Nonexistence of Time-periodic Solutions of the Dirac Equation in Kerr-Newman-(A)dS Spacetime

TL;DR

This paper proves the nonexistence of nontrivial time-periodic solutions of the Dirac equation in Kerr-Newman-(A)dS spacetime, establishing conditions under which such solutions cannot exist, especially in non-extreme cases.

Contribution

It demonstrates the nonexistence of nontrivial $L^p$ solutions in non-extreme Kerr-Newman-(A)dS spacetime and derives necessary conditions for solutions in extreme cases.

Findings

No nontrivial $L^p$ solutions in non-extreme spacetime.

Relations between energy eigenvalues and spacetime parameters in extreme cases.

Necessary conditions for existence of solutions in extreme Kerr-Newman-(A)dS and AdS.

Abstract

In this paper, we study the nonexistence of nontrivial time-periodic solutions of the Dirac equation in Kerr-Newman-(A)dS spacetime. In the non-extreme Kerr-Newman-dS spacetime, we prove that there is no nontrivial $L^p$ integrable Dirac particle for arbitrary $(\lambda,p)\in \mathbb{R}\times[2,+\infty)$. In the extreme Kerr-Newman-dS and extreme Kerr-Newman-AdS spacetime, we show the equation relations between the energy eigenvalue $\omega$, the horizon radius, the angular momentum, the electric charge and the cosmological constant if there exists nontrivial $L^p$ integrable time-periodic solution of the Dirac equation, and further give the necessary conditions for the existence of nontrivial solutions.