三维有挠率引力中的守恒荷

Conserved charge in three-dimensional gravity with torsion

由于引力场的微分同胚不变性,定义能量一直是引力理论中的难题,人们为此发展了一系列方法.本文将Wald基于拉格朗日形式体系构造引力场的准局域能量的方法推广到三维有挠率引力的情形,给出了Mielke-Baekler (MB)模型中的守恒的能量与角动量,并计算了有挠率的BTZ黑洞解的守恒荷.所得结果与基于哈密顿形式体系的方法给出的守恒荷相一致.

The definition of energy is a long-standing difficult problem in gravity theory because of the diffeomorphism invariance of the gravity field.Various approaches have been developed.We have generalized Wald’s approach for the constructing quasi-local energy of gravity field,which is based on the Lagrangian formulation,to the three-dimensional gravity with torsion,and obtained the conserved energy and angular momentum for the Mielke-Baekler(MB)model.For BTZ black hole with torsion,the conserved charges are consistent with those obtained from the approach based on Hamiltonian formulation.