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arXiv 1502.00688gr-qc
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膨胀爱因斯坦-德西特宇宙中的带电黑洞

Charged black holes in expanding Einstein-de Sitter universes

Manuela G. Rodrigues, Vilson T. Zanchin

摘要:

受McClure和Dyer(Classical量子引力23,1971(2006))先前工作的启发,我们分析了爱因斯坦-麦克斯韦方程组的一些解,这些方程组最初是为了描述宇宙学背景下的带电黑洞而编写的。对一个足够一般的度规的电磁源进行了详细的分析,然后我们着重推导了每个度规的电磁四流以及守恒电荷。带电的McVittie解决方案是重新审视和其因果结构进行了简要的研究,表明它可能代表一个带电的黑洞在膨胀的宇宙中,与黑洞视界形成在无限晚的时间。还分析了Vaidya(Vd)和Sultana和Dyer(SD)最初提出的解决方案的荷电版本。结果表明,带电的Sultana-Dyer度规除了需要一个中心(点状)电荷外,还需要一个全局电流.为了与带电McVittie度规进行比较,考虑了Vd和SD型的新带电解.在这些情况下,原始的质量和电荷参数被宇宙学时间的特定函数所取代。在新的广义带电Vaidya度规中,黑洞视界永远不会形成,而在新的广义Sultana-Dyer度规中,柯西视界和黑洞视界都在无限晚的时间发展。一个收费版本的Thakurta度量也在这里研究。这也是一种新的解决方案。在带电的Sultana-Dyer例子中,电磁场的自然源是一个中心电荷和一个附加的全局电流。简要地研究了其整体结构,并证实了在宇宙学背景下,相应的时空可能代表一个带电的黑洞。所有的解决方案目前的初始奇点发现在McVittie度量。

英文摘要:

Inspired in a previous work by McClure and Dyer (Classical Quantum Gravity 23, 1971 (2006)), we analyze some solutions of the Einstein-Maxwell equations which were originally written to describe charged black holes in cosmological backgrounds. A detailed analysis of the electromagnetic sources for a sufficiently general metric is performed, and then we focus on deriving the electromagnetic four-current as well as the conserved electric charge of each metric. The charged McVittie solution is revisited and a brief study of its causal structure is performed, showing that it may represent a charged black hole in an expanding universe, with the black hole horizon being formed at infinite late times. Charged versions of solutions originally put forward by Vaidya (Vd) and Sultana and Dyer (SD) are also analyzed. It is shown that the charged Sultana-Dyer metric requires a global electric current, besides a central (pointlike) electric charge. With the aim of comparing to the charged McVittie metric, new charged solutions of Vd and SD type are considered. In these cases, the original mass and charge parameters are replaced by particular functions of the cosmological time. In the new generalized charged Vaidya metric the black hole horizon never forms, whereas in the new generalized Sultana-Dyer case both the Cauchy and the black hole horizons develop at infinite late times. A charged version of the Thakurta metric is also studied here. It is also a new solution. As in the charged Sultana-Dyer case, the natural source of the electromagnetic field is a central electric charge with an additional global electric current. The global structure is briefly studied and it is verified that the corresponding spacetime may represent a charged black hole in a cosmological background. All the solutions present initial singularities as found in the McVittie metric.

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