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D维黑洞内部的有效聚合物动力学

Effective Polymer Dynamics of D-Dimensional Black Hole Interiors

A. Peltola, G. Kunstatter

备注：
14 pages, 4 figures. Added discussion about the dependency on auxiliary structures. Matches with the published version
发表信息：
Phys.Rev.D80:044031,2009
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摘要：

我们考虑两种不同的有效的聚合计划适用于D维，球对称黑洞内部。它表明，聚合的广义面积变量单独导致一个完整的，定期的，单视界时空中的经典奇异性被取代的反弹。反弹半径与均匀内部坐标的重新缩放无关，但取决于任意基准单元的大小。因此，该模型必然是不完整的。尽管如此，它还是有许多有趣的特征：在反弹之后，内部区域渐近于无限膨胀的Kantowski-Sachs时空。如果解在视界上解析地连续，则黑洞的外部由于聚合而呈现出渐近消失的量子修正。在除了四维以外的所有时空维度中，这种衰减太慢，以至于不能保证在庞加莱变换下的外渐近区域的不变性。因此，四维解是唯一满足渐近平坦性准则的例子。在这种情况下，可以计算量子校正的温度和熵。我们还表明，聚合的相空间变量，面积和共形模式的度量，一般会导致一个多视界的解决方案，这是让人想起聚合的迷你超空间模型的球对称黑洞圈量子引力。

英文摘要：

We consider two different effective polymerization schemes applied to D-dimensional, spherically symmetric black hole interiors. It is shown that polymerization of the generalized area variable alone leads to a complete, regular, single-horizon spacetime in which the classical singularity is replaced by a bounce. The bounce radius is independent of rescalings of the homogeneous internal coordinate, but does depend on the arbitrary fiducial cell size. The model is therefore necessarily incomplete. It nonetheless has many interesting features: After the bounce, the interior region asymptotes to an infinitely expanding Kantowski-Sachs spacetime. If the solution is analytically continued across the horizon, the black hole exterior exhibits asymptotically vanishing quantum-corrections due to the polymerization. In all spacetime dimensions except four, the fall-off is too slow to guarantee invariance under Poincare transformations in the exterior asymptotic region. Hence the four-dimensional solution stands out as the only example which satisfies the criteria for asymptotic flatness. In this case it is possible to calculate the quantum-corrected temperature and entropy. We also show that polymerization of both phase space variables, the area and the conformal mode of the metric, generically leads to a multiple horizon solution which is reminiscent of polymerized mini-superspace models of spherically symmetric black holes in Loop Quantum Gravity.

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