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2
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84927829205
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Alternatively, this identification follows from a semiclassical evaluation of the partition function or the density of states in quantum gravity with any action, as has been shown explicitly in the case of Einstein gravity. See, for example, S.W. Hawking, in General Relativity, An Einstein Centenary Survey, edited by S.W. Hawking and W. Israel (Cambridge University Press, Cambridge, England, 1979);
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5
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84927829204
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see also Ref. citewtext.
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24
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33645930935
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In higher dimensions, one has the possibility of commuting rotations in totally orthogonal planes. Hence the black hole is characterized by the set of angular momenta J(α) associated with rotations in the maximal set of mutually orthogonal planes. For example, see
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(1986)
Ann. Phys. (N.Y.)
, vol.172
, pp. 304
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Myers, R.C.1
Perry, M.J.2
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26
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84927829203
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this result applies for Einstein gravity in any number of spacetime dimensions, but then the surface area A refers to the volume of a spacelike cross section of the horizon, which is a (D 2) dimensional hypersurface in D dimensions.
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30
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84927829202
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It may be of interest to extend our discussion to spacetimes with asymptotically constant curvature. To start such an investigation, one might begin by adapting Wald's derivation of the first law citewald1 to spaces with these new asymptotic boundary conditions.
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42
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84927829201
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We assume that the singularities in the individual terms in the stress energy tensor of Eq. ( refmoving) do not cancel to avoid a curvature singularity.
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47
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84927829200
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The starting point for such a perturbative analysis is a solution of Einstein's equations. A vacuum solution with R=0 would therefore be unaffected perturbatively for the theories considered in Secs. III and IV. It is only in the presence of matter that R ne0, and hence that the special class of higher curvature terms considered there would play a role in modifying the solutions and the black hole entropy.
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51
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0039176116
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edited by, K.S. Thorne, R.H. Price, D.A. MacDonald, Yale University Press, New Haven, CT
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(1986)
Black Holes: The Membrane Paradigm
, pp. 280
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Thorne, K.S.1
Zurek, W.H.2
Price, R.H.3
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55
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84927829199
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R.M. Wald, in Highlights in Gravitation and Cosmology, edited by B.R. Iyer et al. (Cambridge University Press, Cambridge, England, 1988);
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58
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84927829198
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35, 3525 (1994);
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63
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33744773641
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A caveat is that the entropy arising from Wald's construction does not appear to provide the full contribution of the long wavelength quantum fields. [See,] It may be that this discrepancy arises from imprecision in specifying the Green's function in the nonlocal action.
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(1994)
Phys. Rev. D
, vol.50
, pp. 3987
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Fiola, T.M.1
Preskill, J.2
Strominger, A.3
Trivedi, S.P.4
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