A Variational Principle for Block Operator Matrices and its Application to the Angular Part of the Dirac Operator in Curved Spacetime

Abstract

The operator associated to the angular part of the Dirac equation in the Kerr-Newman background metric is a block operator matrix with bounded diagonal and unbounded off-diagonal entries. The aim of this paper is to establish a variational principle for block operator matrices of this type and to derive thereof upper and lower bounds for the angular operator mentioned above. In the last section, these analytic bounds are compared to numerical values from the literature.

References in corpus (2)

• On the eigenvalues of operators with gaps. Application to Dirac operators
• Spectral Analysis of Radial Dirac Operators in the Kerr-Newman Metric and its Applications to Time-periodic Solutions

Cited by in corpus (5)

• The massive Dirac field on a rotating black hole spacetime: Angular solutions
• The effective method to calculate eigenvalues of Chandrasekhar-Page angular equations
• On the eigenvalues of the fermionic angular eigenfunctions in the Kerr metric
• On the existence of eigenvalues of a one-dimensional Dirac operator
• Sharp eigenvalue enclosures for the perturbed angular Kerr-Newman Dirac operator