Embedding into flat spacetime and black hole thermodynamics

Govindarajan, T. R.; Chakraborty, Sumanta

doi:10.1142/s0217732320500133

Cited by 3 publications

(9 citation statements)

References 53 publications

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“…3.4) and one can compute approximate form of the modes -and through them -the propagator G(x, x ′ ). A large class of spacetimes with horizons can be embedded in a higher dimensional flat spacetime; one can then use the form of the propagator in higher dimensions to perform a similar analysis [22]. All these will lead to the same result as above.…”

Section: Generalization To Curved Spacetimementioning

confidence: 85%

“…Consider a spacetime with a bifurcate Killing horizon expressed in two coordinate systems (u, v, x ⊥ ) and (U, V, x ⊥ ) with the null coordinates related by Eq. (22). The reason for the universal behaviour of spacetimes with bifurcate Killing horizon is closely related to the fact that, near H ± , a scalar field theory undergoes dimensional reduction (see e.g., section 2.5 of [18]) and behaves (essentially) as a twodimensional conformal field theory (CFT).…”

Section: Horizon Cft and Thermalitymentioning

confidence: 99%

“…Close to the horizon H + one can also introduce the freely-falling-frame (FFF) coordinates (U, V, x ⊥ ) as discussed around Eq. (22). Within the domain of validity of the FFF, which straddles the horizon H + , we can also introduce the inertial modes (e −iΩU , e −iΩV ).…”

Section: Horizon Cft and Thermalitymentioning

confidence: 99%

“…So the main result arises from the nature of the Bogoliubov transformations 14 between the modes exp ±iΩU and exp ±iωu when the null coordinates are related by Eq. (22). One may worry about the fact that the FFF is defined only close to the horizon.…”

Section: Horizon Cft and Thermalitymentioning

confidence: 99%

“…These three numbers are the signatures of our universe. 22 Thus, Eq. (131) describes the universe as a physical system (like, for e.g.…”

Section: Cosmic Constants and Their Problemsmentioning

confidence: 99%

See 4 more Smart Citations

Gravity and quantum theory: Domains of conflict and contact

Padmanabhan

2019

Int. J. Mod. Phys. D

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There are two strong clues about the quantum structure of spacetime and the gravitational dynamics, which are almost universally ignored in the conventional approaches to quantize gravity. The first clue is that null surfaces exhibit (observer dependent) thermal properties and possess a heat density. This suggests that spacetime, like matter, has microscopic degrees of freedom and its long wavelength

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Section: Generalization To Curved Spacetimementioning

confidence: 85%

Section: Horizon Cft and Thermalitymentioning

confidence: 99%

Section: Horizon Cft and Thermalitymentioning

confidence: 99%

Section: Horizon Cft and Thermalitymentioning

confidence: 99%

“…These three numbers are the signatures of our universe. 22 Thus, Eq. (131) describes the universe as a physical system (like, for e.g.…”

Section: Cosmic Constants and Their Problemsmentioning

confidence: 99%

See 3 more Smart Citations

Gravity and quantum theory: Domains of conflict and contact

Padmanabhan

2019

Int. J. Mod. Phys. D

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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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Explicit isometric embeddings of collapsing dust ball

Kapustin,

Ioffe,

Paston

2020

Preprint

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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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Embedding into flat spacetime and black hole thermodynamics

Cited by 3 publications

References 53 publications

Gravity and quantum theory: Domains of conflict and contact

Gravity and quantum theory: Domains of conflict and contact

Explicit isometric embeddings of collapsing dust ball

Explicit isometric embeddings of collapsing dust ball

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