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