引力自作用力的严格推导
A Rigorous Derivation of Gravitational Self-force
摘要：
人们普遍认为，MisaTaQuWa方程应该描述广义相对论中的“小物体”的运动，并考虑到主导阶的自作用力效应。然而，这些方程的先前推导已经做出了一些特别的假设和/或包含一些不令人满意的特征。例如，所有以前的推导都调用了，没有适当的理由，“洛伦兹规范弛豫”的步骤，其中线性化爱因斯坦方程以适合洛伦兹规范的形式写下，但洛伦兹规范条件则不强加-从而使所得的度量微扰方程不等价于线性化爱因斯坦方程。在本文中，我们分析了“粒子运动”在广义相对论中的问题，在一个系统的和严格的方式，考虑一个参数的家庭的度量，$g_{ab} (λ)$，对应于有一个机构（或黑洞），是“缩小”到零的大小和质量以适当的方式。我们证明了这样一个单参数族的极限世界线必须是背景度量$g_{ab} (λ=0)$的测地线。引力自作用力--以及由于物体的自旋与曲率的耦合而产生的力--然后作为$λ$中对这个世界线的一阶微扰修正而产生。在我们的分析中，没有假设，除了平滑度和限制性能的单参数家庭的度量。我们的方法应该提供一个框架，系统地计算高阶修正引力自作用力，包括更高的多极效应，虽然我们不试图超越一阶计算在这里。的MisaTaQuWa方程的状态进行解释。
英文摘要：
There is general agreement that the MiSaTaQuWa equations should describe the motion of a "small body" in general relativity, taking into account the leading order self-force effects. However, previous derivations of these equations have made a number of ad hoc assumptions and/or contain a number of unsatisfactory features. For example, all previous derivations have invoked, without proper justification, the step of "Lorenz gauge relaxation", wherein the linearized Einstein equation is written down in the form appropriate to the Lorenz gauge, but the Lorenz gauge condition is then not imposed--thereby making the resulting equations for the metric perturbation inequivalent to the linearized Einstein equations. In this paper, we analyze the issue of "particle motion" in general relativity in a systematic and rigorous way by considering a one-parameter family of metrics, $g_{ab} (λ)$, corresponding to having a body (or black hole) that is "scaled down" to zero size and mass in an appropriate manner. We prove that the limiting worldline of such a one-parameter family must be a geodesic of the background metric, $g_{ab} (λ=0)$. Gravitational self-force--as well as the force due to coupling of the spin of the body to curvature--then arises as a first-order perturbative correction in $λ$ to this worldline. No assumptions are made in our analysis apart from the smoothness and limit properties of the one-parameter family of metrics. Our approach should provide a framework for systematically calculating higher order corrections to gravitational self-force, including higher multipole effects, although we do not attempt to go beyond first order calculations here. The status of the MiSaTaQuWa equations is explained.
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