Black Holes and Boson Stars with One Killing Field in Arbitrary Odd Dimensions

TL;DR

This paper generalizes recent five-dimensional results to arbitrary odd dimensions, constructing rotating black hole and boson star solutions with scalar hair in AdS space, and analyzing their properties and thermodynamics.

Contribution

It extends the construction of scalar-hairy rotating black holes and boson stars to all odd dimensions, providing explicit perturbative solutions and thermodynamic analysis.

Findings

Scalar field carries most of the angular momentum in D>5.

In D>5, scalar field dominates the energy content.

Thermodynamics are primarily governed by the scalar field in D>5.

Abstract

We extend the recent D=5 results of Dias, Horowitz and Santos by finding asymptotically AdS rotating black hole and boson star solutions with scalar hair in arbitrary odd spacetime dimension. Both the black holes and the boson stars are invariant under a single Killing vector field which co-rotates with the scalar field and, in the black hole case, is tangent to the generator of the horizon. Furthermore, we explicitly construct boson star and small black hole ($r_+ \ll \ell$) solutions perturbatively assuming a small amplitude for the scalar field, resulting in solutions valid for low energies and angular momenta. We find that just as in D=5, the angular momentum is primarily carried by the scalar field in $D>5$, whereas unlike D=5 the energy is also primarily carried by the scalar field in $D>5$; the thermodynamics in D=5 are governed by both the black hole and scalar field whereas in $D>5$ they are governed primarily by the scalar field alone. We focus on cataloguing these solutions for the spacetime dimensions of interest in string theory, namely $D=5,7,9,11$.