论文标题
由于灰尘壳的崩溃，BTZ黑洞形成的量子分析
Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell
论文作者
论文摘要
我们执行一个模型的哈密顿还原，其中2+1维重力（负宇宙常数）与圆柱形对称的灰尘壳耦合。最终的行动仅包含有限数量的自由度。相位空间由$ ads^2 $的两个副本组成 - 坐标和动量空间都弯曲。可以用$ ADS^2 $动量空间的不同贴片来识别Penrose图中的不同区域。在地平线附近，动量表示中的量化变得特别简单，在那里人们可以忽略动量非交换性。在该区域，我们计算壳半径的光谱。事实证明，这种频谱在地平线外是连续的，并且在地平线内变得离散，特征值间距与黑洞质量的平方根成正比。我们还计算了地平线附近的penrose图的不同区域之间的数值量子过渡幅度。该计算显示了将壳量子隧穿到彭罗斯图的经典区域的量子隧穿的可能性，尽管有指数降低的速率远离地平线。
We perform Hamiltonian reduction of a model in which 2+1 dimensional gravity with negative cosmological constant is coupled to a cylindrically symmetric dust shell. The resulting action contains only a finite number of degrees of freedom. The phase space consists of two copies of $ADS^2$ -- both coordinate and momentum space are curved. Different regions in the Penrose diagram can be identified with different patches of $ADS^2$ momentum space. Quantization in the momentum representation becomes particularly simple in the vicinity of the horizon, where one can neglect momentum non-commutativity. In this region, we calculate the spectrum of the shell radius. This spectrum turns out to be continuous outside the horizon and becomes discrete inside the horizon with eigenvalue spacing proportional to the square root of the black hole mass. We also calculate numerically quantum transition amplitudes between different regions of the Penrose diagram in the vicinity of the horizon. This calculation shows a possibility of quantum tunneling of the shell into classically forbidden regions of the Penrose diagram, although with an exponentially damped rate away from the horizon.
