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arXiv 1009.0633hep-thgr-qcmath-phmath.MP
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热力学几何与霍金辐射

Thermodynamic Geometry and Hawking Radiation

S. Bellucci, B. N. Tiwari

摘要:

本文探讨了热力学涨落在双参数霍金辐射黑洞组态中的作用。该系统的特点是由任意质量和辐射频率的黑洞的合奏。在研究霍金辐射的过程中,我们发现内禀几何描述呈现出一组有趣的精确的对修正函数和全局关联长度。我们研究了等振幅辐射的性质,发现它在质量和频率的涨落下是不稳定的。随后,考虑约克模型的振幅递减辐射表明,热力学涨落是全局稳定的小频率区域。在量子引力修正中,我们考虑了对霍金辐射的常振幅和约克振幅的对数修正。在这两种考虑中,我们注意到,可能的参数涨落的性质可以精确地确定,而不需要任何近似。在频域$w \in (0, \infty)$中,我们观察到辐射能流的局部和全局热力学涨落在s通道中是稳定的。内禀几何证明了热力学涨落具有一定的稳定性,并且在参数曲面上存在1000多个拓扑缺陷时,这一概念对于常振幅模型和York模型几乎保持不变。在平衡辐射能流和涨落视界组态上的高斯涨落,对于辐射参数的所有物理容许域,实现了一个定义良好的、非退化的、弯曲的和规则的内禀黎曼流形. PACS编号:04.70。s:黑洞物理学; 04.70.-经典黑洞; 04.70.Dy黑洞的量子方面,蒸发,热力学; 04.60.Cf弦论的引力方面。保留字:量子引力,霍金辐射;视界微扰; Vaidya几何; York模型;统计涨落;热力学涨落

英文摘要:

This work explores the role of thermodynamic fluctuations in the two parameter Hawking radiating black hole configurations. The system is characterized by an ensemble of arbitrary mass and radiation frequency of the black holes. In the due course of the Hawking radiations, we find that the intrinsic geometric description exhibits an intriguing set of exact pair correction functions and global correlation lengths. We investigate the nature of the constant amplitude radiation and find that it's not stable under fluctuations of the mass and frequency. Subsequently, the consideration of the York model decreasing amplitude radiation demonstrates that thermodynamic fluctuations are globally stable in the small frequency region. In connection with quantum gravity refinements, we take an account of the logarithmic correction into the constant amplitude and York amplitude over the Hawking radiation. In both considerations, we notice that the nature of the possible parametric fluctuations may precisely be ascertained without any approximation. In the frequency domain $w \in (0, \infty)$, we observe that both the local and the global thermodynamic fluctuations of the radiation energy flux are stable in the s-channel. The intrinsic geometry exemplifies a definite stability character to the thermodynamic fluctuations, and up to finitely many topological defects on the parametric surface, the notion remains almost the same for both the constant amplitude and the York model. The Gaussian fluctuations over equilibrium radiation energy flux and fluctuating horizon configurations accomplish a well-defined, non-degenerate, curved and regular intrinsic Riemannian manifolds, for all the physically admissible domains of the radiation parameters. PACS numbers: 04.70.-s: Physics of black holes; 04.70.-Bw: Classical black holes; 04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics; 04.60.Cf Gravitational aspects of string theory. Keywords: Quantum Gravity, Hawking Radiation; Horizon Perturbations; Vaidya Geometry; York Model; Statistical Fluctuations; Thermodynamic Configurations

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