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Aharony, O.1
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A. Ashtekar, J. Baez, A. Corichi, and K. Krasnov, Phys. Rev. Lett. 80, 904 (1998).
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0000137796
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Phys. Rev. 128, 2851 (1962).
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(1962)
Phys. Rev.
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31
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33750556099
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note
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In general, the hypersurface orthogonality holds only on the horizon. However, in the case of static and spherically symmetric spacetimes, it is globally valid.
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32
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85107715213
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note
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μν are analytic without loss of generality, because higher-order terms in υ do not make any contribution.
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33
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85107715434
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note
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(h)β)/2 give the same value of the surface gravity as that defined by Eq. (2.9). These definitions of the surface gravity result from Eq. (2.9), by using Eqs. (2.6) and (2.8).
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35
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33750539665
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note
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In the Euclidean approach to black hole thermodynamics [25], the temperature of a black hole is derived by imposing regular periodicity near the horizon in the Euclidean section. However, in this case also, we will need to specify the global behavior of the Euclidean section, so that the system is in thermal equilibrium, i.e., the Hartle-Hawking state. In fact, the energy-momentum tensor is singular on the horizon when we consider a quantum field out of equilibrium in a static spacetime [26].
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37
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0004048969
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edited by S. Hawking and W. Israel Cambridge University Press, Cambridge, England
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S. Hawking, in General Relativity, edited by S. Hawking and W. Israel (Cambridge University Press, Cambridge, England, 1979).
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(1979)
General Relativity
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Hawking, S.1
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39
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33750565970
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note
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The Euclidean approach to black hole thermodynamics played a crucial role in choosing a specific form of the symmetry vectors in Refs. [11,12].
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40
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85107712448
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note
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βα(g;ζ) in Eq. (4.20) are defined only up to ambiguity [17]. Here, we make a natural choice, and the effects of the ambiguity will be discussed in future investigations.
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41
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85107712130
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note
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ζ2 in Ref. [12].
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45
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33750547926
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A. Strominger, hep-th/0106113
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A. Strominger, hep-th/0106113.
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