Kerr-AdS黑洞的基于独立联络形式拉氏量的守恒量

基于爱因斯坦引力理论的独立联络形式, 由诺特定理可以导出一个含任意参考背景仿射联络的推广Katz-Bicak-Lynden-Bell(KBL)势, 借此得到一个守恒量定义式. 本文把该定义式应用于渐近anti-de Sitter(AdS)且转动的Kerr-AdS黑洞时空的质量与角动量的定义, 给出了与其他标准方法一致的结果. 特别地, 本文首次构造了一个比通常KBL超势中的参考背景联络更具一般性的新联络, 相关结果表明KBL方法中的参考背景联络不具有唯一性, 而对它的基本要求就是保持理论的协变性.

Conserved quantities of Kerr-AdS black holes based on a connection independent Lagrangian

On the basis of a connection-independent Lagrangian for Einstein gravity, a generalized Katz-Bicak- Lynden-Bell (KBL) potential that contains an arbitrary affine connection is derived. In light of the potential, a formula for conserved charges can be proposed. In the present paper, such a formula succeeds in the definition of the mass and angular momentum for Kerr-AdS black holes. Particularly, we have constructed a new more general reference background connection in comparison with the Levi-Civita one adopted in the KBL superpotential. This further demonstrates that the reference background connection in the KBL method is not unique and it plays a fundamental role in preserving the covariance of the gravity theory.