Black hole evaporation in an expanding universe
Black hole evaporation in an expanding universe
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DOI：
10.1088/0264-9381/24/18/011
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发表时间：
2007-05
影响因子：
3.5
通讯作者：
H. Saida;T. Harada;H. Maeda
中科院分区：
文献类型：
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作者：
H. Saida;T. Harada;H. Maeda
本文计算了在空间无限和零无限处渐近于Einstein-de Sitter宇宙的黑洞的量子辐射功率。我们考虑两个限制质量吸积的情况下，没有吸积和显着的吸积。我们发现，辐射功率强烈地依赖于不仅渐近条件，而且质量吸积的情况。对于没有吸积的情况下，我们考虑爱因斯坦-斯特劳斯解决方案，其中一个恒定质量的黑洞居住在尘埃弗里德曼宇宙。除了预期的红移因子外，我们还发现了负的宇宙学修正。这是以黑洞大小与宇宙学视界之比的立方根给出的，所以目前的数量级是10−5（M/106 M）1/3（t/14 Gyr）−1/3，但在原始黑洞形成时期可能是重要的。由于宇宙学效应，这个黑洞还没有稳定到平衡状态。这种宇宙学修正可以用一个在平坦时空中移动的镜子的辐射来类比解释。对于显著的吸积情况，我们考虑Sultana-Dyer解，其中黑洞倾向于按宇宙尺度因子成比例地增加其质量。在这个模型中，我们发现辐射功率显然与质量为时刻增长质量的Schwarzschild黑洞的Hawking辐射功率相同。因此，能量损失率随着时间的推移而减小并趋于消失。因此，与黑洞上巨大的质量吸积相比，蒸发造成的能量损失微不足道。基于这个模型，我们给出了一般共形稳态黑洞的准平衡温度的定义。
We calculate the quantum radiation power of black holes which are asymptotic to the Einstein–de Sitter universe at spatial and null infinities. We consider two limiting mass accretion scenarios, no accretion and significant accretion. We find that the radiation power strongly depends on not only the asymptotic condition but also the mass accretion scenario. For the no accretion case, we consider the Einstein–Straus solution, where a black hole of constant mass resides in the dust Friedmann universe. We find negative cosmological correction besides the expected redshift factor. This is given in terms of the cubic root of ratio in size of the black hole to the cosmological horizon, so that it is currently of order 10−5(M/106M⊙)1/3(t/14Gyr)−1/3 but could have been significant at the formation epoch of primordial black holes. Due to the cosmological effects, this black hole has not settled down to an equilibrium state. This cosmological correction may be interpreted in an analogy with the radiation from a moving mirror in a flat spacetime. For the significant accretion case, we consider the Sultana–Dyer solution, where a black hole tends to increase its mass in proportion to the cosmological scale factor. In this model, we find that the radiation power is apparently the same as the Hawking radiation from the Schwarzschild black hole of which mass is that of the growing mass at each moment. Hence, the energy loss rate decreases and tends to vanish as time proceeds. Consequently, the energy loss due to evaporation is insignificant compared to huge mass accretion onto the black hole. Based on this model, we propose a definition of quasi-equilibrium temperature for general conformal stationary black holes.