论文标题
一般固定空间中的重力多物
Gravitational Multipoles in General Stationary Spacetimes
论文作者
论文摘要
Geroch-Hansen和Thorne（ACMC）形式主义给出了严格而同等的定义，用于固定真空空间中的重力多物。然而，尽管它们在引力物理学中使用了无处不在，但尚未证明这些形式主义可以推广到非vacuum固定溶液，但在少数特殊情况下。本文展示了如何将Geroch-Hansen形式主义推广到无限度足够光滑的指标的任意非vacuum固定空间。关键是构造改进的扭曲矢量，该矢量在时空的温和拓扑状态下定义明确（对黑洞自动满足）。通过施加自然规格的固定条件，讨论并固定了这种改进的扭曲载体的含义，这也立即导致了Geroch-Hansen和Thorne形式主义之间的等效性，以进行这种任意的固定空间。
The Geroch-Hansen and Thorne (ACMC) formalisms give rigorous and equivalent definitions for gravitational multipoles in stationary vacuum spacetimes. However, despite their ubiquitous use in gravitational physics, it has not been shown that these formalisms can be generalized to non-vacuum stationary solutions, except in a few special cases. This paper shows how the Geroch-Hansen formalism can be generalized to arbitrary non-vacuum stationary spacetimes for metrics that are sufficiently smooth at infinity. The key is the construction of an improved twist vector, which is well-defined under a mild topological condition on the spacetime (which is automatically satisfied for black holes). Ambiguities in the construction of this improved twist vector are discussed and fixed by imposing natural gauge fixing conditions, which also immediately lead to the equivalence between the Geroch-Hansen and Thorne formalisms for such arbitrary stationary spacetimes.
