KRETSCHMANN INVARIANT AND RELATIONS BETWEEN SPACETIME SINGULARITIES ENTROPY AND INFORMATION

Abstract

Using a Yukawa type of metric we derive the Kretschmann scalar (KS) for a general static black hole of mass M. The scalar gives the curvature of the spacetime as a function of the radial distance r in the vicinity as well as inside of the black hole. Furthermore, the Kretschmann scalar helps us understand the black hole's appearance as a "whole entity". It can be applied in solar mass size black holes, neutron stars or supermassive black holes at the center of various galaxies. In an effort to investigate the connection of geometry to entropy and information, the Kretschmann scalar for a solar mass Yukawa Schwarzschild and simple Schwarzschild black holes are derived. Moreover, the curvature's dependence on the entropy and number of information N in nats is derived.