The exact dynamical Chern–Simons metric for a spinning black hole possesses a fourth constant of motion: a dynamical-systems-based conjecture
The exact dynamical Chern–Simons metric for a spinning black hole possesses a fourth constant of motion: a dynamical-systems-based conjecture
复制标题
旋转黑洞的精确动力学陈-西蒙斯度量拥有第四个运动常数：基于动力学系统的猜想
DOI：
10.1088/1361-6382/aad06f
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发表时间：
2018
影响因子：
3.5
通讯作者：
N. Yunes
中科院分区：
文献类型：
--
作者：
A. Cárdenas;Andrés. F. Gutiérrez;L. Pachon;N. Yunes
最近LIGO/Virgo合作的引力波观测允许在极端引力状态下对广义相对论进行首次测试，当质量相当的黑洞和中子星碰撞时。未来的空间探测器，如激光干涉仪空间天线，将允许爱因斯坦的理论测试与引力波发射时，一个小黑洞福尔斯落入一个超大质量的极端质量比螺旋。为此类灵感量身定制的一个特殊测试是在极端重力下寻找混乱。在这里，我们研究是否存在混沌的运动中的测试粒子周围的旋转黑洞的宇称违反修改的重力，特别是专注于动态陈-西蒙斯引力。我们开发了一个remation策略，恢复广义相对论极限中的所有自旋项，同时保留高达五阶的自旋项的动态陈-西蒙斯修正克尔度规。然后，我们计算庞加莱表面的部分和旋转数的广泛家庭的测地线这个mammed度量。我们发现了测地线混乱的证据，由变形的不变环面包围的薄混乱层描绘。这种混沌层的尺寸缩小，因为高阶自旋项包含在克尔度规的动态陈-西蒙斯修正中。我们的数值结果表明，在这个理论中，自旋黑洞的精确解的测地线可能是可积的，因此可能存在与这个精确解相关的第四个运动积分。本文的研究开始为用激光干涉仪空间天线观测极端质量比的螺旋线的混沌检验奠定了基础。
The recent gravitational wave observations by the LIGO/Virgo collaboration have allowed the first tests of general relativity in the extreme gravity regime, when comparable-mass black holes and neutron stars collide. Future space-based detectors, such as the Laser Interferometer Space Antenna, will allow tests of Einstein’s theory with gravitational waves emitted when a small black hole falls into a supermassive one in an extreme mass-ratio inspiral. One particular test that is tailor-made for such inspirals is the search for chaos in extreme gravity. We here study whether chaos is present in the motion of test particles around spinning black holes of parity-violating modified gravity, focusing in particular on dynamical Chern–Simons gravity. We develop a resummation strategy that restores all spin terms in the general relativity limit, while retaining up to fifth-order-in-spin terms in the dynamical Chern–Simons corrections to the Kerr metric. We then calculate Poincaré surfaces of section and rotation numbers of a wide family of geodesics of this resummed metric. We find evidence for geodesic chaos, portrayed by thin chaotic layers surrounded by deformed invariant tori. This chaotic layers shrink in size as terms of higher-order in spin are included in the dynamical Chern–Simons corrections to the Kerr metric. Our numerical findings suggest that the geodesics of the as-of-yet unknown exact solution for spinning black holes in this theory may be integrable, and that there may thus exist a fourth integral of motion associated with this exact solution. The studies presented here begin to lay the foundations for chaotic tests of general relativity with the observation of extreme mass ratio inspirals with the Laser Interferometer Space Antenna.