Electric Charges and Magnetic Monopoles in Gravity's Rainbow

TL;DR

This paper investigates how quantum fluctuations in Gravity's Rainbow could induce electric and magnetic charges, estimating their sizes and exploring implications for fundamental particles like electrons and magnetic monopoles.

Contribution

It introduces a semi-classical approach to compute graviton one-loop effects in Gravity's Rainbow, linking quantum fluctuations to induced charges without regularization schemes.

Findings

Electron and monopole sizes are of Planckian scale.

Magnetic monopole radius exceeds electron radius.

Results are consistent across Schwarzschild and de Sitter backgrounds.

Abstract

In this work, we explore the possibility that quantum fluctuations induce an electric or magnetic charge or both, in the context of Gravity's Rainbow. A semi-classical approach is adopted, where the graviton one-loop contribution to a classical energy in a background spacetime is computed through a variational approach with Gaussian trial wave functionals. The energy density of the graviton one-loop contribution, in this context, acts as a source for the electric/magnetic charge. The ultraviolet (UV) divergences, which arise analyzing this procedure, are kept under control with the help of an appropriate choice of the Rainbow's functions. In this way we avoid the introduction of any regularization/renormalization scheme. A comparison with the observed data lead us to determine the size of the electron and of the magnetic monopole which appear to be of Planckian size. Both results seem to be of the same order for a Schwarzschild and a de Sitter background, respectively. Estimates on the magnetic monopole size have been done with the help of the Dirac quantization procedure. We find that the monopole radius is larger than the electron radius. Even in this case the ratio between the electric and magnetic monopole radius appears to be of the same order for both geometries.