Black string and velocity frame dragging

TL;DR

This paper studies velocity frame dragging effects in boosted black string and Kaluza-Klein bubble solutions, revealing how compactification affects the observer independence of velocity and the formation of an ergoregion.

Contribution

It demonstrates that compactification prevents nullification of frame dragging effects and identifies the momentum parameter as an observer-independent quantity.

Findings

Velocity frame dragging cannot be removed in compactified spacetimes.

A spherical ergoregion forms around the black string due to dragging.

The momentum parameter along the compact dimension is observer-independent.

Abstract

We investigate velocity frame dragging with the boosted Schwarzschild black string solution and the boosted Kaluza-Klein bubble solution, in which a translational symmetry along the boosted $z$-coordinate is implemented. The velocity frame dragging effect can be nullified by the motion of an observer using the boost symmetry along the $z-$coordinate if it is not compact. However, in spacetime with the compact $z-$coordinate, we show that the effect cannot be removed since the compactification breaks the global Lorentz boost symmetry. As a result, the comoving velocity is dependent on $r$ and the momentum parameter along the $z-$coordinate becomes an observer independent characteristic quantity of the black string and bubble solutions. The dragging induces a spherical ergo-region around the black string.