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arXiv 2008.00429gr-qchep-th
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渐进非平坦黑洞时空中的非平凡量子涨落

Non-trivial quantum fluctuations in asymptotically non-flat black-hole space-times

Manu Srivastava, S. Shankaranarayanan

摘要:

霍金辐射仍然是半经典引力的一个重要理论预测,被认为是对量子引力模型的关键检验之一。然而,霍金最初的推导是在固定的背景下使用量子场论。人们努力把引力本身的动力学自由度量子化所引起的时空涨落包括在内,并研究它对霍金粒子的影响。利用半经典分析方法,研究了渐近非平坦球对称黑洞时空中标量场应力张量的量子涨落效应。使用两种不同的方法,我们得到了一个临界长度尺度从地平线上的引力相互作用变得很大,即,当由于标量场而对度量的反作用变得显著时。对于四维Schwarzschild AdS(SAdS)和Schwarzschild de Sitter(SdS),仅当M/L(其中M是黑洞的质量,L与宇宙学常数的模有关)的值在特定范围内时,反反应的相关模的数量是有限的。对于SAdS(SdS),对于M/L $\sim$ 1(0.2 < M/L < $\frac{1}{3\sqrt{3}}$),相关模式的数量是无限的。我们讨论了这些结果的后期阶段的黑洞蒸发的影响。

英文摘要:

Hawking radiation remains a crucial theoretical prediction of semi-classical gravity and is considered one of the critical tests for a model of quantum gravity. However, Hawking's original derivation used quantum field theory on a fixed background. Efforts have been made to include the spacetime fluctuations arising from the quantization of the dynamical degrees of freedom of gravity itself and study the effects on the Hawking particles. Using semi-classical analysis, we study the effects of quantum fluctuations of scalar field stress-tensors in asymptotic non-flat spherically symmetric black-hole space-times. Using two different approaches, we obtain a critical length-scale from the horizon at which gravitational interactions become large, i.e., when the back reaction to the metric due to the scalar field becomes significant. For 4-D Schwarzschild AdS (SAdS) and Schwarzschild de Sitter (SdS), the number of relevant modes for the back-reaction is finite only for a specific range of values of M/L (where M is the mass of the black-hole, and L is related to the modulus of the cosmological constant). For SAdS (SdS), the number of relevant modes is infinite for M/L $\sim$ 1 (0.2 < M/L < $\frac{1}{3\sqrt{3}}$). We discuss the implications of these results for the late stages of black-hole evaporation.

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