Nonexistence of Majorana fermions in Kerr-Newman type spacetimes with nontrivial charge

TL;DR

This paper demonstrates that in Kerr-Newman and related spacetimes with nonzero charge, time-periodic Majorana fermions cannot exist outside the event horizon due to the structure of the Dirac equation.

Contribution

It provides a proof of the nonexistence of differentiable Majorana fermions in charged Kerr-Newman spacetimes, extending understanding of fermionic solutions in these backgrounds.

Findings

No time-periodic Majorana fermions outside the horizon when charge is nonzero.

Four differential equations lead to algebraic identities constraining fermion solutions.

Majorana fermions cannot be transformed into radial and angular equations in this context.

Abstract

We show that the Dirac equation is separated into four differential equations for time-period Majarana fermions in Kerr-Newman, Kerr-Newman-(A)dS spacetimes. Although they can not be transformed into radial and angular equations, the four differential equations yield two algebraic identities. When the electric or magnetic charge is nonzero, they conclude that there is no differentiable time-periodic Majorana fermions outside the event horizon in Kerr-Newman and Kerr-Newman-AdS spacetimes, or between the event horizon and the cosmological horizon in Kerr-Newman-dS spacetime.