Gravitational self-force from radiation-gauge metric perturbations
Gravitational self-force from radiation-gauge metric perturbations
复制标题
辐射计度量扰动产生的重力自力
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
L. Barack
中科院分区：
文献类型：
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作者：
A. Pound;C. Merlín;L. Barack
计算弯曲时空中点质量上的引力自作用力（GSF）需要输入足够规则规范中的度规微扰。计算克尔黑洞周围轨道的GSF的程序中的一个基本挑战是，重建度量扰动的标准程序是在一类“辐射”规范中制定的，其中粒子奇异性是各向异性的，并且远离粒子的位置。在这里，我们提出了两个实用的计划，用于计算GSF使用辐射计重建度量作为输入。该方案是基于对辐射计中粒子奇异性的局部结构的详细分析。我们表明，存在三种类型的辐射规范：两个包含一个径向弦状奇点从粒子发出的，无论是在一个方向（“半弦”规范）或两个方向（“全弦”规范）;和第三种类型不包含字符串，但跳跃不连续（可能是一个三角函数）跨越表面相交的粒子。基于一个平面空间的例子，我们认为，标准的模式模式的模式重建过程产生的“正规的一半”的半弦的解决方案，或（等价地）任何一个正规的一半的非弦的解决方案。对于半弦的情况下，我们制定了GSF在局部变形的辐射规范，消除了弦奇异性附近的粒子。我们推导出一个模式和公式的GSF在这个规范，这是类似于标准的洛伦兹规范公式，但需要修正的正则化参数的值。对于无弦的情况下，我们制定的GSF直接，没有局部变形，我们推导出一个模式和公式，不需要校正的正则化参数，但涉及一定的平均过程。我们解释了我们的结果与Gralla的正则化参数的不变性定理的一致性，我们讨论了我们的方法和弗里德曼等人的相关方法之间的对应关系。
Calculations of the gravitational self-force (GSF) on a point mass in curved spacetime require as input the metric perturbation in a sufficiently regular gauge. A basic challenge in the program to compute the GSF for orbits around a Kerr black hole is that the standard procedure for reconstructing the metric perturbation is formulated in a class of “radiation” gauges, in which the particle singularity is nonisotropic and extends away from the particle’s location. Here we present two practical schemes for calculating the GSF using a radiation-gauge reconstructed metric as input. The schemes are based on a detailed analysis of the local structure of the particle singularity in the radiation gauges. We show that three types of radiation gauge exist: two containing a radial stringlike singularity emanating from the particle, either in one direction (“half-string” gauges) or both directions (“full-string” gauges); and a third type containing no strings but with a jump discontinuity (and possibly a delta function) across a surface intersecting the particle. Based on a flat-space example, we argue that the standard mode-by-mode reconstruction procedure yields the “regular half” of a half-string solution, or (equivalently) either of the regular halves of a no-string solution. For the half-string case, we formulate the GSF in a locally deformed radiation gauge that removes the string singularity near the particle. We derive a mode-sum formula for the GSF in this gauge, which is analogous to the standard Lorenz-gauge formula but requires a correction to the values of the regularization parameters. For the no-string case, we formulate the GSF directly, without a local deformation, and we derive a mode-sum formula that requires no correction to the regularization parameters but involves a certain averaging procedure. We explain the consistency of our results with Gralla’s invariance theorem for the regularization parameters, and we discuss the correspondence between our method and a related approach by Friedman et al.