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arXiv 2210.04056gr-qchep-thquant-ph
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通过近视界不稳定性的视界热性:一种路径积分方法

Thermality of horizon through near horizon instability: a path integral approach

Gaurang Ramakant Kane, Bibhas Ranjan Majhi

AI总结:

本研究通过路径积分方法,从近视界哈密顿量的不稳定性出发,计算态密度和复有效路径,推导出霍金温度,并推广至克尔时空,支持视界热化源于局部不稳定性的观点。

摘要:

近期研究表明,在静态及稳态黑洞中,无质量、无电荷的出射粒子在其特定运动下的近视界哈密顿量有效形式为$\sim xp$型。这种哈密顿量本质上是不稳定的,有潜力解释一些有趣的物理现象。通过路径积分核,我们首先计算了态密度。同时,遵循[Phys. Rev. D 85, 025011 (2012)]的思想,在视界附近,我们通过路径积分方法计算了其薛定谔形式哈密顿量对应的有效路径。后者结果在性质上表现为复数,并携带粒子穿过视界逃逸概率的信息。通过这两种方式,我们确定了霍金温度的正确表达式。此外,我们成功地将复路径方法推广到更一般的黑洞,如克尔时空。我们认为这种复路径是视界提供的近视界不稳定性的结果,因此再次强化了视界热化机制可以通过上述局部不稳定性来解释的事实。

英文摘要:

Recent investigations revealed that the near horizon Hamiltonian of a massless, chargeless outgoing particle, for its particular motion in static as well as stationary black holes, is effectively $\sim xp$ kind. This is unstable by nature and has the potential to explain a few interesting physical phenomena. From the path integral kernel, we first calculate the density of states. Also, following the idea of [Phys. Rev. D 85, 025011 (2012)] here, in the vicinity of the horizon, we calculate the effective path corresponding to its Schrodinger version of Hamiltonian through the path integral approach. The latter result appears to be complex in nature and carries the information of escaping the probability of the particle through the horizon. In both ways, we identify the correct expression of Hawking temperature. Moreover, here we successfully extend the complex path approach to a more general black hole like Kerr spacetime. We feel that such a complex path is an outcome of the nature of near horizon instability provided by the horizon and, therefore, once again bolstered the fact that the thermalization mechanism of the horizon may be explained through the aforesaid local instability.

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