三維及四維廣義相對論之重力能量

Abstract

在本論文中,我們回顧了3+1維廣義相對論定義能量-動量的方法,並且說明 了在2+1維廣義相對論之不適用性,而且提出2+1維重力能量是尤拉不變量 的概念.總能量可以分成物質能量與重力能量之和,重力場能量和二維曲面 的外稟曲率有關,此外我們還指出2+1維廣義相對論和電磁場阿哈羅諾夫- 玻姆效應相似之處. In this thesis,we review the energy-momentum pseudotensor method in 3+1 dimensional general relativity,and we also indicate the failure of energy-momentum pseudotensor method in 2+1 dimensional general relativity.We proposedthe energy of 2+1 dimensional general relativity as Euler invariance.The totalenergy can be decomposed into matter part and gravitational part,the gravitational part depends on the extrinsic curvature of spatial two surface.And we also point out the resemblance between 2+1 dimensional general relativity and Aharonov-Bohm effect in Electromagnetism.