Note on Kerr/CFT correspondence in a first order formalism

Abstract

In symmetry based approaches to black hole entropy, we calculate the central charge of the Virasoro algebra in the first order formulation of gravity for both Palatini and Holst actions. In these calculations, we made use of the NHEK metric and the Kerr-CFT correspondence. For the Palatini action the results obtained in the second order formulation are reproduced. We also argue that the Holst term does not contribute to the charge algebra no matter what geometry/boundary conditions one is considering.

Magnetized Kerr/CFT correspondence

“…Getting the corresponding central charge which is related to the near horizon geometry under consideration is an important step in Kerr/CFT correspondence prescription [1], since this central charge is needed in the dual calculation of entropy using Cardy formula. Subsequently, the Kerr/CFT correspondence [1] was extended to many cases of extremal rotating black holes [3], even to the static charged ones [4].…”

Extremal RN/CFT in both hands revisited

“…The central charge of the dual CFT reproduces the exact Bekenstein-Hawking entropy of the 4-dimensional extremal Kerr black hole by Cardy's formula. This method has been extensively studied for Kerr black hole and other more general rotating black holes [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. However, in the original Kerr/CFT method, the Virasoro algebra was realized only from an enhancement of the rotational U (1) isometry, which corresponds to left hand central charge, not from the SL (2, R).…”

Quasilocal conformal Killing horizons: Classical phase space and the first law

“…One must find ways to extract quantum degrees of freedom of general relativity. The framework of Killing Horizon was broadened to understand the origin of entropy and black hole thermodynamics [9][10][11][12][13][14][15]. It turned out that the framework of Isolated Horizons (IH) was more suited to address these questions from the perspective of loop quantum gravity [16][17][18][19][20][21][22].…”