show that the Hawking temperature of the Schwarzschild metric agrees with the Unruh temperature measured by an observer moving along hyperbolae in R 4,1 . Date

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“…It must be noted that there are many types of embedding for the static BTZ metric (11). For example, it is possible to embed it globally in the 2+3-dimensional ambient spacetime [34], so our global embedding is not minimal.…”

Section: Global Embedding Of Static Btz Spacetimementioning

confidence: 99%

“…Moreover, there is an evidence that Kruskal knew this embedding when he was constructing his famous coordinates, but did not publish it. Many other embeddings of static black holes have been constructed since then [11][12][13][14][15], but only a few of them are both minimal (i.e. the number of ambient space dimensions is equal to minimal possible for this metric, see below) and global [16].…”

Section: Introductionmentioning

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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On the imbedding of the Schwarzschild space-time I.

Cited by 19 publications

References 0 publications

Operational Restrictions on Morphing of Quasi-Geometric 4D Physical Spaces

Operational Restrictions on Morphing of Quasi-Geometric 4D Physical Spaces

Conformally isometric embeddings and Hawking temperature

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

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