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We obtain necessary and sufficient conditions for the existence of "conservation laws" on null hypersurfaces for the wave equation on general four-dimensional Lorentzian manifolds.
10 exact gravitationally conserved quantities
Newman, E. T., and Penrose, R · 1965
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Invariant transformations and Newman-Penrose constants
Goldberg, J. N · 1967
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Green’s theorem and invariant tranformations
Goldberg, J. N · 1968
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New conservation laws for zero rest mass fields in asympotically flat space-time
Newman, E. T., and Penrose, R · 1968
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Conserved quantities in the Einstein-Maxwell theory
Exton, A. R., Newman, E. T., and Penrose, R · 1969
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Conserved quantities of Newman and Penrose
Robinson, D. C · 1969
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Non-conservation of the Newman–Penrose conserved quantities
Press, W. H., and Bardeen, J. M · 1971
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Conservation of the Newman–Penrose conserved quantities
Goldberg, J. N · 1972
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The large scale structure of spacetime
Hawking, S., and G.F.R. Ellis · 1973
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Gaussian beams and the propagation of singularities
Ralston, J · 1983
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Wald, R. M · 1984
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The null condition and global existence to nonlinear wave equations
Klainerman, S · 1986
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Nonlinear nature of gravitation and gravitational-wave experiments
Christodoulou, D · 1991
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The Global Nonlinear Stability of the Minkowski Space
Christodoulou, D., and Klainerman, S · 1994
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Gravitational waves in general relativity XIV. Bondi expansions and the “polyhomogeneity” of Scri
Chruściel, P. T., MacCallum, M. A. H., and Singleton, D. B · 1995
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Perturbation theory for linear operators
Kato, T · 1995
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Partial Differential Equations
Evans, L. C · 1998
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Conserved quantities for polyhomogeneous spacetimes
Kroon, J. A. V · 1998
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Logarithmic Newman–Penrose constants for arbitrary polyhomogeneous spacetimes
Kroon, J. A. V · 1999
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On Killing vector fields and Newman–Penrose constants
Kroon, J. A. V · 2000
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Decay of axisymmetric solutions of the wave equation on extreme Kerr backgrounds
Aretakis, S · 2012
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Horizon instability of extremal black holes
Aretakis, S · 2012
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The wave equation on the extreme Reissner–Nordström black hole
Dain, S., and Dotti, G · 2012
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Gravitational instability of an extreme Kerr black hole
Lucietti, J., and Reall, H · 2012
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On a foliation-covariant elliptic operator on null hypersurfaces
Aretakis, S · 2013
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On a non-linear instability of extremal black holes
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Extremum problems for eigenvalues of elliptic operators
Henrot, A · 2006
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Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes
Andersson, L., Mars, M., and Simon, W · 2008
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A local energy estimate on Kerr black hole backgrounds
Tataru, D., and Tohaneanu, M · 2008
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The formation of black holes in general relativity
Christodoulou, D · 2009
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Dafermos, M., and Rodnianski, I · 2010
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Stability and instability of extreme Reissner–Nordström black hole spacetimes for linear scalar perturbations I
Aretakis, S · 2011
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Aretakis, S · 2013
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A remark about the wave equations on the extreme Reissner–Nordström black hole exterior
Bizon, P., and Friedrich, H · 2013
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Lectures on black holes and linear waves
Dafermos, M., and Rodnianski, I · 2013
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On the horizon instability of an extreme Reissner–Nordström black hole
Lucietti, J., Murata, K., Reall, H. S., and Tanahashi, N · 2013
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Instability of higher dimensional extreme black holes
Murata, K · 2013
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What happens at the horizon(s) of an extreme black hole?
Murata, K., Reall, H. S., and Tanahashi, N · 2013
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Late-time tails in extremal Reissner-Nordström spacetime
Ori, A · 2013
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Characterisation of the energy of Gaussian beams on Lorentzian manifolds with applications to black hole spacetimes
Sbierski, J · 2013
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