Kerr-AdS黑洞的基于独立联络形式拉氏量的守恒量

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

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.

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.