摘要
我們首先回顧了Kerr黑洞在極端以及近極端的情況下與共形場論之間的對應關係。根據在共形場與在黑洞視界表面上計算出的熵是相等的，我們可以相信極端Kerr黑洞與共形場之間的確存在對應關係。更進一步藉由無質量的純量場在Kerr黑洞背景之中的散射，計算出在Kerr背景下純量場的吸收截面，與在邊界上的共形場中的兩點函數是一致的，所以Kerr黑洞在近極端的情況下與共形場之間也存在有對應關係。特別的，當無質量的純量場在頻率很低的情況下，其徑向波方程的解空間本身就含有SL(2,R)×SL(2,R)的共形對稱。我們利用這種特性研究Kerr-Newman黑洞，發現有兩種不一樣的共形場的對應關係，我們稱之為J圖像以及Q圖像。最後我們將原先在黑洞背景下計算的兩點函數推廣至三點函數，其結果與共形場中的三點函數相符。
並列摘要
We review the conjecture of Kerr/CFT correspondence in extremal and near-extremal limit. By the matching of the CFT (Cardy formula) and black hole (Bekenstein- Hawking formula) entropies, the conjecture of extreme Kerr/CFT correspondence is confirmed. From the scattering of scalar field near the superradiance region in kerr geometry, the matching of the absorption cross section and the finite-temperature two-point function of dual CFT operator also implies the validity of near-extreme Kerr/CFT correspondence. Moreover, for generic Kerr black holes, the SL(2, R) × SL(2, R) conformal symmetry can be obtained in the solution space of the radial wave equation at low frequency. The black hole/CFT can be extended to the Kerr-Newman (KN) black holes in which there are two individual pictures of dual CFT description, called J- and Q-pictures. Finally we discuss the generalization the computation of two- point function to the three-point function by assuming that there is a cubic interaction in the bulk geometry. The three-point functions in both J- and Q-pictures of KN geometry have a divergent term in the bulk integration near the boundary region. It is consistent with the CFT finite-temperature three-point function.