A minisuperspace approach for the Supersymmetric Reissner-Nordstr\"om spacetime

TL;DR

This paper develops a supersymmetric quantum cosmological model of the Reissner-Nordstr"om spacetime using a minisuperspace approach, revealing quantum and classical differences from the standard solution, including new singularities and geodesic behaviors.

Contribution

It introduces a supersymmetric extension of the Reissner-Nordstr"om spacetime within quantum cosmology using a minisuperspace approach, comparing different quantization methods.

Findings

Supersymmetry modifies the Wheeler-DeWitt equation for the model.

New singularities appear in the supersymmetric solutions.

Differences in geodesic motion are observed in supersymmetric regions.

Abstract

In this work we present a supersymmetric extension of the Reissner-Nordstr\"om spacetime in the framework of quantum cosmology. We achieve this by supersymmetrizing the Wheeler-DeWitt equation for a Kantowski-Sachs cosmological model defined in the interior region between the event and Cauchy horizons. We carry out this analysis following the Dirac and the reduced phase space quantization approaches and compare them. In the quantum regime we describe the novelties introduced by supersymmetry and highlight the differences with the pure bosonic case. At the classical level we analyse some limits that lead to metrics which are different than the usual Reissner-Nordstr\"om form. We show that in some regions of the spacetime, true singularities arise. In addition, we study the geodesics equation of a massive particle moving in the region where supersymmetry contributions are dominant.