广义相对论中的八极矩与自由落体的非普遍性
Octupole moments and the non-universality of free-fall in general relativity
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中文总结 AI 辅助
研究广义相对论中八极矩对自由落体非普遍性的影响，通过证明八极矩无迹分量影响物体运动并给出分解，应用于牛顿时空和彼得罗夫D型时空，揭示八极矩与四极矩效果不同。
中文摘要 AI 辅助
广义相对论中的扩展物体不一定沿测地线下落，可能会加速。这些加速度取决于物体的角动量以及四极矩、八极矩和更高阶矩。但不同物体的多极矩演化不同，导致自由落体具有非普遍性。本文研究八极矩如何导致广义相对论中自由落体的非普遍性。首先表明在任意真空时空中，只有八极矩的无迹分量能影响物体运动，40个八极矩分量中至少16个与运动定律解耦。接着得到无迹八极矩的两种分解，应用于一般牛顿时空和彼得罗夫D型全相对论真空时空的运动。在牛顿时空中，质量矩有普通牛顿效应，动量矩决定物体的隐藏动量；在彼得罗夫D型时空（如克尔时空）中，八极矩能产生一些四极矩不可能产生的扭矩，其效果与四极矩有质的不同。
英文摘要
Extended bodies in general relativity do not necessarily fall along geodesics, but can be accelerated. These accelerations depend on an object's angular momentum, as well as on its quadrupole, octupole, and higher-order moments. However, these multipole moments can evolve differently from one body to another. Different bodies can thus fall differently, even with identical initial data. This paper examines how octupole moments contribute to the non-universality of free-fall in general relativity. We begin by showing that in arbitrary vacuum spacetimes, only the trace-free component of an octupole moment can affect an object's motion. It follows that at least 16 out of 40 octupole components decouple from the laws of motion. Then, we obtain two decompositions for trace-free octupole moments, one in terms of a timelike frame vector and the other in terms of a null tetrad. These decompositions are applied to motion both in generic Newtonian spacetimes and in fully-relativistic vacuum spacetimes that are of Petrov type D. In Newtonian spacetimes, the mass moments are shown to have their ordinary Newtonian effects, while the momentum moments determine a body's hidden momentum---the misalignment between its momentum and its velocity. In Petrov type D spacetimes (such as Kerr), we show that some torques that are impossible with quadrupole moments are possible with octupole moments. Octupole moments can thus have qualitatively-different effects from quadrupole moments.
