Tidal properties of D-dimensional Tangherlini black holes

TL;DR

This paper analyzes tidal forces in higher-dimensional Tangherlini black holes, providing explicit solutions for geodesic deviation and revealing how tidal effects vary with dimension and charge.

Contribution

It offers explicit solutions for tidal forces in D-dimensional Tangherlini black holes and explores their behavior near singularities, including effects of charge and angular momentum.

Findings

Radial tidal stretch increases with dimension.

Transverse tidal compression remains largely unaffected by charge.

Solutions involve elliptic integrals for dimensions 5-7.

Abstract

This paper investigates tidal forces in multidimensional spherically symmetric spacetimes. We consider geodesic deviation equation in Schwarzschild-Tangherlini 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 non-radial geodesics, the presence of black hole electric charge does not affect the force of transverse compression in the leading order. For non-radial geodesics with non-zero angular momentum, the local properties of solutions of geodesic deviation equations in the vicinity of a singularity are studied.