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arXiv 1207.6004gr-qc
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扩展Palatini理论中的Reissner-Nordström黑洞

Reissner-Nordström black holes in extended Palatini theories

Gonzalo J. Olmo, D. Rubiera-Garcia

摘要:

我们研究静态的,球对称的解决方案与电场在广义相对论(GR)的扩展包含一个Ricci平方项和制定的Palatini形式主义。我们发现,所有的解决方案提出了一个中央核心,其面积是正比于普朗克面积乘以收费的数量。在远离核心的地方,曲率不变量很快就趋向于通常的Reissner-Nordström解,尽管视界的结构可能不同。事实上,除了在GR的Reissner-Nordström解中发现的结构外,我们还发现了只有一个非简并视界(Schwarzschild类)的黑洞解,以及非奇异的黑洞和裸核。非奇异解的荷质比意味着核心物质密度与具体的电荷和质量的量以及普朗克密度的阶数无关。我们讨论了这些结果对天体物理和微观黑洞的物理意义,构造了一些说明性情况的彭罗斯图,并表明非奇异解的最大解析扩展意味着径向坐标的反弹。

英文摘要:

We study static, spherically symmetric solutions with an electric field in an extension of general relativity (GR) containing a Ricci-squared term and formulated in the Palatini formalism. We find that all the solutions present a central core whose area is proportional to the Planck area times the number of charges. Far from the core, curvature invariants quickly tend to those of the usual Reissner-Nordström solution, though the structure of horizons may be different. In fact, besides the structures found in the Reissner-Nordström solution of GR, we find black hole solutions with just one nondegenerate horizon (Schwarzschild-like), and nonsingular black holes and naked cores. The charge-to-mass ratio of the nonsingular solutions implies that the core matter density is independent of the specific amounts of charge and mass and of order the Planck density. We discuss the physical implications of these results for astrophysical and microscopic black holes, construct the Penrose diagrams of some illustrative cases, and show that the maximal analytical extension of the nonsingular solutions implies a bounce of the radial coordinate.

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