Quantum Fluctuation of Event Horizon of Black Hole

黑洞是指一个时空区域，在那里没有人可以向无限远处的观测者发送信号。这种时空可以分为两个区域：一个是与无限大因果相连的外部区域，另一个是内部区域（黑洞）。我们把以上两个区域的边界称为“视界”。然而，如果我们考虑到黑洞周围的量子效应，“什么都不能从黑洞中发射出来”的经典黑洞图景就会发生巨大变化。霍金教授已经证明，黑洞发出的辐射是由黑洞形成时真空的变化引起的。这种所谓的霍金辐射被认为是黑洞中最有趣的现象之一。霍金辐射是这个研究项目的核心问题。黑洞的辐射应该上升到非常深的势能，以便达到无穷大。由此可见，即使辐射处于实验室的普通能量范围内，其能量也可以超过视界附近的普朗克尺度。这表明我们有可能通过霍金辐射来了解普朗克尺度之外的物理。在这个研究项目中，我们研究了如果我们在标量和电磁场中引入一个更高的导数项，这似乎模仿了普朗克尺度之外的物理效应，那么辐射的频谱是如何改变的。此外，针对视界的作用，我们提出了一个流体实验来观察可以被认为是霍金辐射的声学模拟现象。在这种情况下，流体速度超过声速的声速点在黑洞中具有视界的作用。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。这种效应提出了具有波动视界的黑洞的新视角。

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.