Chaotic motion in multi-black hole spacetimes and holographic screens

TL;DR

This paper studies chaotic geodesic motion in multi-black hole spacetimes across dimensions and explores how fractal structures in phase space influence holographic screens, revealing universal chaotic features.

Contribution

It demonstrates that chaotic geodesic behavior and fractal phase space structures are present in higher-dimensional multi-black hole spacetimes, extending known 4D results.

Findings

Chaotic motion occurs in higher dimensions similar to 4D cases.

Phase space exhibits fractal boundaries with a specific fractal dimension.

Fractal structures on holographic screens are induced by phase space chaos.

Abstract

We investigate the geodesic motion in $D-$dimensional Majumdar-Papapetrou multi-black hole spacetimes and find that the qualitative features of the D=4 case are shared by the higher dimensional configurations. The motion of timelike and null particles is chaotic, the phase space being divided into basins of attraction which are separated by a fractal boundary, with a fractal dimension $d_B$. The mapping of the geodesic trajectories on a screen placed in the asymptotic region is also investigated. We find that the fractal properties of the phase space induces a fractal structure on the holographic screen, with a fractal dimension $d_B-1$.