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Previous work has found a higher-dimensional generalization of the "geodesic part" of the Goldberg-Sachs theorem.
A theorem on Petrov types
J. N. Goldberg and R. K. Sachs · 1962
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.
Instability of the Kaluza-Klein vacuum
E. Witten · 1982
Earlier work this paper cites.
Conformal geometry of flows in n n dimensions
I. Robinson and A. Trautman · 1983
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Black holes in higher dimensional space-times
R. C. Myers and M. J. Perry · 1986
Earlier work this paper cites.
Spinors and Space-Time
R. Penrose and W. Rindler · 1986
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Electric and magnetic Weyl tensors: classification and analysis
C. B. G. McIntosh, R. Arianrhod, S. T. Wade, and C. Hoenselaers · 1994
Earlier work this paper cites.
Decay of magnetic fields in Kaluza-Klein theory
F. Dowker, J. P. Gauntlett, G. W. Gibbons, and G. T. Horowitz · 1995
Earlier work this paper cites.
Black holes on cylinders are not algebraically special
P.-J. De Smet · 2002
Earlier work this paper cites.
Robinson manifolds as the Lorentzian analogs of Hermite manifolds
P. Nurowski and A. Trautman · 2002
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Robinson manifolds and Cauchy-Riemann spaces
A. Trautman · 2002
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Robinson manifolds and the shear-free condition
A. Trautman · 2002
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Exact Solutions of Einstein’s Field Equations
H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt · 2003
Cited alongside, same era.
Particle and light motion in a space-time of a five-dimensional rotating black hole
V. P. Frolov and D. Stojković · 2003
Cited alongside, same era.
Classification of the Weyl tensor in higher dimensions
A. Coley, R. Milson, V. Pravda, and A. Pravdová · 2004
Cited alongside, same era.
WANDs of the black ring
V. Pravda and A. Pravdová · 2005
Cited alongside, same era.
Robinson-Trautman spacetimes in higher dimensions
J. Podolský and M. Ortaggio · 2006
Cited alongside, same era.
Type D Einstein spacetimes in higher dimensions
V. Pravda, A. Pravdová, and M. Ortaggio · 2007
Cited alongside, same era.
Higher dimensional Kerr-Schild spacetimes
M. Ortaggio, V. Pravda, and A. Pravdová · 2009
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Type II Einstein spacetimes in higher dimensions
M. Durkee · 2009
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Asymptotically flat, algebraically special spacetimes in higher dimensions
M. Ortaggio, V. Pravda, and A. Pravdová · 2009
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Bel-Debever criteria for the classification of the Weyl tensor in higher dimensions
M. Ortaggio · 2009
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Generalization of the Geroch-Held-Penrose formalism to higher dimensions
M. Durkee, V. Pravda, A. Pravdová, and H. S. Reall · 2010
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Type III and N Einstein spacetimes in higher dimensions: general properties
M. Ortaggio, V. Pravda, and A. Pravdová · 2010
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Bianchi identities in higher dimensions
V. Pravda, A. Pravdová, A. Coley, and R. Milson · 2007
Cited alongside, same era.
Ricci identities in higher dimensions
M. Ortaggio, V. Pravda, and A. Pravdová · 2007
Cited alongside, same era.
The Newman-Penrose formalism in higher dimensions: vacuum spacetimes with a non-twisting geodetic multiple Weyl aligned null direction
A. Pravdová and V. Pravda · 2008
Cited alongside, same era.
Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation
M. Godazgar and H. S. Reall · 2009
Cited alongside, same era.
A higher-dimensional generalization of the geodesic part of the Goldberg-Sachs theorem
M. Durkee and H. S. Reall · 2009
Cited alongside, same era.
Refinements of the Weyl tensor classification in five dimensions, arXiv:1203.1846 [gr-qc]
A. Coley, S. Hervik, M. Ortaggio, and L. Wylleman
Cited in the paper.
Expanding perfect fluid generalizations of the C metric
L. Wylleman and D. Beke · 2010
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Kerr-Schild spacetimes with (A)dS background
T. Málek and V. Pravda · 2011
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Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions
A. Taghavi-Chabert · 2011
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On higher dimensional Einstein spacetimes with a warped extra dimension
M. Ortaggio, V. Pravda, and A. Pravdová · 2011
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A new special class of Petrov type D vacuum space-times in dimension five
A. Garcia-Parrado Gómez-Lobo and L. Wylleman · 2011
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