Dirty black holes: spacetime geometry and near-horizon symmetries

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

doi:10.1088/0264-9381/21/13/003

Cited by 77 publications

(161 citation statements)

References 36 publications

(56 reference statements)

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“…On a more favorable note, the results of the current derivation do happen to agree with those of our prior and completely independent work [17,18]. Nonetheless, this "loophole" is rather bothersome, and we hope to (somehow) rigorously address this issue at a later time.…”

Section: A Discussionsupporting

confidence: 78%

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Symmetries at stationary Killing horizons

Medved

2005

Gen Relativ Gravit

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It has often been suggested (especially by Carlip) that spacetime symmetries in the neighborhood of a black hole horizon may be relevant to a statistical understanding of the Bekenstein-Hawking entropy. A prime candidate for this type of symmetry is that which is exhibited by the Einstein tensor. More precisely, it is now known that this tensor takes on a strongly constrained (block-diagonal) form as it approaches any stationary, non-extremal Killing horizon. Presently, exploiting the geometrical properties of such horizons, we provide a particularly elegant argument that substantiates this highly symmetric form for the Einstein tensor. It is, however, duly noted that, on account of a "loophole", the argument does fall just short of attaining the status of a rigorous proof. I. THE MOTIVATIONNo one seriously disputes the notion of black holes as thermodynamic entities; nevertheless, the Bekenstein-Hawking entropy [1,2] remains as enigmatic as ever from a statistical viewpoint. The "company line" has been, more often than not, to hope that quantum gravity will eventually provide the resolution; but this could require, cynically speaking, a rather long wait. A more pragmatic expectation might be to hope for a statistical explanation that interpolates between the quantum-gravitational and semi-classical regimes, and that is not particularly sensitive to the fundamental micro-constituents. Such a perspective appears to be in compliance with the general stance of S. Carlip -who has long advocated for horizon boundary conditions as a means of altering the physical content of the theory, thereby inducing new degrees freedom that can account for the black hole entropy [3].One might then query as to what physical principle determines the correct choice of boundary conditions. On this point, Carlip has stressed the importance of asymptotic symmetries 1 in the neighborhood of the horizon [4]. Ideally, these symmetries should be based on semi-classical concepts that can be enhanced into a quantum environment 1 Asymptotic in the sense that such symmetries need only be exact at the horizon itself.

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Section: A Discussionsupporting

confidence: 78%

“…This is to be accomplished by a purely geometrical argument that, unlike the prior method [17,18], does not have to be reformulated in going from the static to the rotating case (or vice versa).…”

Section: Some Preliminariesmentioning

confidence: 99%

Symmetries at stationary Killing horizons

Medved

2005

Gen Relativ Gravit

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“…To see this, we construct the set {T } as follows. Focussing on the lower row of the alternating tensor in the expression (18) for L (D) m , we have 2m choices for the location of the index value t. Due to the symmetries of the alternating tensor and the Riemann tensor, each choice results in the same term, and we can write,…”

Section: Gravity With the Complete Lanczos-lovelock Actionmentioning

confidence: 99%

Thermodynamic route to field equations in Lanczos-Lovelock gravity

2006

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Spacetimes with horizons show a resemblance to thermodynamic systems and one can associate the notions of temperature and entropy with them. In the case of Einstein-Hilbert gravity, it is possible to interpret Einstein's equations as the thermodynamic identity T dS = dE + P dV for a spherically symmetric spacetime and thus provide a thermodynamic route to understand the dynamics of gravity. We study this approach further and show that the field equations for LanczosLovelock action in a spherically symmetric spacetime can also be expressed as T dS = dE +P dV with S and E being given by expressions previously derived in the literature by other approaches. The Lanczos-Lovelock Lagrangians are of the form L = Q bcd a R a bcd with ∇ b Q bcd a = 0. In such models, the expansion of Q bcd a in terms of the derivatives of the metric tensor determines the structure of the theory and higher order terms can be interpreted quantum corrections to Einstein gravity. Our result indicates a deep connection between the thermodynamics of horizons and the allowed quantum corrections to standard Einstein gravity, and shows that the relation T dS = dE + P dV has a greater domain of validity that Einstein's field equations.

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“…Pravda and Zaslavskii [4] studied curvature scalars in a general static spacetime possessing Killing horizon (generalizing previous results of [5] on high degree of symmetry of the Einstein tensor to the non-extremal case). They assumed regularity of all polynomial invariants of the Riemann tensor on a horizon and used two naturally preferred frames for calculations -the static observer and the freely falling observer frames.…”

Section: Killing Horizonsmentioning

confidence: 75%