  Degree of mobility of a (pseudo-Riemannian) metric is the dimension of the
space of metrics geodesically equivalent to it. We describe all possible values
of the degree of mobility on a simply connected n-dimensional manifold of
lorentz signature. As an application we calculate all possible differences
between the dimension of the projective and the isometry groups. One of the
main new technical results in the proof is the description of all parallel
symmetric (0,2)-tensor fields on cone manifolds of signature $(n-1,2).
