Black Hole in Discrete Gravity

We study the metric corresponding to a three-dimensional coset space $SO(4)\mathrm{/}SO(3)$ in the lattice setting. With the use of three integers $n_1,n_2$, and $n_3$, and a length scale, $l_{\mu }$, the continuous metric is transformed into a discrete space. The numerical outcomes are compared with the continuous ones. The singularity of the black hole is explored and different domains are studied.