动力学Chern-Simons修正引力中的极端和中等质量比激励
Extreme- and Intermediate-Mass Ratio Inspirals in Dynamical Chern-Simons Modified Gravity
摘要：
Chern-Simons（CS）修正引力是一个四维有效理论，它起源于弦论和圈量子引力，通过加入标量场和宇称破坏的庞特里亚金密度的乘积来修正爱因斯坦-希尔伯特作用量。在这个理论中，自旋黑洞的引力场由修正的克尔几何描述，它的多极矩只在第四个多极子l = 4处偏离克尔矩。我们调查可能的签名，这一理论在引力波发射产生的恒星紧凑的对象到大质量的黑洞，无论是中间和极端的质量比的螺旋。我们使用半相对论近似，其中的轨迹是测地线的大规模黑洞的几何形状和重力波形从多极分解的辐射场。主要的CS修正波形产生的修改测地线的轨迹，由于大规模的黑洞的几何形状的变化，并表现为一个积累的退相相对于广义相对论的情况下。我们还讨论了该理论中引力波的传播和应力能量张量。我们发现，虽然这个张量具有相同的形式在广义相对论，能量和角动量平衡定律确实是通过CS标量场的应力-能量张量修改。这些平衡定律可以通过轨道参数的绝热变化来描述内旋，这反过来又会增强退相效应。用先进的地面探测器或激光干涉仪对中等或极端质量比的引力波进行观测，可以利用这种失相来测试动力学理论，达到前所未有的水平。
英文摘要：
[abridged] Chern-Simons (CS) modified gravity is a 4D effective theory that descends both from string theory and loop quantum gravity, and that corrects the Einstein-Hilbert action by adding the product of a scalar field and the parity-violating, Pontryagin density. In this theory, the gravitational field of spinning black holes is described by a modified Kerr geometry whose multipole moments deviate from the Kerr ones only at the fourth multipole, l = 4. We investigate possible signatures of this theory in the gravitational wave emission produced in the inspiral of stellar compact objects into massive black holes, both for intermediate- and extreme-mass ratios. We use the semi-relativistic approximation, where the trajectories are geodesics of the massive black hole geometry and the gravitational waveforms are obtained from a multipolar decomposition of the radiative field. The main CS corrections to the waveforms arise from modifications to the geodesic trajectories, due to changes to the massive black hole geometry, and manifest themselves as an accumulating dephasing relative to the general relativistic case. We also explore the propagation and the stress-energy tensor of gravitational waves in this theory. We find that, although this tensor has the same form as in General Relativity, the energy and angular momentum balance laws are indeed modified through the stress-energy tensor of the CS scalar field. These balance laws could be used to describe the inspiral through adiabatic changes in the orbital parameters, which in turn would enhance the dephasing effect. Gravitational-wave observations of intermediate- or extreme-mass ratio inspirals with advanced ground detectors or with LISA could use such dephasing to test the dynamical theory to unprecedented levels.
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