Built on

W. Israel, “Event horizons in static vacuum space-times,” Phys. Rev. 164
1967
Earlier work this paper cites.
W. Israel, “Event horizons in static electrovac space-times,” Commun. Math. Phys. 8
1968
Earlier work this paper cites.
B. Carter, “Axisymmetric Black Hole Has Only Two Degrees of Freedom,” Phys. Rev. Lett. 26
1971
Earlier work this paper cites.
D. C. Robinson, “Uniqueness of the Kerr black hole,” Phys. Rev. Lett. 34
1975
Earlier work this paper cites.
R. M. Wald, General Relativity (Chicago Univ. Pr., Chicago, USA, 1984)
1984
Earlier work this paper cites.
B. Carter, “Mathematical foundations of the theory of relativistic stellar and black hole configurations.” in Gravitation in Astrophysics - Cargèse 1986 , edited by B. Carter and J. B. Hartle (1987) pp. 63–122
1987
Earlier work this paper cites.
B. Carter, “Has the black hole equilibrium problem been solved?” in Recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theories. Proceedings, 8th Marcel Grossmann meeting, MG8, Jerusalem, Israel, June 22-27, 1997. Pts. A, B (1997) pp. 136–155, arXiv:gr-qc/9712038 [gr-qc]
1997
Earlier work this paper cites.
P. O. Mazur, “Black hole uniqueness theorems,” (2000), arXiv:hep-th/0101012 [hep-th]
2000
Earlier work this paper cites.
P. O. Mazur and E. Mottola, “Gravitational vacuum condensate stars,” Proc. Nat. Acad. Sci. 101
2004
Earlier work this paper cites.
M. Visser and D. L. Wiltshire, “Stable gravastars: An Alternative to black holes?” Class. Quant. Grav. 21
2004
Earlier work this paper cites.

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2019

Generalized no-hair theorems without horizons

Barceló, Carlos, Carballo-Rubio, Raúl, Liberati, Stefano

Understand

The simplicity of black holes, as characterized by no-hair theorems, is one of the most important mathematical results in the framework of general relativity.

Are these theorems unique to black hole spacetimes, or do they also constrain the geometry around regions of spacetime with arbitrarily large (although finite) redshift? This paper presents a systematic study of this question and illustrates that no-hair theorems are not restricted to spacetimes with event horizons but are instead characteristic of spacetimes with deep enough gravitational wells, extending Israel's theorem to static spacetimes without event horizons that contain small deviations from spherical symmetry.
Instead of a uniqueness result, we obtain a theorem that constrains the allowed deviations from the Schwarzschild metric and guarantees that these deviations decrease with the maximum redshift of the gravitational well in the external vacuum region.
Israel's theorem is recovered continuously in the limit of infinite redshift.

Built on

W. Israel, “Event horizons in static vacuum space-times,” Phys. Rev. 164
1967
Earlier work this paper cites.
W. Israel, “Event horizons in static electrovac space-times,” Commun. Math. Phys. 8
1968
Earlier work this paper cites.
B. Carter, “Axisymmetric Black Hole Has Only Two Degrees of Freedom,” Phys. Rev. Lett. 26
1971
Earlier work this paper cites.
D. C. Robinson, “Uniqueness of the Kerr black hole,” Phys. Rev. Lett. 34
1975
Earlier work this paper cites.
R. M. Wald, General Relativity (Chicago Univ. Pr., Chicago, USA, 1984)
1984
Earlier work this paper cites.
B. Carter, “Mathematical foundations of the theory of relativistic stellar and black hole configurations.” in Gravitation in Astrophysics - Cargèse 1986 , edited by B. Carter and J. B. Hartle (1987) pp. 63–122
1987
Earlier work this paper cites.
B. Carter, “Has the black hole equilibrium problem been solved?” in Recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theories. Proceedings, 8th Marcel Grossmann meeting, MG8, Jerusalem, Israel, June 22-27, 1997. Pts. A, B (1997) pp. 136–155, arXiv:gr-qc/9712038 [gr-qc]
1997
Earlier work this paper cites.
P. O. Mazur, “Black hole uniqueness theorems,” (2000), arXiv:hep-th/0101012 [hep-th]
2000
Earlier work this paper cites.
P. O. Mazur and E. Mottola, “Gravitational vacuum condensate stars,” Proc. Nat. Acad. Sci. 101
2004
Earlier work this paper cites.
M. Visser and D. L. Wiltshire, “Stable gravastars: An Alternative to black holes?” Class. Quant. Grav. 21
2004
Earlier work this paper cites.