On the spectral flow in Lorentzian manifolds (Q2568754)

Techniques from functional analysis are used in this paper in order to find the differential equation satisfied by the eigenvalues of a smooth family of Fredholm operators obtained from the index form along a geodesic in semi-Riemannian geometry of Lorentzian type. The derived formula is applied to the study of the evolution for the index function and, using a perturbation argument, a version of classical Morse index theorem for stationary Lorentzian manifold is given.