Tidal properties of Ddimensional Tangherlini black holes
Abstract
This paper investigates tidal forces in multidimensional spherically symmetric spacetimes. We consider geodesic deviation equation in SchwarzschildTangherlini metric and its electrically charged analog. It was shown that for radial geodesics these equations can be solved explicitly as quadratures in spaces of any dimension. In the case of five, six and seven dimensional spaces, these solutions can be represented in terms of elliptic integrals. For spacetimes of higher dimension, we find the asymptotics of the solution. It was found that in the physical singularity vicinity tidal stretch along the radial direction is the stronger the greater the dimension of space. Whereas the tidal compression in transverse to radial directions, starting from a certain dimension, does not change in the main order. Also in the case of nonradial geodesics, the presence of black hole electric charge does not affect the force of transverse compression in the leading order. For nonradial geodesics with nonzero angular momentum, the local properties of solutions of geodesic deviation equations in the vicinity of a singularity are studied.
 Publication:

arXiv eprints
 Pub Date:
 July 2022
 arXiv:
 arXiv:2207.00631
 Bibcode:
 2022arXiv220700631V
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 17 pages