论文标题
几乎杀死方程及其含义的扰动
Perturbations of the almost Killing equation and their implications
论文作者
论文摘要
杀死向量在表征给定时空的对称性方面起着至关重要的作用。但是，在大多数情况下，现实的天体物理系统仅大致对称。即使在天体物理黑洞的情况下，人们也可能期望仅由于外部物质领域的扰动而在近似意义上存在杀戮对称性。在这项工作中，我们考虑了几乎杀死方程提供的杀死向量的普遍概念，并研究了背景时空的扰动所引起的扰动。在一阶的情况下，我们证明，对于对称真空空间的非放射性度量扰动（即具有非变化痕迹的度量扰动），几乎扰动的杀伤方程避免了无界的汉密尔顿人对超质量参数选择的问题。对于无可接触的度量扰动，我们获得了几乎杀死方程的二阶扰动的相似结果，并带有一些其他警告。还探讨了热力学意义。
Killing vectors play a crucial role in characterizing the symmetries of a given spacetime. However, realistic astrophysical systems are in most cases only approximately symmetric. Even in the case of an astrophysical black hole, one might expect Killing symmetries to exist only in an approximate sense due to perturbations from external matter fields. In this work, we consider the generalized notion of Killing vectors provided by the almost Killing equation, and study the perturbations induced by a perturbation of a background spacetime satisfying exact Killing symmetry. To first order, we demonstrate that for nonradiative metric perturbations (that is, metric perturbations with nonvanishing trace) of symmetric vacuum spacetimes, the perturbed almost Killing equation avoids the problem of an unbounded Hamiltonian for hyperbolic parameter choices. For traceless metric perturbations, we obtain similar results for the second-order perturbation of the almost Killing equation, with some additional caveats. Thermodynamical implications are also explored.
