Black holes in Truncated Higher Spin AdS$_3$ Gravity

TL;DR

This paper explores black hole solutions in truncated higher spin AdS$_3$ gravity theories with finite spins, analyzing their symmetries, thermodynamics, and novel features of black holes with single higher spin hair.

Contribution

It introduces and analyzes black hole solutions in truncated higher spin gravity with specific spins, revealing their symmetries and thermodynamic properties, and extends to a G2-generated higher spin gravity case.

Findings

Asymptotic symmetry is a classical W(2,4)-symmetry.

Black holes with pure spin 4 or spin 6 hair have compact entropy expressions.

These black holes are unique examples with single higher spin hair, besides spin 3 black holes.

Abstract

We study the higher spin black holes in a truncated version of higher spin gravity in $AdS_3$. This theory contains only finite number of even spins s=2,4,...,2N. We mainly focus on the simplest case, so-called (Type I and II) spin ${\tilde 4}$ gravity, which contains only spin 2 and spin 4 fields. This spin ${\tilde 4}$ gravity is as simple as spin 3 gravity, thus provides another example to test various ideas on higher spin gravity. We find that the asymptotical symmetry of this spin ${\tilde 4}$ gravity is a classical W(2,4)-symmetry. Moreover, we study the black hole solution with pure spin 4 hair and discuss its thermodynamics. One important feature of this black hole is that its entropy could be written in compact forms. Furthermore, we investigate a $G_2$ generated higher spin gravity. This higher spin gravity only contains spin 2 and spin 6 fields which makes it different from other kinds of higher spin gravity. We find the corresponding black hole with spin 6 hair, and discuss its thermodynamics analytically. It turns out that the black holes with spin 4 or spin 6 hair constructed in this paper are the only black holes with single higher spin hair, besides the spin 3 black hole found in arXiv:1103.4304.