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In this paper we will review some facts, both classical and recent, concerning the geometry and analysis of the Kerr and related black hole spacetimes.
On the compatibility of relativistic wave equations for particles of higher spin in the presence of a gravitational field
H. Buchdahl · 1958
Earlier work this paper cites.
Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics
R. P. Kerr · 1963
Earlier work this paper cites.
Existence of a new conservation law in electromagnetic theory
D. M. Lipkin · 1964
Earlier work this paper cites.
Global Structure of the Kerr Family of Gravitational Fields
B. Carter · 1968
Earlier work this paper cites.
Time decay for the nonlinear Klein-Gordon equations
C. S. Morawetz · 1968
Earlier work this paper cites.
Type D Vacuum Metrics
W. Kinnersley · 1969
Earlier work this paper cites.
Spinor structure of space-times in general relativity. II
R. Geroch · 1970
Earlier work this paper cites.
On quadratic first integrals of the geodesic equations for type { \{ 2,2 } \} spacetimes
M. Walker and R. Penrose · 1970
Earlier work this paper cites.
Rotating Black Holes: Separable Wave Equations for Gravitational and Electromagnetic Perturbations
S. A. Teukolsky · 1972
Earlier work this paper cites.
A space-time calculus based on pairs of null directions
R. Geroch, A. Held, and R. Penrose · 1973
Earlier work this paper cites.
Naked Singularities
R. Penrose · 1973
Earlier work this paper cites.
Perturbations of a Rotating Black Hole. I. Fundamental Equations for Gravitational, Electromagnetic, and Neutrino-Field Perturbations
S. A. Teukolsky · 1973
Earlier work this paper cites.
Electromagnetic fields in curved spaces: A constructive procedure
J. M. Cohen and L. S. Kegeles · 1974
Earlier work this paper cites.
Teukolsky equation and Penrose wave equation
M. P. Ryan · 1974
Earlier work this paper cites.
On the Relationship between Killing Tensors and Killing-Yano Tensors
C. D. Collinson · 1976
Earlier work this paper cites.
Black hole electrodynamics and the Carter tetrad
R. L. Znajek · 1977
Earlier work this paper cites.
Gravitational instantons in H-spaces
S. Hacyan · 1979
Earlier work this paper cites.
The mathematical theory of black holes
S. Chandrasekhar · 1983
Earlier work this paper cites.
LETTER TO THE EDITOR: Classification of Euclidean metrics
A. Karlhede · 1986
Earlier work this paper cites.
Spinors and Space-time I & II
R. Penrose and W. Rindler · 1986
Earlier work this paper cites.
The Poincaré group as the symmetry group of canonical general relativity
R. Beig and N. Ó Murchadha · 1987
Earlier work this paper cites.
A mathematical theory of gravitational collapse
D. Christodoulou · 1987
Earlier work this paper cites.
Teukolsky-Starobinsky identities for arbitrary spin
E. G. Kalnins, W. Miller, Jr., and G. C. Williams · 1989
Earlier work this paper cites.
Physics of black holes
I. D. Novikov and V. P. Frolov · 1989
Earlier work this paper cites.
Parallel spinors and parallel forms
M. Y. Wang · 1989
Earlier work this paper cites.
Twistor equation in a curved spacetime
J. Lewandowski · 1991
Earlier work this paper cites.
Preserving parallel spinors under metric deformations
M. Y. Wang · 1991
Cited alongside, same era.
The complete sets of conservation laws for the electromagnetic field
W. I. Fushchich and A. G. Nikitin · 1992
Cited alongside, same era.
Real Killing spinors and holonomy
C. Bär · 1993
Cited alongside, same era.
The global nonlinear stability of the Minkowski space
D. Christodoulou and S. Klainerman · 1993
Cited alongside, same era.
The geometry of Kerr black holes
B. O’Neill · 1995
Cited alongside, same era.
Killing vectors in asymptotically flat space-times. I. Asymptotically translational Killing vectors and the rigid positive energy theorem
R. Beig and P. T. Chruściel · 1996
Cited alongside, same era.
