The Hamiltonian dynamics of bounded spacetime and black hole entropy: the canonical method

Abstract

From first principles, I present a concrete realization of Carlip's idea on the black hole entropy from the conformal field theory on the horizon in any dimension. New formulation is free of inconsistencies encountered in Carlip's. By considering a correct gravity action, whose variational principle is well defined at the horizon, I derive a correct classical Virasoro generator for the surface deformations at the horizon through the canonical method. The existence of the classical Virasoro algebra is crucial in obtaining an operator Virasoro algebra, through canonical quantization, which produce the right central charge and conformal weight ∼ A + /hG for the semiclassical black hole entropy. The coefficient of proportionality depends on the choice of ground state, which has to be put in by hand to obtain the correct numerical factor 1/4 of the Bekenstein-Hawking (BH) entropy. The appropriate ground state is different for the rotating and the non-rotating black holes but otherwise it has a universality for a wide variety of black holes. As a byproduct of my results, I am led to conjecture that non-commutativity of taking the limit to go to the horizon and computing variation is proportional to the Hamiltonian and momentum constraints. It is shown that almost all the known uncharged black hole solutions satisfy the conditions for the universal entropy formula.

Aspects of the BMS/CFT correspondence

“…More recently, a similar analysis has been used to derive the Bekenstein-Hawking entropy of an extreme 4-dimensional Kerr black hole [13]. One of our hopes is to make progress along these lines in the non extreme case, either directly from an analysis at null infinity or by making a similar analysis at the horizon, as discussed previously for instance in [14,15,16,17,18,19,20,21,22,23,24,25,26].…”

“…and the explicit parameterizationγ AB dx 19) while the general solution to (2.18) is 20) with Ξ ±± (x ± ) 2 arbitrary functions of their arguments. Using (2.15), one then gets…”

Testing Holographic Principle from Logarithmic and Higher Order Corrections to Black Hole Entropy

“…For the BTZ black hole, the holographic correspondence with the screen at spatial infinity has some disagreement beyond the logarithmic correction ( by the factor of 2 at the logarithmic order), which may be in contrast to the AdS/CFT predictions. On the other hand, a holography at the event horizon from Carlip's horizon-CFT approach of black hole entropy in any dimension [12,13,14] is more flexible, and can be made to be satisfied by choosing an appropriate period parameter P , which has been arbitrary for the leading-order computation. The analysis on the higher dimensional Schwarzschild black holes in AdS space shows a universality of the choice P , except for a dimension-dependent factor.…”

“…This may be in contrast to the AdS/CFT predictions. On the other hand, the holography at the horizon may be satisfied by choosing an appropriate period P , which has been arbitrary for the leading-order computations, of the metric diffeomorphism parameter ξ µ in Carlip's horizon-CFT approach of black hole entropy in any dimension [12,13,14]. The higher dimensional generalization is considered from the Schwarzschild-anti-de Sitter black holes in d ≥ 4 to see a universality of the parameter choice.…”

On the general Kerr/CFT correspondence in arbitrary dimensions

“…Such activity has also generated renewed interest in the earlier effort [3,4,9] that seeks to study the conformal symmetries on the horizons directly. In particular, it has been shown in [10,11] that it is possible to use the "stretched horizon" method to re-derive some results known in the usual literature of Kerr/CFT correspondence [5].…”