Minimal length in quantum gravity and gravitational measurements

¹ Department of Physics, Florida State University, Tallahassee - FL 32306, USA
² Department of Physics, Faculty of Science, Benha University - Benha, 13518, Egypt
³ Department of Electrical Engineering, Alexandria University - Alexandria 12544, Egypt
⁴ Theoretical Physics Group, Department of Physics, Kuwait University - P.O. Box 5969, Safat 13060, Kuwait

^(a) ahmed.ali@fsc.bu.edu.eg
^(b) afali@fsu.edu
^(c) moh.m.khalil@gmail.com
elias.vagenas@ku.edu.kw

Received: 5 August 2015
Accepted: 21 October 2015

Abstract

The existence of a minimal length is a common prediction of various theories of quantum gravity. This minimal length leads to a modification of the Heisenberg uncertainty principle to a Generalized Uncertainty Principle (GUP). Various studies showed that a GUP modifies the Hawking radiation of black holes. In this paper, we propose a modification of the Schwarzschild metric based on the modified Hawking temperature derived from the GUP. Based on this modified metric, we calculate corrections to the deflection of light, time delay of light, perihelion precession, and gravitational redshift. We compare our results with gravitational measurements to set an upper bound on the GUP parameter.