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arXiv 0811.2196gr-qchep-th
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圈量子黑洞的时空结构

Space-Time Structure of Loop Quantum Black Hole

Leonardo Modesto

备注：
17 pages, 19 figures
发表信息：
Int. J. Theor. Phys. 49, 1649 (2010)
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摘要：

本文改进了圈量子黑洞（LQBH）的常聚合参数守恒方法的半经典分析。特别是，我们把注意力集中在时空结构上。我们已经介绍了一个非常简单的修改球对称哈密顿约束在其完整的版本。当聚合物参数趋于零时，新的量子约束退化为经典约束，利用这一修正，我们得到了一大类由聚合物参数的泛函数参数化的半经典解。我们已经发现，只有这个函数的一个特定的选择再现黑洞解与正确的渐近平坦的限制。在r=0时，半经典度规是正则的，Kretschmann不变量在L-Planck有一个极大值。拨子的径向位置不依赖于黑洞质量和聚合物参数。半经典解与Reissner-Nordstrom度规非常相似。我们明确地构建了卡特-彭罗斯图，给出了时空及其最大扩展的因果描述。LQBH度量在两个渐近平坦区域之间插值，r到无穷大区域和r到0区域。我们研究了半经典溶液的热力学。温度，熵和蒸发过程是有规律的，可以独立于聚合物参数定义。研究了聚合参数趋于零时的特殊度规。这个度规在r=0时是正则的，在r = 2 m时只有一个事件视界。Kretschmann不变最大值只依赖于L-Planck。聚合参数对黑洞奇异性分辨没有任何影响。热力学是一样的。

英文摘要：

In this paper we have improved the semiclassical analysis of loop quantum black hole (LQBH) in the conservative approach of constant polymeric parameter. In particular we have focused our attention on the space-time structure. We have introduced a very simple modification of the spherically symmetric Hamiltonian constraint in its holonomic version. The new quantum constraint reduces to the classical constraint when the polymeric parameter goes to zero.Using this modification we have obtained a large class of semiclassical solutions parametrized by a generic function of the polymeric parameter. We have found that only a particular choice of this function reproduces the black hole solution with the correct asymptotic flat limit. In r=0 the semiclassical metric is regular and the Kretschmann invariant has a maximum peaked in L-Planck. The radial position of the pick does not depend on the black hole mass and the polymeric parameter. The semiclassical solution is very similar to the Reissner-Nordstrom metric. We have constructed the Carter-Penrose diagrams explicitly, giving a causal description of the space-time and its maximal extension. The LQBH metric interpolates between two asymptotically flat regions, the r to infinity region and the r to 0 region. We have studied the thermodynamics of the semiclassical solution. The temperature, entropy and the evaporation process are regular and could be defined independently from the polymeric parameter. We have studied the particular metric when the polymeric parameter goes towards to zero. This metric is regular in r=0 and has only one event horizon in r = 2m. The Kretschmann invariant maximum depends only on L-Planck. The polymeric parameter does not play any role in the black hole singularity resolution. The thermodynamics is the same.

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