Ergosphere Geometry and Thermodynamic Properties of Boosted Kerr-Taub-NUT Solutions in Kaluza-Klein Theory

TL;DR

This paper studies boosted Kerr-Taub-NUT black holes in Kaluza-Klein theory, revealing how boosts affect ergoregion size and thermodynamics, highlighting geometric signatures of extra dimensions.

Contribution

It demonstrates the invariance of the stationary limit surface under boosts and shows how boosts enlarge the ergoregion volume without changing horizon properties.

Findings

Boosts enlarge the ergoregion volume significantly.

The stationary limit surface location remains invariant under boosts.

The first law of thermodynamics holds with dyonic contributions.

Abstract

We investigate rotating black holes obtained by applying a Kaluza-Klein boost to the Kerr-Taub-NUT spacetime and study the resulting four-dimensional geometry and thermodynamics after dimensional reduction. The boost along the compact direction generates an Einstein-Maxwell-Dilaton black hole in which the electric charge originates purely from higher-dimensional momentum rather than from an independent matter source. We demonstrate that the coordinate location of the stationary limit surface, defined by the condition $g_{tt}=0$ in the Einstein frame, is invariant under the Kaluza-Klein boost. Nevertheless, the boost induces a substantial enlargement of the \emph{physical} ergoregion, as measured by the proper spatial volume on constant-time hypersurfaces, through its modification of the induced spatial metric. We further verify the first law of black-hole thermodynamics with both the electric and magnetic Kaluza-Klein work terms included -- the latter being a genuinely dyonic feature generated by the interplay of the boost with the NUT charge -- and carefully distinguish the seed mass parameter from the asymptotic ADM mass and from the horizon Komar mass. Our results establish a clear separation between boost-invariant horizon thermodynamics and boost-dependent global geometric properties. In particular, higher-dimensional momentum enhances the effective inertial-frame rotation measured by ZAMOs and ergoregion volume without altering the horizon radius, entropy, or temperature, providing a clean geometric signature of extra dimensions in rotating black hole spacetimes.