Lifshitz black holes in higher spin gravity

TL;DR

This work constructs and analyzes Lifshitz spacetimes within three-dimensional higher spin gravity using $SL(3,\mathbb{R})\times SL(3,\mathbb{R})$ Chern-Simons theory. It demonstrates a realizable Lifshitz algebra at the boundary and develops a holonomy-based framework to define regular Lifshitz black holes, deriving their thermodynamics through a canonical action and holonomy constraints. The study identifies multiple thermodynamic branches, isolates a physically sensible one that supports a regular-horizon gauge, and extends the construction to Lifshitz vacua and black holes in $hs(\lambda)$, offering a route to Lifshitz holography with higher spin fields. These results provide a gauge-invariant characterization of Lifshitz black holes in higher spin gravity and pave the way for exploring finite-temperature dynamics of Lifshitz-like dual field theories.

Abstract

We study asymptotically Lifshitz solutions to three dimensional higher spin gravity in the SL(3,R)xSL(3,R) Chern-Simons formulation. We begin by specifying the most general connections satisfying Lifshitz boundary conditions, and we verify that their algebra of symmetries contains a Lifshitz sub-algebra. We then exhibit connections that can be viewed as higher spin Lifshitz black holes. We show that when suitable holonomy conditions are imposed, these black holes obey sensible thermodynamics and possess a gauge in which the corresponding metric exhibits a regular horizon.

Figures (3)

• Figure 1: Temperature, entropy and chemical potential of the $n=0$ branch
• Figure 2: Temperature, entropy and chemical potential of the $n=5$ branch
• Figure 3: Entropies, Grand potentials and extensive variables for the four branches as a function of the temperature, at fixed $\alpha$. I,II and III branches have been plotted for $\alpha=3$, while branch IV has $\alpha=-3$