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In this survey we review the progress made in the last ten years in understanding the Black Hole Rigidity problem in the setting of smooth spacetimes.
K. Nomizu, On local and global existence of Killing vector fields, Ann. of Math. 72
1960
Earlier work this paper cites.
E.T. Newman and R. Penrose, An approach to gravitational radiation by a method of spin coefficients
1962
Earlier work this paper cites.
W. Israel, Event horizons in static vacuum space-times
1967
Earlier work this paper cites.
B. Carter, An axi-symmetric black hole has only two degrees of freedom
1971
Earlier work this paper cites.
S. Kobayashi Transformations groups in differential geometry
1972
Earlier work this paper cites.
S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time
1973
Earlier work this paper cites.
D.C. Robinson, Uniqueness of the Kerr black hole
1975
Earlier work this paper cites.
R. Beig and W. Simon, The stationary gravitational field near spatial infinity
1980
Earlier work this paper cites.
R. Beig and W. Simon, On the multipole expansion for stationary space-times
1981
Earlier work this paper cites.
P. O. Mazur, Proof of uniqueness of the Kerr-Newman black hole solution
1982
Earlier work this paper cites.
S. Chandrasekhar, The mathematical theory of black holes
1983
Earlier work this paper cites.
J. Isenberg and V. Moncrief, Symmetries of Cosmological Cauchy Horizons
1983
Earlier work this paper cites.
W. Simon, Characterization of the Kerr metric
1984
Earlier work this paper cites.
L. Hörmander, The analysis of linear partial differential operators IV. Fourier integral operators
1985
Cited alongside, same era.
G. Bunting and A.K.M. Massood ul Alam, Non-existence of multiple black holes in asymptotically euclidean static vacuum space-time
1987
Cited alongside, same era.
A. D. Rendall, Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations, Proc. R. Soc. Lond. A 427
1990
Cited alongside, same era.
G. Weinstein, On rotating black holes in equilibrium in General Relativity
1990
Cited alongside, same era.
I. Racz and R. Wald Extensions of space-times with Killing horizons
1992
Cited alongside, same era.
D. Christodoulou and S. Klainerman, The global nonlinear stability of the Minkowski space
M. Mars, A spacetime characterization of the Kerr metric, Classical Quantum Gravity 16
1999
Later among the works it cites.
M. Mars, Uniqueness properties of the Kerr metric, Classical Quantum Gravity 17
2000
Later among the works it cites.
H. Friedrich, I. Racz, R. Wald, On the rigidity theorem for spacetimes with a stationary Event or Cauchy horizon
2002
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S. Klainerman and F. Nicolò, The evolution problem in general relativity
2003
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A. Ionescu and S. Klainerman, On the uniqueness of smooth, stationary black holes in vacuum
2009
Later among the works it cites.
A. Ionescu and S. Klainerman, Uniqueness results for ill posed characteristic problems in curved space-times
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1993
Cited alongside, same era.
J.L. Friedman, K. Schleich, D.M. Witt, Topological censorship
1993
Cited alongside, same era.
D. Sudarski and R.M. Wald, Mass formulas for stationary Einstein Yang-Mills black holes and a simple proof of two staticity theorems
1993
Cited alongside, same era.
P.T. Chrusciel, “No Hair” Theorems-Folclore, Conjecture, Results
1994
Cited alongside, same era.
P.T. Chrusciel and R.M. Wald Maximal hypersurfaces in A.F. space-times
1994
Cited alongside, same era.
P.T. Chrusciel, Uniqueness of stationary, electro-vaccum black holes revisited
1996
Cited alongside, same era.
P.T. Chrusciel, Uniqueness of black Holes revisited
1996
Cited alongside, same era.
2009
Later among the works it cites.
W. Wai-Yeung Wong, A spacetime characterization of the Kerr-Newmann metric
2009
Later among the works it cites.
W. Wai-Yeung Wong, On the uniqueness of Kerr-Newman black holes, Ph.D. thesis, Princeton University, 2009
2009
Later among the works it cites.
S. Alexakis, A. D. Ionescu, and S. Klainerman, Hawking’s local rigidity theorem without analyticity
2010
Later among the works it cites.
S. Alexakis, A. D. Ionescu, and S. Klainerman, Uniqueness of smooth stationary black holes in vacuum: small perturbations of the Kerr spaces
2010
Later among the works it cites.
Pin Yu, On the rigidity of Black Holes
2010
Later among the works it cites.
A. Ionescu and S. Klainerman, On the local extension of Killing vectorfields in Ricci flat manifolds
2013
Later among the works it cites.
S. Alexakis, A. D. Ionescu, and S. Klainerman, Rigidity of stationary black holes with small angular momentum on the horizon
2014
Later among the works it cites.