发表机构
Universidad Complutense de Madrid（马德里康普顿斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文计算了含类时奇点的爱因斯坦方程各类渐近解的引力能量，采用Hawking-Horowitz定义，发现奇点能量贡献有限为正，仅AdS孤子相对AdS空间能量为负，负质量黑洞能量分别对应AdS与平直空间。
AI 中文摘要
本文计算了具有类时奇点且满足时间平移不变性的爱因斯坦方程的各类渐近AdS（反德西特）与渐近平直解的能量，其中包括带有Kasner类时奇点的空间以及负质量黑洞。文中采用的引力能量定义是Hawking与Horowitz三十年前提出的物理经典作用量的壳上哈密顿量，该定义与Abbott-Deser和ADM表达式一致。为处理奇点，引入了围绕奇点、与恒定时间切片的良好叶状结构兼容的类时正则化截断边界，计算在正则化参数的有限值下进行，最终能量表达式中该参数被设为零。在所有研究的实例中，奇点的能量贡献有限且为正，其值取决于奇点周围的几何结构，使得总引力能量为正。在考察的解中，仅AdS孤子（无奇点）相对于AdS空间具有负引力能量；负质量AdS黑洞与负质量Schwarzschild黑洞的能量分别与AdS空间和Minkowski空间相同。
英文摘要
The gravitational energies of timelike singularities in some asymptotically AdS spaces and in the Schwarzschild black hole with negative mass are explicitly computed. In all cases considered, the energy is finite and positive, depends on the geometry around the singularity, and compensates negative energy contributions from the asymptotic boundary, rendering the total gravitational energy positive. The definition used for energy is the on-shell Hamiltonian of the physical classical action proposed by Hawking and Horowitz~\cite{Hawking-Horowitz}. To deal with the singularity, spacetime is cut off by a timelike regulating boundary surrounding the singularity that is compatible with a foliation of spacetime in constant-time slices. It is shown that the total energy of static AdS-Kasner solutions with timelike Kasner singularities is equal to the energy of the planar AdS black hole, and that the Schwarzschild black hole with negative mass has the same energy as Minkowski space.
Comments12 pages, 1 figure
