# Stationary solutions of the second-order equation for fermions in Kerr-Newman space-time

## TL;DR

This paper investigates stationary solutions of the second-order fermion equation in Kerr-Newman space-time, revealing bound states near horizons, their absence in extreme fields, and discrete spectra in naked singularities, challenging cosmic censorship.

## Contribution

It demonstrates the existence of bound states and discrete spectra for fermions in Kerr-Newman space-time using a second-order quantum equation, differing from Dirac equation results.

## Key findings

- Bound states exist near event horizons for non-extreme Kerr-Newman fields.
- No stationary bound states in extreme Kerr-Newman fields.
- Discrete energy spectra are found in naked Kerr-Newman singularities.

## Abstract

When using the quantum mechanical second-order equation with the effective potential of the Kerr-Newman (KN) field for fermions, results were obtained that qualitatively differ from results obtained when using the Dirac equation. In presence of two event horizons, existence of degenerate stationary bound states was proved for charged and uncharged fermions with square integrable wave functions vanishing on event horizons. The fermions in such states are localized near the event horizons with the maxima of probability densities away from the event horizons by fractions of the Compton wave length of fermions versus the values of coupling constants, the values of angular and orbital momenta $j,l$ and the value of the azimuthal quantum number $m_{\varphi}$. In the case of extreme KN fields, absence of stationary bound states of fermions was shown for any values of coupling constants. Existence of discrete energy spectra was shown for charged and uncharged fermions in the field of naked KN singularity at definite values of physical parameters. The KN naked singularity poses no threat to cosmic censorship because of the regular behavior of the effective potentials of the KN field in quantum mechanics with the second-order equation.

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Source: https://tomesphere.com/paper/1904.05791