1 | For independent arguments pointing to the presence of conformal symmetry around arbitrary black holes, see [63, 245, 180]. We will not discuss these approaches here. | |
2 | Nevertheless, let us mention that some classes of black holes admit a vanishing horizon area ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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3 | That has been proven for any non-extremal black hole in ![]() ![]() ![]() |
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4 | The original proofs were limited to non-extremal black holes, which have a bifurcation surface [66, 163![]() ![]() |
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5 | Nevertheless, one can describe the process of spontaneous creation of extremal black holes in an electromagnetic field as an analogue to the Schwinger process of particle creation [126]. | |
6 | We thank the anonymous referee for pointing out this reference. | |
7 | In some special cases, there may be some continuous dependence of the near-horizon parameters on the scalar moduli, but
the entropy is constant under such continuous changes [17![]() |
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8 | We fix the range of ![]() ![]() ![]() ![]() ![]() |
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9 | In singular limits where both the temperature and horizon area of black holes can be tuned to zero, while keeping the
area-over-temperature–ratio fixed, singular near-horizon geometries can be constructed. Such singular near-horizon geometries
contain a local AdS3 factor, which can be either a null self-dual orbifold or a pinching orbifold, as noted in [33![]() ![]() ![]() ![]() ![]() |
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10 | Our conventions for the infinitesimal charges associated with symmetries is as follows: the energy is ![]() ![]() ![]() ![]() ![]() |
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11 | The sign choice in this expansion is motivated by the fact that the central charge to be derived in Section 4.3 will be
positive with this choice. Also, the zero mode ![]() |
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12 | Compère, in preparation, (2012). | |
13 | We thank Tom Hartman for helping deriving this central charge during a private communication. | |
14 | There is a ![]() ![]() ![]() ![]() |
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15 | The two-point function (189![]() ![]() ![]() ![]() |
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16 | Note that at extremality ![]() ![]() ![]() ![]() |
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17 | Alternatively, it was suggested in [73, 71] that one can describe the dynamics of the scalar field in the near-horizon region
using the truncated expansion of ![]() ![]() ![]() ![]() ![]() |
http://www.livingreviews.org/lrr-2012-11 |
Living Rev. Relativity 15, (2012), 11
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