Multitemporal generalization of the Tangherlini solution

The n-time generalization of the Tangherlini solution [1] is considered. The equations of geodesics for the metric are integrated. For $n=2$ it is shown that the naked singularity is absent only for two sets of parameters, corresponding to the trivial extensions of the Tangherlini solution. The motion of a relativistic particle in the multitemporal background is considered. This motion is governed by the gravitational mass tensor. Some generalizations of the solution, including the multitemporal analogue of the Myers-Perry charged black hole solution, are obtained.