论文标题
从量子降低的环重力中了解量子黑洞
Understanding quantum black holes from quantum reduced loop gravity
论文作者
论文摘要
我们系统地研究了Alesci,Bahrami和Pranzetti(ABP)最近得出的回路量子黑洞(LQBHS)的自上而下模型。为了了解模型的结构,我们首先通过适当的限制来得出几种众所周知的LQBH解决方案。其中包括Böhmer-Vandersloot和Ashtekar-Olmedo-Singh模型,这些模型都是通过在MinisuperSpace量化框架内的所谓自下而上的聚合中获得的。然后,我们研究ABP模型,并发现仅当两球的半径为Planck尺寸时,逆体积校正才变得很重要。对于宏观黑洞,在过渡表面获得的最小半径总是比普朗克尺度大得多,因此这些校正始终是亚领先的。过渡表面将整个时空划分为两个区域,在其中一个区域中,时空是渐近的schwarzschild,而在另一个区域中,渐近行为敏感地取决于模型中涉及的两个旋转数的比率,并且可以分为三个不同的类别。在一个类别中,两个球体正交的2平面正交中的时空在渐近上是平坦的,在第二个球体上,它甚至都不是共形的,而在第三个球体中,它可以通过选择模型的自由参数来适当地渐近地构型。在后者中,它是渐近的保姆。但是,在这三个类别中的任何一个中,与自下而上的方法获得的模型形成鲜明对比的是,时空已经完成,并且在过渡表面的两侧不需要其他扩展。特别是,不存在相同的多个黑洞和白洞结构。
We systematically study the top-down model of loop quantum black holes (LQBHs), recently derived by Alesci, Bahrami and Pranzetti (ABP). To understand the structure of the model, we first derive several well-known LQBH solutions by taking proper limits. These include the Böhmer-Vandersloot and Ashtekar-Olmedo-Singh models, which were all obtained by the so-called bottom-up polymerizations within the framework of the minisuperspace quantizations. Then, we study the ABP model, and find that the inverse volume corrections become important only when the radius of the two-sphere is of the Planck size. For macroscopic black holes, the minimal radius obtained at the transition surface is always much larger than the Planck scale, and hence these corrections are always sub-leading. The transition surface divides the whole spacetime into two regions, and in one of them the spacetime is asymptotically Schwarzschild-like, while in the other region, the asymptotical behavior sensitively depends on the ratio of two spin numbers involved in the model, and can be divided into three different classes. In one class, the spacetime in the 2-planes orthogonal to the two spheres is asymptotically flat, and in the second one it is not even conformally flat, while in the third one it can be asymptotically conformally flat by properly choosing the free parameters of the model. In the latter, it is asymptotically de Sitter. However, in any of these three classes, sharply in contrast to the models obtained by the bottom-up approach, the spacetime is already geodesically complete, and no additional extensions are needed in both sides of the transition surface. In particular, identical multiple black hole and white hole structures do not exist.