Minimal Length in quantum gravity and gravitational measurements

TL;DR

This paper explores how a minimal length predicted by quantum gravity modifies classical gravitational effects, proposing a GUP-based metric correction and comparing theoretical predictions with measurements to constrain quantum gravity parameters.

Contribution

It introduces a modified Schwarzschild metric derived from GUP-influenced Hawking temperature and applies it to calculate corrections to key gravitational phenomena.

Findings

Upper bound on GUP parameter established from observational data

Modified predictions for light deflection and gravitational redshift

Demonstrates impact of quantum gravity on classical tests of general relativity

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.