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We establish a new criterion for the dynamical stability of black holes in $D \geq 4$ spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamical stability is equivalent to the positivity of the canonical energy, $\E$, on a subspace, $\mathcal T$, of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon.
T. Regge and J. A. Wheeler, “Stability of a Schwarzschild singularity,” Phys. Rev. 108
1957
Earlier work this paper cites.
M. Schechter, “General boundary value problems for elliptic partial differential equations”, Commun. Pure and App. Math., Vol XII, 457-486 (1959)
1959
Earlier work this paper cites.
C. B. Morrey: Multiple integrals in the calculus of variation,
1966
Earlier work this paper cites.
F. J. Zerilli, “Effective potential for even parity Regge-Wheeler gravitational perturbation equations,” Phys. Rev. Lett. 24
1970
Earlier work this paper cites.
S. A. Teukolsky, “Rotating Black Holes: Separable Wave Equations for Gravitational and Electromagnetic Perturbations,” Phys. Rev. Lett. 29
1972
Earlier work this paper cites.
T. Regge and C. Teitelboim, “Role of surface integrals in the Hamiltonian formulation of general relativity,” Ann. Phys. 88
1974
Earlier work this paper cites.
J. L. Friedman, B. F. Schutz: “Gravitational radiation instability in rotating stars,” Astrophys. J. 199
1975
Earlier work this paper cites.
J. L. Friedman, B. F. Schutz: “Lagrangian perturbation theory of nonrelativistic fluids”, Astrophys. J. 221
1978
Earlier work this paper cites.
J. L. Friedman and B. F. Schutz, “Secular instability of rotating Newtonian stars,” Astrophys. J. 222
1978
Earlier work this paper cites.
J. L. Friedman: “Generic instability of rotating relativistic stars,” Commun. Math. Phys. 62
1978
Earlier work this paper cites.
C. X. Habisohn, “Calculation of radiated gravitational energy using the second-order Einstein tensor,” J. Math. Phys. 27
1986
Earlier work this paper cites.
R. C. Myers and M. J. Perry, “Black Holes in Higher Dimensional Space-Times,” Annals Phys. 172
1986
Earlier work this paper cites.
G. A. Burnett and R. M. Wald: “A conserved tensor for perturbations of Einstein-Maxwell systems,” Proc. R. Soc. Lond. A 430
1990
Earlier work this paper cites.
R. Gregory and R. Laflamme, “Black strings and p-branes are unstable,” Phys. Rev. Lett. 70
1993
Cited alongside, same era.
P. T. Chrusciel and R. M. Wald, “Maximal Hypersurfaces in Stationary, Asymptotically Flat Spacetimes,” Commun. Math. Phys. 163
1994
Cited alongside, same era.
V. Iyer and R. M. Wald, “Some properties of Noether charge and a proposal for dynamical black hole entropy,” Phys. Rev. D 50
1994
Cited alongside, same era.
V. Iyer and R. M. Wald, “A Comparison of Noether charge and Euclidean methods for computing the entropy of stationary black holes,” Phys. Rev. D 52
1995
Cited alongside, same era.
R. D. Sorkin and M. Varadarajan, “Energy extremality in the presence of a black hole,” Class. Quant. Grav. 13
1996
Cited alongside, same era.
S. Hollands and A. Ishibashi, “Asymptotic flatness and Bondi energy in higher dimensional gravity,” J. Math. Phys. 46
2005
Later among the works it cites.
G. J. Galloway and R. Schoen, “A Generalization of Hawking’s black hole topology theorem to higher dimensions,” Commun. Math. Phys. 266
2006
Later among the works it cites.
S. Hollands, A. Ishibashi and R. M. Wald, “A Higher dimensional stationary rotating black hole must be axisymmetric,” Commun. Math. Phys. 271
2007
Later among the works it cites.
M. D. Seifert and R. M. Wald, “A General variational principle for spherically symmetric perturbations in diffeomorphism covariant theories,” Phys. Rev. D 75
2007
Later among the works it cites.
V. Moncrief and J. Isenberg, “Symmetries of Higher Dimensional Black Holes,” Class. Quant. Grav. 25
2008
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J. Corvino, Scalar curvature deformation and a gluing construction for the Einstein constraint equations, Commun. Math. Phys. 214
2000
Cited alongside, same era.
R. M. Wald and A. Zoupas, “A General definition of ’conserved quantities’ in general relativity and other theories of gravity,” Phys. Rev. D 61
2000
Cited alongside, same era.
D. Gilbarg, N. S. Trudinger: Elliptic partial differential equations of second order,
2001
Cited alongside, same era.
S. S. Gubser and I. Mitra, “The Evolution of unstable black holes in anti-de Sitter space,” JHEP 0108
2001
Cited alongside, same era.
H. S. Reall, “Classical and thermodynamic stability of black branes,” Phys. Rev. D 64
2001
Cited alongside, same era.
P. T. Chrusciel and E. Delay, “On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications,” Mem. Soc. Math. France 94
2003
Cited alongside, same era.
S. Hollands and R. M. Wald, “Conformal null infinity does not exist for radiating solutions in odd spacetime dimensions,” Class. Quant. Grav. 21
2004
Cited alongside, same era.
Later among the works it cites.
2008
Later among the works it cites.
2010
Later among the works it cites.
M. Durkee and H. S. Reall, “Perturbations of higher-dimensional spacetimes,” Class. Quant. Grav. 28
2011
Later among the works it cites.
2011
Later among the works it cites.
2011
Later among the works it cites.
2011
Later among the works it cites.