Dirty black holes: Symmetries at stationary nonstatic horizons

Medved, A. J. M.; Martin, Damien; Visser, Matt

doi:10.1103/physrevd.70.024009

Cited by 124 publications

(232 citation statements)

References 28 publications

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“…However, this simple relation concerning the mode spacing does not seem to hold when m ≤ 0. Analytic derivations for the spacing in the QNM imaginary parts have been provided in [45] and [46]. These calculations use the fact that QNM's are poles in the scattering amplitude of the relevant wave equation.…”

Section: Discussionmentioning

confidence: 99%

Highly damped quasinormal modes of Kerr black holes

Cardoso²,

et al. 2003

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Motivated by recent suggestions that highly damped black hole quasinormal modes (QNM's) may provide a link between classical general relativity and quantum gravity, we present an extensive computation of highly damped QNM's of Kerr black holes. We perform the computation using two independent numerical codes based on Leaver's continued fraction method. We do not limit our attention to gravitational modes, thus filling some gaps in the existing literature. As already observed in [19], the frequency of gravitational modes with l = m = 2 tends to ωR = 2Ω, Ω being the angular velocity of the black hole horizon. We show that, if Hod's conjecture is valid, this asymptotic behaviour is related to reversible black hole transformations. Other highly damped modes with m > 0 that we computed do not show a similar behaviour. The real part of modes with l = 2 and m < 0 seems to asymptotically approach a constant value ωR ≃ −m̟, ̟ ≃ 0.12 being (almost) independent of a. For any perturbing field, trajectories in the complex plane of QNM's with m = 0 show a spiralling behaviour, similar to the one observed for Reissner-Nordström (RN) black holes. Finally, for any perturbing field, the asymptotic separation in the imaginary part of consecutive modes with m > 0 is given by 2πTH (TH being the black hole temperature). We conjecture that for all values of l and m > 0 there is an infinity of modes tending to the critical frequency for superradiance (ωR = m) in the extremal limit. Finally, we study in some detail modes branching off the so-called "algebraically special frequency" of Schwarzschild black holes. For the first time we find numerically that QNM multiplets emerge from the algebraically special Schwarzschild modes, confirming a recent speculation.

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Section: Discussionmentioning

confidence: 99%

Highly damped quasinormal modes of Kerr black holes

Cardoso²,

et al. 2003

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“…These observers have the four velocity u α = ξ α / −ξ β ξ β . After some straightforward tensor manipulations (for similar calculations, see [16] ), we find that the on-horizon (η = 0) components of the Einstein tensor, as seen by the stationary observers, are…”

Section: Kerr-newman Spacetimementioning

confidence: 99%

“…If the thermodynamic interpretation of gravity is to be generic, one needs to go beyond these assumptions and check whether the results remain valid for more general spacetimes. Intuitively we expect these results to hold more generally because one of the crucial inputs (arising from spherical symmetry) is the equality of T t t and T r r on the horizon and it has been shown that this result is valid even for general stationary killing horizons [16]. So a step forward would be to study the near horizon structure of the field equations for a more general spacetimes.…”

Section: Introductionmentioning

confidence: 99%

Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons

2007

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There is an intriguing analogy between the gravitational dynamics of the horizons and thermodynamics. In case of general relativity, as well as for a wider class of Lanczos-Lovelock theories of gravity, it is possible to interpret the field equations near any spherically symmetric horizon as a thermodynamic identity T dS = dE + P dV . We study this approach further and generalize the results to two more generic cases within the context of general relativity: (i) stationary axis-symmetric horizons and (ii) time dependent evolving horizons . In both the cases, the near horizon structure of Einstein equations can be expressed as a thermodynamic identity under the virtual displacement of the horizon. This result demonstrates the fact that the thermodynamic interpretation of gravitational dynamics is not restricted to spherically symmetric or static horizons but is quite generic in nature and indicates a deeper connection between gravity and thermodynamics.

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“…Even before imposing any field equations, it can be shown that the requirement of finite curvature at the horizon sharply restricts the behavior of the metric: it must have a near-horizon expansion [66] …”

Section: A Generic (3 + 1)-dimensional Black Holementioning

confidence: 99%

Effective Conformal Descriptions of Black Hole Entropy

Carlip

2011

Entropy

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It is no longer considered surprising that black holes have temperatures and entropies. What remains surprising, though, is the universality of these thermodynamic properties: their exceptionally simple and general form, and the fact that they can be derived from many very different descriptions of the underlying microscopic degrees of freedom. I review the proposal that this universality arises from an approximate conformal symmetry, which permits an effective "conformal dual" description that is largely independent of the microscopic details.

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Dirty black holes: Symmetries at stationary nonstatic horizons

Cited by 124 publications

References 28 publications

Highly damped quasinormal modes of Kerr black holes

Highly damped quasinormal modes of Kerr black holes

Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons

Effective Conformal Descriptions of Black Hole Entropy

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