Black holes in Truncated Higher Spin AdS${}_3$ Gravity

Abstract

We study the higher spin black holes in a truncated version of higher spin gravity in $Ad{S}_3$. 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.

23 pages;minor revision, references added; published version

References in corpus (3)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Symmetries of Holographic Minimal Models

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