Twofold hidden conformal symmetry of Kerr Bolt black holes

Abstract

Previously we have shown that a four-dimensional Kerr—Bolt black hole in non-extremal and also in extremal cases could be described by a holographic two-dimensional (2D) conformal field theory (CFT) [Ghezelbash A M, Kamali V and Setare M R 2010 Phys. Rev. D 82 124051; Setare M R and Kamali V 2010 JHEP 10 074]. Motivated by recent work [Chen C M, Huang Y M, Sun J R, Wu M F and Zou S J 2010 Phys. Rev. D 82 066004], we show that there is another holographic description for these black holes. The first description is called the J-picture, whose construction is based on the black hole angular momentum. The new description is called the Q-picture, whose constructions originate from the nut charge of the black hole. Similar to the previous cases [Ghezelbash A M, Kamali V and Setare M R 2010 Phys. Rev. D 82 124051; Setare M R and Kamali V 2010 JHEP 10 074], we show that this new picture for a low frequency limit of the wave equation of a massless charged scalar field in the background of a Kerr—Bolt black hole can be written as the Casimir of SL(2, R) symmetry. Our result shows that the entropy of the black hole is reproduced by the Cardy formula. In addition, the absorption cross section is consistent with the finite temperature absorption cross section for a two-dimensional CFT.