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arXiv 0802.0908astro-ph
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Blandford-Znajek单极子解Kerr参数的高阶项

Higher Order Terms of Kerr Parameter for Blandford-Znajek Monopole Solution

Kentarou Tanabe, Shigehiro Nagataki

摘要:

Blandford-Znajek机制是利用电磁场提取黑洞转动能量的机制,是研究伽马射线暴等致密天体的核心动力学过程之一。这个机制的唯一已知的解析解是Kerr参数α到二阶项的微扰解。为了将Blandford-Znajek机制应用于快速旋转的黑洞,我们试图得到四阶微扰解.结果发现,矢量势的四阶项在无穷远处发散,这意味着微扰方法在离黑洞很远的地方失效。虽然由于四阶项无穷远边界条件未知,使得解存在一些不确定性,但我们可以导出从黑洞中提取的总能流的估计,直到a的四阶,而没有任何歧义。此外,通过对0<a<1的数值解与四阶解的比较,发现四阶解比二阶解更能再现数值结果。同时,由于四阶解在大α时与数值结果不匹配,我们得出结论,需要更多的高阶项来再现数值结果。

英文摘要:

Blandford-Znajek mechanism, by which the rotational energy of a black hole is extracted through electromagnetic fields, is one of the promising candidates as an essential process of the central engine of active compact objects such as Gamma-Ray Bursts. The only known analytical solution of this mechanism is the perturbative monopole solution for Kerr parameter a up to the second order terms. In order to apply Blandford-Znajek mechanism to rapidly rotating black holes, we try to obtain the perturbation solution up to the fourth order. As a result, we find that the fourth order terms of the vector potential diverge at infinity, which implies that the perturbation approach breaks down at large distance from the black hole. Although there are some uncertainties about the solution due to the unknown boundary condition at infinity for the fourth order terms, we can derive the evaluation of the total energy flux extracted from the black hole up to fourth order of a without any ambiguity. Further more, from the comparison between the numerical solution that is valid for 0<a<1 and the fourth order solution, we find that the fourth order solution reproduces the numerical result better than the second order solution. At the same time, since the fourth order solution does not match well with numerical result at large a, we conclude that more higher order terms are required to reproduce the numerical result.

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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