Multitemporal generalization of the Tangherlini solution

TL;DR

This paper extends the Tangherlini solution to multiple temporal dimensions, analyzing geodesics, singularities, and particle motion, and introduces generalizations including multitemporal Myers-Perry solutions.

Contribution

It presents the n-time generalization of the Tangherlini solution, analyzes geodesic equations, and explores multitemporal black hole solutions with new properties.

Findings

Naked singularities are absent only for specific parameter sets in the two-time case.

The motion of particles is governed by a gravitational mass tensor in multitemporal backgrounds.

Generalizations include multitemporal analogues of Myers-Perry charged black holes.

Abstract

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.