Kretschmann Invariant and Relations Between Spacetime Singularities, Entropy and Information

TL;DR

This paper derives the Kretschmann scalar for static black holes using a Yukawa-type metric and explores its relation to entropy and information, providing insights into spacetime curvature and black hole properties.

Contribution

It introduces a novel application of the Kretschmann scalar to relate spacetime curvature with entropy and information in black holes using a Yukawa metric.

Findings

Derived the Kretschmann scalar for various black hole models.

Established a mathematical relation between curvature, entropy, and information.

Applicable to different black hole sizes, including solar mass and supermassive black holes.

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.