Discreteness of Curved Spacetime from GUP

Abstract EN

Diverse theories of quantum gravity expect modifications of the Heisenberg's uncertainty principle near the Planck scale to a so-called Generalized uncertainty principle (GUP).

It was shown by some authors that the GUP gives rise to corrections to the Schrodinger , Klein-Gordon, and Dirac equations.

By solving the GUP corrected equations, the authors arrived at quantization not only of energy but also of box length, area, and volume.

In this paper, we extend the above results to the case of curved spacetime (Schwarzschild metric).

We showed that we arrived at the quantization of space by solving Dirac equation with GUP in this metric.