激光干涉引力波探测器中一般引力扰动的固有时可观测量
Proper Time Observables of General Gravitational Perturbations in Laser Interferometry-based Gravitational Wave Detectors
AI总结：
本文提出用分束器观测者的固有时作为激光干涉引力波探测器中一般引力扰动的规范不变观测量，证明其对平面引力波等价于常用探测器应变，并可推广至暗物质团块和量子引力时空涨落等信号。
摘要：
我们提出了一个显式规范不变的观测量，用于描述激光干涉引力波探测器中的任意一般引力扰动 $h_{μν}$（不一定是引力波（GWs）引起的），将该信号识别为分束器观测者在两个事件之间所经历的固有时：一个光子穿过分束器的时刻，以及同一光子在穿过干涉臂并从远端反射镜反射后返回分束器的时刻。我们的形式适用于简单的迈克尔逊干涉仪，并可推广到更复杂的装置。我们证明，平面引力波的固有时观测量等价于引力波领域常用的探测器应变，但现在这一共同框架可以容易地推广到其他类型的信号，例如暗物质团块或来自量子引力的时空涨落。我们提供了一个简单的计算方案，用于在线性化引力中计算一般度规扰动的固有时观测量，并明确证明该观测量在扰动的微分同胚变换下保持不变，正如任何物理观测量所应当满足的那样。
英文摘要：
We present an explicitly gauge-invariant observable of {\em any} general gravitational perturbation, $h_{μν}$ (\textit{not} necessarily due to gravitational waves (GWs)), in a laser interferometry-based GW detector, identifying the signature as the proper time elapsed of the beamsplitter observer, between two events: when a photon passes through the beamsplitter, and when the same photon returns to the beamsplitter after traveling through the interferometer arm and reflecting off the far mirror. Our formalism applies to simple Michelson interferometers and can be generalized to more advanced setups. We demonstrate that the proper time observable for a plane GW is equivalent to the detector strain commonly used by the GW community, though now the common framework can be easily generalized for other types of signals, such as dark matter clumps or spacetime fluctuations from quantum gravity. We provide a simple recipe for computing the proper time observable for a general metric perturbation in linearized gravity and explicitly show that it is invariant under diffeomorphisms of the perturbation, as any physical observable should be.
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