Sharp eigenvalue enclosures for the perturbed angular Kerr-Newman Dirac operator
Provides rigorous eigenvalue bounds for a specific class of operators in mathematical physics, but is incremental as it extends existing techniques to a particular problem.
The paper presents a certified strategy for computing sharp eigenvalue enclosures for matrix differential operators with singular coefficients, applied to the angular Kerr-Newman Dirac operator. The method sharpens existing benchmarks by several orders of magnitude for unperturbed cases.
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.