The structure of the extreme Schwarzschild-de Sitter space-time

J. Podolsky

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The structure of the extreme Schwarzschild-de Sitter space-time

J. Podolsky

General Relativity and Quantum Cosmology · Submitted 8 Oct 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim By a careful investigation of the geodesics and the equations of geodesic deviation, it is shown that specific families of observers escape from falling into the singularity and approach nonsingular asymptotic regions which are represented by special "points" in the complete conformal diagram.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.33 · compares with prior results 0.04 · mentions code or data availability 0.02.

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The extreme Schwarzschild-de Sitter space-time is a spherically symmetric solution of Einstein's equations with a cosmological constant Lambda and mass parameter m>0 which is characterized by the condition that 9 Lambda m^2=1. The global structure of this space-time is here analyzed in detail. Conformal and embedding diagrams are constructed, and synchronous coordinates which are suitable for a discussion of the cosmic no-hair conjecture are presented. The permitted geodesic motions are also analyzed. By a careful investigation of the geodesics and the equations of geodesic deviation, it is shown that specific families of observers escape from falling into the singularity and approach nonsingular asymptotic regions which are represented by special "points" in the complete conformal diagram. The redshift of signals emitted by particles which fall into the singularity, as detected by those observers which escape, is also calculated.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The extreme Schwarzschild-de Sitter space-time is a spherically symmetric solution of Einstein's equations with a cosmological constant Lambda and mass parameter m>0 which is characterized by the condition that 9 Lambda m^2=1.	background 0.99	0.09	0.04	asserted 1.00
s1	The global structure of this space-time is here analyzed in detail.	contribution 0.99	0.92	0.03	asserted 0.94
s2	Conformal and embedding diagrams are constructed, and synchronous coordinates which are suitable for a discussion of the cosmic no-hair conjecture are presented.	method 0.56	0.95	0.06	asserted 1.00
s3	The permitted geodesic motions are also analyzed.	contribution 0.98	0.91	0.03	asserted 0.91
s4	By a careful investigation of the geodesics and the equations of geodesic deviation, it is shown that specific families of observers escape from falling into the singularity and approach nonsingular asymptotic regions which are represented by special "points" in the complete conformal diagram.	result 1.00	0.95	0.71	asserted 1.00
s5	The redshift of signals emitted by particles which fall into the singularity, as detected by those observers which escape, is also calculated.	result 0.77	0.93	0.09	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original abstract

The extreme Schwarzschild-de Sitter space-time is a spherically symmetric solution of Einstein's equations with a cosmological constant Lambda and mass parameter m>0 which is characterized by the condition that 9 Lambda m^2=1. The global structure of this space-time is here analyzed in detail. Conformal and embedding diagrams are constructed, and synchronous coordinates which are suitable for a discussion of the cosmic no-hair conjecture are presented. The permitted geodesic motions are also analyzed. By a careful investigation of the geodesics and the equations of geodesic deviation, it is shown that specific families of observers escape from falling into the singularity and approach nonsingular asymptotic regions which are represented by special "points" in the complete conformal diagram. The redshift of signals emitted by particles which fall into the singularity, as detected by those observers which escape, is also calculated.

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References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Non-Supersymmetric Attractors
hep-th 2005-07 accept novelty 7.0 of 10

Extremal black holes attract scalar moduli to charge-determined horizon values whenever the charge-dependent effective potential has a positive-definite critical point, with or without supersymmetry.
Semiclassical effects on ultramassive spacetimes
gr-qc 2026-10 conditional novelty 6.0 of 10

Applying the Polyakov approximation to ultramassive spacetimes, the paper finds Hawking radiation during adiabatic accretion and shows that backreaction can in principle prevent the ultramassive limit, while vacuum-en...
(Anti-)evaporation of Schwarzschild-de Sitter black holes revisited
gr-qc 2019-08 conditional novelty 6.0 of 10

Within the Bousso-Hawking effective action, the Schwarzschild-de Sitter asymptotic is excluded, which undermines earlier anti-evaporation results that used the Nariai limit.

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7 arXiv papers cite this in 11 sentences

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Compares with it 1 paper

From this we conclude that the extremal Schwarzschild–de Sitter black hole investigated in [ref] is more physically relevant than Nariai solution.

(Anti-)evaporation of Schwarzschild-de Sitter black holes revisited · Summary and future work · 0.88

Cites it as background 4 papers

Its global structure was investigated in [ref] .

(Anti-)evaporation of Schwarzschild-de Sitter black holes revisited · Extremal Kottler black hole · 0.90
The horizons of the S-deS spacetime (2.2) are well studied (see, for example, [ref] ).

On a conformal Schwarzschild-de Sitter spacetime · Conformal Schwarzschild-de Sitter metric · 0.98
Various properties concerning the global structure of the extremal Schwarzschild-de Sitter black hole were worked out in Ref. [ref] .

The Entropy Function for the Black Holes of Nariai Class · Basics of Extremal Schwarzschild-de Sitter Black Holes · 0.98

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