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arXiv 2407.00348gr-qc
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简并费米气体在Reissner-Nordström黑洞上的吸积

Accretion of the degenerate Fermi gas onto a Reissner-Nordström black hole

Hunan Province Key Laboratory Integration and Optical Manufacturing Technology（湖南省光机电一体化制造技术重点实验室）；Center for Astrophysics, Guangzhou University（广州大学天体物理中心）

Ping Li, Jiang-he Yang, Siwei Xu

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AI总结：

本文扩展Rioseco和Sarbach模型研究简并费米气体在Reissner-Nordström黑洞上的吸积，推导了相关物理量表达式，发现吸积率随黑洞电荷增加而降低，不违反宇宙监督假设，并指出Vlasov气体吸积表现为各向异性流体。

摘要：

我们将Rioseco和Sarbach模型扩展至Reissner-Nordström黑洞吸积简并相对论性费米气体。该吸积理论基于Boyer-Lindquist坐标，且费米气体在无限远处遵循费米-狄拉克统计。我们推导了粒子流密度、应力能量-动量张量以及三种吸积率的表达式。我们首先研究了Risoseco和Sarbach模型对黑洞电荷演化的影响。结果表明，质量吸积率和电荷吸积率均与粒子吸积率成正比。我们还提供了这些量在无限远处的解析结果和有限范围内的数值结果。我们的结果表明，吸积率随黑洞电荷的增加而降低，表明我们的吸积模型不违反宇宙监督假设。本文首次指出Vlasov气体的吸积表现为包含两个完美流体分量的各向异性流体。一个分量代表费米气体的各向同性流体，另一个代表零流体。当使用Boyer-Lindquist坐标系时，我们观察到零流体的贡献即使在无限远处依然存在，导致径向压力始终小于切向压力。因此，在无限远处将吸积模型视为完美流体是不恰当的。

英文摘要：

We extend the Rioseco and Sarbach model into Reissner-Nordström black hole accretes degenerate relativistic Fermi gas. The accretion theory is based on the Boyer-Lindquist coordinates and the Fermi gas follows Fermi-Dirac statistics at infinity. The expressions for the particle current density, the stress energy-momentum tensor, and three accretion rates are derived. We first investigated the impact of Risoseco and Sarbach model on the evolution of a black hole's charge. The results show that both the mass accretion rate and charge accretion rate are proportional to the particle accretion rate. We have also provided analytical results at infinity and numerical results within a finite range for these quantities. Our results indicate that the accretion rate decreases as the charge of the black hole increases, suggesting that our accretion model does not violate the cosmic censorship hypothesis. In this paper, we first point out that the accretion of Vlasov gas behaves as an anisotropic fluid containing two perfect-fluid components. One component represents the isotropic fluid of Fermi gas, while the other represents a null fluid. When using the Boyer-Lindquist coordinate system, we observed that the contribution from the null fluid persists even at infinity, which led to the radial pressure always smaller than the tangential pressure. Therefore, it's not appropriate to treat the accretion model as a perfect fluid at infinity.

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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