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arXiv 1202.5273hep-thgr-qc
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量子黑洞的波函数

Wave function of the quantum black hole

Ram Brustein, Merav Hadad

摘要:

我们证明了Wald Noether荷熵与视界的开度角正则共轭。使用这个正则关系,我们扩展惠勒-德威特方程的Schroedinger方程的开口角,以下Carlip和Teitelboim。我们用对应原理在半经典近似下求解方程,发现解是具有连续熵谱的最小不确定性波函数,因此也是黑洞视界面积的连续谱。开度角偏离其经典值2 π的事实表明,量子黑洞是无水平态的叠加。具有视界的经典几何只用于计算严格经典极限下的量子期望值。

英文摘要:

We show that the Wald Noether charge entropy is canonically conjugate to the opening angle at the horizon. Using this canonical relation we extend the Wheeler-DeWitt equation to a Schroedinger equation in the opening angle, following Carlip and Teitelboim. We solve the equation in the semiclassical approximation by using the correspondence principle and find that the solutions are minimal uncertainty wavefunctions with a continuous spectrum for the entropy and therefore also of the area of the black hole horizon. The fact that the opening angle fluctuates away from its classical value of 2 pi indicates that the quantum black hole is a superposition of horizonless states. The classical geometry with a horizon serves only to evaluate quantum expectation values in the strict classical limit.

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