交替引力理论中的凹凸黑洞
Bumpy Black Holes in Alternate Theories of Gravity
摘要：
我们推广了凹凸不平的黑洞框架，以允许替代理论变形。我们构建两个模型独立的参数偏差的克尔度量：一个建立从广义的准克尔和凹凸度量和直接从扰动的克尔时空的刘易斯-Papapetrou形式。我们找到了这些“凸块”必须满足的条件，使得存在近似的二阶Killing张量，使得扰动时空仍然具有三个运动常数（变形能量、角动量和卡特常数），测地线方程可以写成一阶形式。我们将这些参数化的度量映射到彼此通过一个同构和已知的分析黑洞解的引力替代理论。这里提出的参数化指标作为系统计算的极端质量比inspiral波形参数化非GR理论和调查的准确性，星载引力波探测器可以约束这种偏差的框架。
英文摘要：
We generalize the bumpy black hole framework to allow for alternative theory deformations. We construct two model-independent parametric deviations from the Kerr metric: one built from a generalization of the quasi-Kerr and bumpy metrics and one built directly from perturbations of the Kerr spacetime in Lewis-Papapetrou form. We find the conditions that these "bumps" must satisfy for there to exist an approximate second-order Killing tensor so that the perturbed spacetime still possesses three constants of the motion (a deformed energy, angular momentum and Carter constant) and the geodesic equations can be written in first-order form. We map these parameterized metrics to each other via a diffeomorphism and to known analytical black hole solutions in alternative theories of gravity. The parameterized metrics presented here serve as frameworks for the systematic calculation of extreme-mass ratio inspiral waveforms in parameterized non-GR theories and the investigation of the accuracy to which space-borne gravitational wave detectors can constrain such deviations.
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