Conformal description of horizon’s states. (English) Zbl 1009.83514

Summary: The existence of black hole horizon is considered as a boundary condition to be imposed on the fluctuating metrics. The coordinate invariant form of the condition for class of spherically symmetric metrics is formulated. The diffeomorphisms preserving this condition act in (arbitrary small) vicinity of the horizon and form the group of conformal transformations of two-dimensional space (\(r-t\) sector of the total space-time). The corresponding algebra recovered at the horizon is one copy of the Virasoro algebra. For general relativity in \(d\) dimensions we find an effective two-dimensional theory which governs the conformal dynamics at the horizon universally for any \(d\geq 3\). The corresponding Virasoro algebra has central charge \(c\) proportional to the Bekenstein-Hawking entropy. Identifying the zero-mode configuration we calculate \(L_0\). The counting of states of this horizon’s conformal field theory by means of Cardy’s formula is in complete agreement with the Bekenstein-Hawking expression for the entropy of black hole in d dimensions.


83C57 Black holes
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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