论文标题
关于Schwarzschild问题的离散版本
On the discrete version of the Schwarzschild problem
论文作者
论文摘要
我们考虑了在路径积分方法中量化的一般相对论的离散regge cyculus公式中的Schwarzschild类型解决方案。早些时候，我们发现了一种机制，即对雷格长度的背景尺度的固定宽松。这个基本长度量表由普朗克量表和该理论的量子扩展的一些自由参数定义。此外，对四面体之间的度量变化的膨胀作用降低了，在主要近似中，是希尔伯特 - 因斯坦作用的有限差异形式。对于Schwarzschild问题，先验一般非球面对称的ANSATZ，我们获得了其离散版本的有限差方程。这定义了一种较大距离的解决方案，该解决方案靠近连续的Schwarzschild几何形状，并且中心的度量和有效曲率在基本长度尺度上切断。也可以考虑缓慢的旋转（刺激性度量）。因此，我们以零顺序获得了量子框架中经典背景的一般方法：这是该理论扰动扩展的最佳起点。有限差方程是经典的，基础长度量表具有量子。奇异性（如果有的话）得到解决。
We consider a Schwarzschild type solution in the discrete Regge calculus formulation of general relativity quantized within the path integral approach. Earlier, we found a mechanism of a loose fixation of the background scale of Regge lengths. This elementary length scale is defined by the Planck scale and some free parameter of such a quantum extension of the theory. Besides, Regge action was reduced to an expansion over metric variations between the tetrahedra and, in the main approximation, is a finite-difference form of the Hilbert-Einstein action. Using for the Schwarzschild problem a priori general non-spherically symmetrical ansatz, we get finite-difference equations for its discrete version. This defines a solution which at large distances is close to the continuum Schwarzschild geometry, and the metric and effective curvature at the center are cut off at the elementary length scale. Slow rotation can also be taken into account (Lense-Thirring-like metric). Thus we get a general approach to the classical background in the quantum framework in zero order: it is an optimal starting point for the perturbative expansion of the theory; finite-difference equations are classical, the elementary length scale has quantum origin. Singularities, if any, are resolved.
