Quantum Fluctuation of Event Horizon of Black Hole

黑洞意味着一个时空区域，没有人可以从那里向无穷远处的观察者发送信号。这种时空可以分为两个区域：一个是外部区域，它与无穷大有因果关系，另一个是内部区域（黑洞）。我们把两个区域的边界称为“事件视界”，然而，如果我们考虑黑洞周围的量子效应，黑洞“什么也不能从黑洞中发射出来”的经典图景将被彻底改变。霍金教授已经证明，黑洞发出的辐射源于黑洞形成时真空的变化。霍金辐射被认为是黑洞中最有趣的现象之一，霍金辐射是本研究项目的核心问题。来自黑洞的辐射应该爬上非常深的势能，以达到无穷大。由此可见，即使辐射位于实验室的普通能量范围内，它的能量在视界附近也可以超过普朗克尺度。这表明我们有可能通过霍金辐射来获得普朗克尺度之外的物理学。在这个研究项目中，我们研究了如果我们在标量场和电磁场中引入高阶导数项，辐射的光谱是如何改变的，这似乎模拟了普朗克尺度之外的物理效应。此外，集中在视界的作用，我们提出了一个实验，在流体中观察的现象，可以被认为是一个声学模拟的霍金辐射。在这种情况下，流体速度超过声速的音速点在黑洞的情况下具有视界的作用。最后，从涨落耗散定理的角度讨论了霍金辐射能量损失引起的噪声项的出现。这一效应为研究具有起伏视界的黑洞提供了新的视角。

A black hole means a space-time region from which nobody can send a signal to observers at infinity. And this sort of the space-time can be devided into two regions : one is exterior region which is causally connected to the infinity, another is interior region (black hole). We call a boundary of abobe two region "event horizon".However classical picture of black holes as "nothing can be emitted from the black hole" is drastically changed, if we take into account of quantum effects arround black holes. Prof.Hawking has been shown that black holes emit radiation originated by change of vacuum due to black hole formation. This so called Hawking radiation is recognized as the one of the most interesting phenomena of black hole.The Hawking radiation is a central issue of this research project. Radiations from black holes should climb up very deep potential in order to reach infinity. It follows that even if the radiation lies in a ordinary energy range of laboratories, its energy can exceed Planck scale near the horizon. This suggests the possibility that we access the physics beyond the Planck scale by means of Hawking radiation. In this research project, we investigated how the spectrum of the radiation modified, if we introduce a higher derivative term into scalar and electromagnetic fields which seems to mimic the effect of physics beyond the planck scale. Furthermore concentrating on the role of horizon, we propose an experiment in fluid to observe the phenomena which can be recognized as a acoustic analogue of the Hawking radiation. In this case, a sonic point where velocity of fluid exeeds sound velocity carries a role of horizon in the case of black hole. Finally, from a viewpoint of the fluctuation-disspation theorem, we discuss emergence of noise term which is caused by energy-loss by Hawking radiation. This effect suggests the new perspective of black hole with a fluctuating horizon.