论文标题
围绕黑洞的量子薄壳
A quantum thin shell surrounding a Black Hole
论文作者
论文摘要
在先前的工作中，我们获得了精确的解决方案，用于稀薄的粉尘壳的适当时间量子力学，并在真空中崩溃。我们将这些结果扩展到围绕预先存在的黑洞的灰尘壳的量子崩溃。迄今为止，该系统难以获得该系统的精确解决方案，我们通过Gentzel-Kramers-brillouin（WKB）近似建立了量子壳的基本特征，仅当壳的质量比Planck质量大得多时，这才有效。与真空崩溃有许多相似之处：仅存在结合状态，并且壳的适当能量光谱不受中央黑洞的存在而影响该阶。在黑洞地平线附近没有波浪函数的特征或区分特征。它在中心消失，并在原点和经典的禁区之间振荡，超越了它的成倍衰减。
In a previous work we obtained exact solutions for the proper time quantum mechanics of a thin dust shell, collapsing in a vacuum. We extend these results to the quantum collapse of a dust shell surrounding a pre-existing black hole. In lieu of exact solutions, which have so far proved difficult to obtain for this system, we establish the essential features of the quantum shell through a Wentzel-Kramers-Brillouin (WKB) approximation, which is valid only when the mass of the shell is much greater than the Planck mass. There are many similarities with the vacuum collapse: only bound states exist and the proper energy spectrum of the shell is unaffected by the presence of the central black hole to this order. There are no peculiar or distinguishing features of the wave function near the black hole horizon. It vanishes at the center and oscillates between the origin and the classically forbidden region, beyond which it decays exponentially.
