Particle creation in the presence of minimal length: The time dependent gauge

TL;DR

This paper investigates how a minimal length affects scalar particle pair creation in a constant electric field, deriving modified probabilities and black hole thermodynamics, and analyzing the limitations of the WKB approximation under these conditions.

Contribution

It provides a closed-form Green's function for pair creation with minimal length and explores the resulting modifications to Hawking temperature and entropy, highlighting the inaccuracy of WKB approximation.

Findings

Minimal length introduces a logarithmic correction to Hawking temperature.

WKB approximation fails to give exact pair production rate with minimal length.

Derived explicit Green's function for scalar pair creation in this context.

Abstract

In this paper we have studied the problem of scalar particles pair creation by a constant electric field in the presence of a minimal length. A closed expression for the corresponding Green's function is obtained via path integral approach. Then by projecting this function on the outgoing particle and antiparticle states we have calculated the probability to create a pair of particles and the number density of created particles. From this, we have deduced the modifications brought by the minimal length to Hawking temperature and black hole entropy. It is shown that the first correction is a logarithmic term with a negative numerical factor. We have also examined the semiclassical WKB approximation in the calculation of the pair production rate. The result is that, unlike the ordinary case, the WKB approximation in the presence of a minimal length does not give the exact rate even for the constant electric field.