Tidal Forces in Kottler Spacetimes

TL;DR

This paper analyzes tidal forces near Kottler black holes, deriving solutions for geodesic deviation, revealing sign changes in tidal components, and comparing with Reissner-Nordstrom black holes, highlighting unique behaviors influenced by the cosmological constant.

Contribution

It provides the first analytical solutions for geodesic deviation in Kottler spacetimes and explores the effects of the cosmological constant on tidal forces.

Findings

Radial tidal force component changes sign outside the horizon for negative cosmological constant.

Sign change of angular tidal components occurs between two horizons for specific cosmological constant values.

Non-analytical behavior of geodesic deviation vectors observed in Anti-de Sitter spacetime.

Abstract

The article considers tidal forces in the vicinity of the Kottler black hole. We find a solution of the geodesic deviation equation for radially falling bodies, which is determined by elliptic integrals. And also the asymptotic behavior of all spatial geodesic deviation vector components were found. We demonstrate that the radial component of the tidal force changes sign outside the single event horizon for any negative values of the cosmological constant, in contrast to the Schwarzschild black hole, where all the components of the tidal force are sign-constant. We also find the similarity between the Kottler black hole and the Reissner-Nordstrom black hole, because we indicate the value of the cosmological constant, which ensures the existence of two horizons of the black hole, between which the angular components of the tidal force change sign. It was possible to detect non-analytical behavior of geodesic deviation vector components in Anti-de Sitter spacetime and to describe it locally.