Axial-vector anomalies and the index theorem in charged Schwarzschild and Taub-NUT spaces

The index theorem gives a topological expression for the excess of zero-eigenvalues of positive chirality over negative chirality solutions of the Dirac equation. These solutions are derived directly from the Dirac equation in charged Euclideanized Schwarzschild and Taub-NUT spaces, and the results are compared with the predictions of the index theorem.