Teukolsky方程中色散关系的唯象包含及其在引力子质量引力波测量中的应用
Phenomenological Inclusion of Alternative Dispersion Relations to the Teukolsky Equation and its Application to Bounding the Graviton Mass with Gravitational-wave Measurements
摘要：
现有的引力波探测对引力子质量的限制依赖于传播过程中不同频率之间的相位差。引力子质量对黑洞衰荡的准正规模频率的影响常常被忽略。虽然黑洞的微扰理论在广义相对论中得到了很好的发展，但修正的引力理论却不是这样。我们提出了一个唯象的修改Teukolsky方程的扰动黑洞，包括色散关系，由于引力场的非零质量。用对数微扰理论解这个修正的Teukolsky方程，我们计算了由于引力子质量的存在而引起的准正规模频率的移动。这种假设的位移可以用来约束重力子质量与衰荡信号，无论是独立的或与相位差积累由于波传播。我们估计，$m_g \lesssim 10^{-15}\,\textrm{eV}$的引力子质量的限制，可以把单独的振铃信号的第二代引力波探测器的检测。
英文摘要：
Existing constraints on the graviton mass from gravitational-wave detections rely on the phase difference developed between different frequencies during the propagation. Effects on the quasinormal-mode frequencies of the black-hole ringdown due to the graviton mass are often ignored. While perturbation theories of black holes have been well developed in the context of general relativity, this is not the case for modified gravity theories. We propose a phenomenological modification to the Teukolsky equation of perturbed black holes to include the dispersion relation due to a gravitational field of nonzero mass. Solving this modified Teukolsky equation by logarithmic perturbation theory, we compute the shift of the quasinormal-mode frequencies due to the presence of a graviton mass. This hypothetical shift can be used to constrain the graviton mass with ringdown signals, either standalone or in conjunction with the phase difference accumulated due to the wave propagation. We estimate that constraints on the graviton mass of $m_g \lesssim 10^{-15}\,\textrm{eV}$ can be put with a detection of the ringdown signal alone by second generation gravitational-wave detectors.
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