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

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