Conserved charges in general relativity
Conserved charges in general relativity
复制标题
广义相对论中的守恒电荷
DOI：
10.1142/s0217751x21500986
复制
发表时间：
2021
影响因子：
1.6
通讯作者：
Yokoyama Shuichi
中科院分区：
文献类型：
--
作者：
Aoki Sinya;Onogi Tetsuya;Yokoyama Shuichi
我们提出了在具有杀死向量的一般弯曲时空中可用的任意协变守恒电流的守恒量的精确定义。这个定义使我们能够通过体积积分来定义物质的能量和动量。因此，我们可以通过 δ 函数奇点的体积积分来计算史瓦西黑洞和 BTZ 黑洞的电荷。利用这个定义，我们还计算了静态致密星的总能量。它包含奥本海默-沃尔科夫方程中称为米斯纳-夏普质量的引力质量和引力结合能。我们表明，在密度恒定的情况下，引力结合能的负贡献最大为引力质量的 68%。最后，我们评论与一般弯曲流形上的矢量场相关的生成元的定义。
We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved space–time with Killing vectors. This definition enables us to define energy and momentum for matter by the volume integral. As a result we can compute charges of Schwarzschild and BTZ black holes by the volume integration of a delta function singularity. Employing the definition we also compute the total energy of a static compact star. It contains both the gravitational mass known as the Misner–Sharp mass in the Oppenheimer–Volkoff equation and the gravitational binding energy. We show that the gravitational binding energy has the negative contribution at maximum by 68% of the gravitational mass in the case of a constant density. We finally comment on a definition of generators associated with a vector field on a general curved manifold.