Hawking Radiation, Quantum Anomalies And Kerr/CFT Correspondence Of (G(?)del) Black Holes

The purpose of this thesis is twofold. Both of them are associated with quantum properties of black holes. On the one hand, we have exploited Hawking radiation of (3+1)- and higher-dimensional black strings via covariant gauge and gravitational anoma-lies. We have derived their Hawking fluxes of electric current, angular momentum and energy momentum tensor. Our analysis is very general in the sense that the determinant of the (1+1)-dimensional effective metric was not constrained to satisfy -g=1. Our results further support that Hawking radiation is a universal quantum phenomenon arising at the event horizon.On the other hand, we have extended the Kerr/CFT (Kerr/conformal field theory) correspondence to the holographic descriptions of five-dimensional rotating (charged) black holes, including five-dimensional extremal Kerr and Cvetic-Youm black holes with squashed horizons, and extremal Kerr-Godel and EMCS-Godel black holes in the five-dimensional Godel universe. We show that the near-horizon quantum states of these ex-tremal black holes are dual to two-dimensional chiral conformal field theories, which rely on the rotational symmetry of space-time. With aid of Cardy formula, we have ob-tained dual CFT entropies identified with their Bekenstein-Hawking ones. Since there are two independent rotations in five dimensions, we got two commuting Virasoro al-gebras. In the charged case, our calculations indicate that the U(1) gauge field makes no contribution to the central charges of the Virasoro algebras. Moreover, based on the fact that the low-frequency massless scalar wave equation in the "near region" exhibits SL(2, R)L xSL(2, R)R conformal symmetry, we conjectured that the general non-extremal rotating Kerr-Godel black hole is dual to a two-dimensional finite temperature CFT. In order to support this conjecture, the CFT entropy and the absorption cross section for the massless scalar were computed. The former agrees with the Bekenstein-Hawking en- tropy, while the latter matches the standard one for the two-dimensional finite temperature CFT with chemical potentials. The same conclusions hold true for the rotating charged EMCS-Godel black holes.In addition, we have also investigated thermodynamics of the black strings and these general non-extremal black holes. Our main results go as follows. Firstly, taking the cosmological constant as a thermodynamical variable, we presented the first law of ther-modynamics for the (3+1)- and higher-dimensional black strings. Secondly, we have ob-tained the generalized Abbott-Deser mass and angular momentum, gravitational tension, dipole charge and dipole potential of the general non-extremal Cvetic-Youm black holes with squashed horizons, which satisfy the integral and differential first law of thermody-namics. Finally, we have reformulated the first laws of thermodynamics associated with the inner and outer horizons of the Kerr-Godel black holes into the forms of conformal thermodynamics by redefining the angular velocity, electric-static potential, temperature and entropy in two new systems.