Observable properties of orbits in exact bumpy spacetimes
J. R. Gair, C. Li, and I. Mandel · 2008
Later among the works it cites.
Hidden symmetries and decay for the wave equation on the Kerr spacetime
L. Andersson and P. Blue · 2009
Later among the works it cites.
Petrov D vacuum spaces revisited: identities and invariant classification
S. B. Edgar, A. G.-P. Gómez-Lobo, and J. M. Martín-García · 2009
Later among the works it cites.
An intrinsic characterization of the Kerr metric
J. J. Ferrando and J. A. Sáez · 2009
Later among the works it cites.
Linear waves in the Kerr geometry: a mathematical voyage to black hole physics
F. Finster, N. Kamran, J. Smoller, and S.-T. Yau · 2009
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Positivity of General Superenergy Tensors
G. Bergqvist · 1999
Cited alongside, same era.
Uniqueness properties of the Kerr metric
M. Mars · 2000
Cited alongside, same era.
Super-energy tensors
J. M. M. Senovilla · 2000
Cited alongside, same era.
Classification of local conservation laws of Maxwell’s equations
S. C. Anco and J. Pohjanpelto · 2001
Cited alongside, same era.
Proof of the Riemannian Penrose inequality using the positive mass theorem
H. L. Bray · 2001
Cited alongside, same era.
The inverse mean curvature flow and the Riemannian Penrose inequality
G. Huisken and T. Ilmanen · 2001
Cited alongside, same era.
Later among the works it cites.
A rigorous treatment of energy extraction from a rotating black hole
F. Finster, N. Kamran, J. Smoller, and S.-T. Yau · 2009
Later among the works it cites.
Geometric Invariant Measuring the Deviation from Kerr Data
T. Bäckdahl and J. A. Valiente Kroon · 2010
Later among the works it cites.
On the construction of a geometric invariant measuring the deviation from Kerr data
T. Bäckdahl and J. A. Valiente Kroon · 2010
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Observable signature of a background deviating from the Kerr metric
G. Lukes-Gerakopoulos, T. A. Apostolatos, and G. Contopoulos · 2010
Later among the works it cites.
Linearized gravity and gauge conditions
S. Aksteiner and L. Andersson · 2011
Later among the works it cites.
The ’non-Kerrness’ of domains of outer communication of black holes and exteriors of stars
T. Bäckdahl and J. A. Valiente Kroon · 2011
Later among the works it cites.
A local energy estimate on Kerr black hole backgrounds
D. Tataru and M. Tohaneanu · 2011
Later among the works it cites.
Constructing “non-Kerrness” on compact domains
T. Bäckdahl and J. A. V. Kroon · 2012
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Charges for linearized gravity
S. Aksteiner and L. Andersson · 2013
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L. Andersson and P. Blue · 2013
Later among the works it cites.
Weyl tensor classification in four-dimensional manifolds of all signatures
C. Batista · 2013
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Geometry and analysis in black hole spacetimes
S. Aksteiner · 2014
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Rigidity of stationary black holes with small angular momentum on the horizon
S. Alexakis, A. D. Ionescu, and S. Klainerman · 2014
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A new tensorial conservation law for Maxwell fields on the Kerr background
L. Andersson, T. Bäckdahl, and P. Blue · 2014
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Second order symmetry operators
L. Andersson, T. Bäckdahl, and P. Blue · 2014
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SymManipulator, 2011-2014
T. Bäckdahl · 2014
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M. Dafermos, I. Rodnianski, and Y. Shlapentokh-Rothman · 2014
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xAct: Efficient tensor computer algebra for Mathematica, 2002-2014
J. M. Martín-García · 2014
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Second Order Symmetries of the Conformal Laplacian
J.-P. Michel, F. Radoux, and J. Šilhan · 2014
Later among the works it cites.
Decay of solutions to the Maxwell equation on the Schwarzschild background
L. Andersson, T. Bäckdahl, and P. Blue · 2015
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