Two approaches for the gravitational self force in black hole spacetime: Comparison of numerical results
Two approaches for the gravitational self force in black hole spacetime: Comparison of numerical results
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黑洞时空中引力自力的两种方法：数值结果比较
DOI：
10.1103/physrevd.78.124024
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发表时间：
2008
影响因子：
5
通讯作者：
S. Detweiler
中科院分区：
文献类型：
--
作者：
N. Sago;L. Barack;S. Detweiler
最近，两个独立的计算已经提出了有限质量（“自作用力”）的影响，对轨道上的点质量围绕史瓦西黑洞。虽然这两种计算都是基于标准的模式和方法，但它们在几个技术方面有所不同，这使得它们的结果之间的比较很困难，但也很有趣。Barack和Sago [Phys. Rev. D 75，064021（2007）]引用了背景时空中自加速运动的概念，并直接计算了洛伦兹规范中的局部内力（使用时域中扰动方程的数值演化）; Detweiler [Phys. Rev. D 77，124026（2008）]用（光滑）扰动时空的测地轨道描述了运动，并计算了Regge-Wheeler规范中的度规扰动（使用频域数值分析）。在这里，我们建立了一个正式的对应关系，这两个分析，并证明其数值结果的一致性。具体来说，我们比较了保守的O（？）转移到UT（在哪里？是粒子的质量，ut是粒子四速度的史瓦西t分量），适当地映射在两个轨道描述之间，并根据规范进行调整。我们发现，这两个分析产生相同的价值，这种转变内仅仅是分数的差异？10-5-10-7（取决于轨道半径）-与估计的数值误差相当。
Recently, two independent calculations have been presented of finite-mass (“self-force”) effects on the orbit of a point mass around a Schwarzschild black hole. While both computations are based on the standard mode-sum method, they differ in several technical aspects, which makes comparison between their results difficult—but also interesting. Barack and Sago [Phys. Rev. D 75, 064021 (2007)] invoke the notion of a self-accelerated motion in a background spacetime, and perform a direct calculation of the local self-force in the Lorenz gauge (using numerical evolution of the perturbation equations in the time domain); Detweiler [Phys. Rev. D 77, 124026 (2008)] describes the motion in terms a geodesic orbit of a (smooth) perturbed spacetime, and calculates the metric perturbation in the Regge-Wheeler gauge (using frequency-domain numerical analysis). Here we establish a formal correspondence between the two analyses, and demonstrate the consistency of their numerical results. Specifically, we compare the value of the conservative O(?) shift in ut (where ? is the particle’s mass and ut is the Schwarzschild t component of the particle’s four-velocity), suitably mapped between the two orbital descriptions and adjusted for gauge. We find that the two analyses yield the same value for this shift within mere fractional differences of ?10-5–10-7 (depending on the orbital radius)—comparable with the estimated numerical error.