Sharp eigenvalue enclosures for the perturbed angular Kerr-Newman Dirac operator

TL;DR

This paper introduces a method for accurately enclosing eigenvalues of matrix differential operators with singular coefficients, using second order spectrum computations, and demonstrates its effectiveness on the angular Kerr-Newman Dirac operator.

Contribution

The paper presents a new certified strategy for sharp eigenvalue enclosures for perturbed angular Kerr-Newman Dirac operators, with explicit convergence rates and validation against benchmarks.

Findings

Validated and sharpened existing benchmarks by several orders of magnitude.

Established explicit convergence rates based on eigenfunction regularity.

Demonstrated effectiveness for smooth perturbations of the angular Kerr-Newman Dirac operator.

Abstract

A certified strategy for determining sharp intervals of enclosure for the eigenvalues of matrix differential operators with singular coefficients is examined. The strategy relies on computing the second order spectrum relative to subspaces of continuous piecewise linear functions. For smooth perturbations of the angular Kerr-Newman Dirac operator, explicit rates of convergence due to regularity of the eigenfunctions are established. Existing benchmarks are validated and sharpened by several orders of magnitude in the unperturbed setting.