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arXiv 1203.2279gr-qchep-th
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荷电坍缩过程中黑洞自由能的数值研究

Black hole free energy during charged collapse: a numerical study

Hugues Beauchesne, Ariel Edery

摘要:

在各向同性坐标系下,对带电(复)标量场坍缩到Reissner-Nordström(RN)黑洞的热力学过程进行了数值研究.最近在各向同性坐标系中对引力坍缩的数值研究表明,总拉格朗日量的负值在坍缩后期接近史瓦西黑洞的亥姆霍兹自由能F= E-TS(其中E是黑洞质量,T是温度,S是熵)。RN黑洞的相关热力学势是吉布斯自由能G=E-TS- $Φ_H$ Q,其中Q是电荷,$Φ_H$是外视界的静电势。在带电坍缩中,有一个大的向外的物质波,它阻止了外部迅速稳定到静态。然而,内部区域不受波的显著影响。我们发现,内部贡献的吉布斯自由能完全是引力和积累在一个薄壳内的地平线。熵的起源是引力,人们动态地观察到它存在于视界上。我们还比较了不同初始状态下的内部拉格朗日量的数值与内部吉布斯自由能的预期分析值,我们发现它们在10- 13%之内一致。这两个值彼此接近,使得它们的差异随着演化时间的增加而减小。

英文摘要:

We perform a numerical investigation of the thermodynamics during the collapse of a charged (complex) scalar field to a Reissner-Nordström (RN) black hole in isotropic coordinates. Numerical work on gravitational collapse in isotropic coordinates has recently shown that the negative of the total Lagrangian approaches the Helmholtz free energy F= E-TS of a Schwarzschild black hole at late times of the collapse (where E is the black hole mass, T the temperature and S the entropy). The relevant thermodynamic potential for the RN black hole is the Gibbs free energy G=E-TS-$Φ_H$ Q where Q is the charge and $Φ_H$ the electrostatic potential at the outer horizon. In charged collapse, there is a large outgoing matter wave which prevents the exterior from settling quickly to a static state. However, the interior region is not affected significantly by the wave. We find numerically that the interior contribution to the Gibbs free energy is entirely gravitational and accumulates in a thin shell just inside the horizon. The entropy is gravitational in origin and one observes dynamically that it resides on the horizon. We also compare the numerical value of the interior Lagrangian to the expected analytical value of the interior Gibbs free energy for different initial states and we find that they agree to within 10-13%. The two values are approaching each other so that their difference decreases with more evolution time.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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