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Black hole fluctuations and negative noise kernel Wang, Qingdi


In 2007, based on stochastic gravity, Bei-Lok Hu and Albert Roura claimed that black hole fluctuations grow and eventually become important when a black hole has evaporated for a sufficiently long period of time but well before the Planckian regime is reached. In this thesis, we investigate their derivation of the black hole fluctuations and propose two analogue examples to better understand the mechanism of large fluctuations. Our analysis clearly shows the classical nature of the large black hole fluctuations. On the other hand, to test the validity of stochastic gravity, we calculate the centerpiece of stochastic gravity, the noise kernel, first for a perfect reflecting mirror and then for a more realistic mirror which becomes transparent at high frequencies. We find that one of the noise kernel components which corresponds to the fluctuations of energy flux is negative and thus seems to give "imaginary" fluctuations. We also perform calculations of both the fluctuations of forces acting on mirrors and of the fluctuations of energy flux radiated by them and divergent results are obtained. We try to give interpretations of these negative and divergent values. They need further investigation in the future.

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