Zitterbewegung in the vicinity of the Chern-Simons black hole

TL;DR

This paper investigates the Zitterbewegung effect near Chern-Simons black holes in four and five dimensions, analyzing how the effect's amplitude and current depend on space dimension and radial distance.

Contribution

It provides a novel analysis of Zitterbewegung in higher-dimensional black hole spacetimes with torsion, revealing how the effect varies with dimension and proximity to the horizon.

Findings

Zitterbewegung amplitude decreases as space dimension increases.

The current density increases with radial distance from the event horizon.

Qualitative similarity of trembling motion observed across dimensions.

Abstract

We consider zitterbewegung (ZB) effect in four and five-dimensional space in the vicinity of the Chern-Simons black hole with torsion. The metric is taken in the traditional spherically symmetric form. We consider the equation for the current in the framework of the Schr\"odinger representation. Dependences of the electric current density on time is calculated for different dimension of space. In particular, it is shown that, with an increase in the space dimension, the effect of trembling motion qualitatively coincides. As the dimension increases, the amplitude of this effect decreases. Also, we investigate the dependence of the current on the radial coordinate for different dimensions of space. We obtain that when away from the event horizon the current ZB increases.