Kretschmann Invariant and Relations Between Spacetime Singularities, Entropy and Information

Abstract

Using a yukawa type of metric we derive the kretschmann scalar for a general static black hole of a certain mass. The scalar gives the curvature of the space time as a function of the radial distance in the vicinity as well as inside of the black hole. Furthermore, the kretschmann scalar helps us understand the appearance of the black hole as a whole entity. It can be applied in solar mass size black holes, neutron stars or super massive 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 dependence of the curvature on the entropy and number of information in nats is derived.