Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime
Scalar self-force for highly eccentric equatorial orbits in Kerr spacetime
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克尔时空中高偏心赤道轨道的标量自力
DOI：
10.1103/physrevd.95.084043
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发表时间：
2016
影响因子：
5
通讯作者：
B. Wardell
中科院分区：
文献类型：
--
作者：
J. Thornburg;B. Wardell
如果一个质量为 $\mu M$（$\mu \ll 1$）的小“粒子”围绕一个质量为 $M$ 的黑洞运行，则主阶辐射反应效应是作用在粒子上的 $\mathcal{O}(\mu^2)$“自力”，以及相应的粒子远离测地线的 $\mathcal{O}(\mu)$“自加速”。这种“极端质量比螺旋”系统可能是未来天基引力波探测器的重要引力波源。在这里，我们考虑计算克尔时空束缚偏心轨道上标量场粒子自力的“玩具模型”问题。我们使用带有 4 阶穿刺场的 Barack-Golbourn-Vega-Detweiler 有效源正则化，然后是 $e^{im\phi}$（“m 模式”）傅立叶分解以及每个 $m$ 在 $2+1$ 维度上的单独时域数值演化。我们引入了一个围绕粒子世界线的有限世界管，并以分段方式定义我们的进化方程，以便有效源仅在世界管内使用。将世界管视为一个空间区域，它会跟随粒子的轨道运动而移动。我们在粒子运动区域使用恒定的 Boyer-Lindquist 时间切片，变形为渐近双曲面并在地平线和 $\mathcal{J}^+$ 附近压缩。我们提供了许多轨道偏心率高达 0.98 美元的测试用例的数值结果。在某些情况下，我们在经过近星体后不久就会发现自力出现较大的振荡（“摆动”）。
If a small "particle" of mass $\mu M$ (with $\mu \ll 1$) orbits a black hole of mass $M$, the leading-order radiation-reaction effect is an $\mathcal{O}(\mu^2)$ "self-force" acting on the particle, with a corresponding $\mathcal{O}(\mu)$ "self-acceleration" of the particle away from a geodesic. Such "extreme--mass-ratio inspiral" systems are likely to be important gravitational-wave sources for future space-based gravitational-wave detectors. Here we consider the "toy model" problem of computing the self-force for a scalar-field particle on a bound eccentric orbit in Kerr spacetime. We use the Barack-Golbourn-Vega-Detweiler effective-source regularization with a 4th order puncture field, followed by an $e^{im\phi}$ ("m-mode") Fourier decomposition and a separate time-domain numerical evolution in $2+1$ dimensions for each $m$. We introduce a finite worldtube that surrounds the particle worldline and define our evolution equations in a piecewise manner so that the effective source is only used within the worldtube. Viewed as a spatial region, the worldtube moves to follow the particle's orbital motion. We use slices of constant Boyer-Lindquist time in the region of the particle's motion, deformed to be asymptotically hyperboloidal and compactified near the horizon and $\mathcal{J}^+$. We present numerical results for a number of test cases with orbital eccentricities as high as $0.98$. In some cases we find large oscillations ("wiggles") in the self-force shortly after periastron passage.