On the existence of turning points in D-dimensionsal Schwarzschild-de Sitter and anti-de Sitter spacetimes

TL;DR

This paper analyzes the motion of test particles in higher-dimensional Schwarzschild-de Sitter and anti-de Sitter spacetimes, revealing how the sign of the cosmological constant affects the existence and number of horizons and turning points.

Contribution

It provides a detailed analysis of particle trajectories in d-dimensional SdS and SAdS spacetimes, highlighting the dependence on the cosmological constant's sign.

Findings

In SdS spacetime, there can be two horizons and two turning points, one horizon and one turning point, or none.

In SAdS spacetime, the horizon is associated with a unique turning point.

The structure of horizons and turning points varies significantly with the sign of .

Abstract

We investigate the motion of a test particle in a d-dimensional, spherically symmetric and static space-time supported by a mass $M$ plus a $\Lambda$-term. The motion is strongly dependent on the sign of $\Lambda$. In Schwarzschild-de Sitter (SdS) space-time ($\Lambda > 0$), besides the physical singularity at $r=0$ there are cases with two horizons and two turning points, one horizon and one turning point and the complete absence of horizon and turning points. For Schwarzschild-Anti de Sitter (SAdS) space-time ($\Lambda < 0$) the horizon coordinate is associated to a unique turning point.