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.
Highlights
When we study any space time, it is important above other things to know whether the spacetime is regular or not
In Equation 18 a formula for the Kretschmann Scalar (KS) is given for a general spherically symmetric metric which we apply to a fifth force metric that incorporates a Yukawa correction and notice that KS possesses an essential singularity at the horizon
We write the metric of a Yukawa type of Schwarzschild black hole that is curved in along both the time and radial coordinate and we notice in Equation 29 that the singularity disappears
Summary
When we study any space time, it is important above other things to know whether the spacetime is regular or not. In many cases one of the most useful ways to check that is by checking for the finiteness of the Kretschmann Scalar (from on KS) which sometimes is called Riemann tensor squared, in other words Equation 1:. Once the Christoffel symbols are calculated we calculate the Riemann tensor to be Equation 3: Ioannis Gkigkitzis et al / Physics International 5 (1): 103-111, 2014. In the case of black holes the calculation of the scalar is required if somebody wants to derive and investigate the curvature of a black hole. The need for calculation of the KS emanates from the fact that in vacuum the field equations of general relativity a zero Gaussian curvature at and in the black hole, giving no information about curvature of the spacetime and the K scalar need to be computed. In an effort to investigate the relation between entropy, information and geometry we write the Yukawa black hole scalar as a function of entropy and information number N
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