Virtual Black Holes in a Third Quantized Formalism

TL;DR

This paper investigates virtual black holes within a third quantization framework, highlighting how quantum fluctuations depend on factor ordering and identifying conditions for consistent spacetime foam models.

Contribution

It introduces a third quantization approach to analyze quantum fluctuations of black holes, revealing the importance of factor ordering in virtual black hole models.

Findings

Quantum fluctuations depend on factor ordering.

Only specific factor orderings support the spacetime foam model.

Certain factor orderings are consistent with virtual black hole existence.

Abstract

In this paper, we will analyse virtual black holes using the third quantization formalism. As the virtual black hole model depends critically on the assumption that the quantum fluctuations dominate the geometry of spacetime at Planck scale, we will analyse the quantum fluctuations for a black hole using third quantization. We will demonstrate that these quantum fluctuations depend on the factor ordering chosen. So, we will show that only certain values of the factor ordering parameter are consistent with virtual black holes model of spacetime foam.