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Advances in High Energy Physics
Volume 2013 (2013), Article ID 124543, 4 pages
http://dx.doi.org/10.1155/2013/124543
Research Article

Discreteness of Curved Spacetime from GUP

Department of Mathematics, Faculty of Science, University of Mansoura, Elmansoura 35516, Egypt

Received 9 October 2013; Revised 13 December 2013; Accepted 16 December 2013

Academic Editor: Elias C. Vagenas

Copyright © 2013 Ahmad Adel Abutaleb. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.