Extremal Charged Black Holes with a Twisted Extra Dimension

TL;DR

This paper constructs extremal charged black hole solutions in odd dimensions with a twisted extra dimension, analyzing their horizon structure, curvature properties, and extensions, including cases with a positive cosmological constant.

Contribution

It introduces new extremal charged black hole solutions with a twisted S^1 dimension on Euclidean Taub-NUT spaces, including their horizon and curvature characteristics.

Findings

Existence of null hypersurfaces with vanishing expansion indicating black hole horizons.

Metrics admit C^0 extension across horizons despite curvature divergences.

Solutions with positive cosmological constant are also constructed.

Abstract

We construct odd-dimensional extremal charged black hole solutions with a twisted S^1 as an extra dimension on generalized Euclidean Taub-NUT spaces. There exists a null hypersurface where an expansion for an outgoing null geodesic congruence vanishes, then these spacetimes look like black holes. We show that the metrics admit C^0 extension across the horizon, but some components of Riemann curvature diverge there if the dimension is higher than five. The singularity is not much strong so that an observer along a free-fall geodesic can traverse the horizon. We also show solutions with a positive cosmological constant.