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arXiv 2304.04427hep-thgr-qc
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再论AdS$_2$黑洞的温度与全息原理

Temperatures of AdS$_2$ black holes and holography revisited

Wontae Kim, Mungon Nam

备注：
14 pages, 2 figures, version published in Modern Physics Letters A
发表信息：
Mod.Phys.Lett.A 39 (2024) 25n26, 2450121
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AI总结：

本文在 dilaton 引力模型中考虑量子反作用，重新研究冲击波形成的蒸发黑洞温度演化，证明其能量先维持后衰减至零，温度从零升至最大值再消失，且不超过永恒 AdS$_2$ 黑洞的 Hawking 温度。

摘要：

在 dilaton 引力模型中，我们重新考察了最初由冲击波形成的蒸发黑洞的温度计算，并考虑了量子反作用。基于全息原理以及边界运动方程的假设，我们证明黑洞能量在蒸发的早期阶段会维持一段时间。随着时间推移，能量逐渐减少并最终消失。因此，根据 Stefan-Boltzmann 定律，由黑洞能量发射率定义的黑洞温度从零温开始，在某个临界时刻达到最大值，最后消失。研究还表明，蒸发黑洞的最高温度不会超过永恒 AdS$_{2}$ 黑洞的 Hawking 温度。我们讨论了蒸发黑洞初始零温的物理意义。

英文摘要：

In a dilaton gravity model, we revisit the calculation of the temperature of an evaporating black hole that is initially formed by a shock wave, taking into account the quantum backreaction. Based on the holographic principle, along with the assumption of a boundary equation of motion, we show that the black hole energy is maintained for a while during the early stage of evaporation. Gradually, it decreases as time goes on and eventually vanishes. Thus, the Stefan-Boltzmann law tells us that the black hole temperature, defined by the emission rate of the black hole energy, starts from zero temperature and reaches a maximum value at a critical time, and finally vanishes. It is also shown that the maximum temperature of the evaporating black hole never exceeds the Hawking temperature of the eternal AdS$_{2}$ black hole. We discuss physical implications of the initial zero temperature of the evaporating black hole.

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