Lifshitz black holes in higher spin gravity

Abstract

We study asymptotically Lifshitz solutions to three dimensional higher spin gravity in the SL(3, R) × SL(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.

Lifshitz spacetimes, solitons, and generalized BTZ black holes in quantum gravity at a Lifshitz point

“…It is interesting to note that the above solution can be obtained from the anti-de Sitter solution, 46) by the "coordinate transformation" (4.10) with…”

Higher spin Lifshitz theory and integrable systems

“…The operator L is now of third order and contains two independent fields u2 and u3 L -d3 + u2d + u3 (3.11) and The Lax equation (3.5) is equivalent to the following system of partial differential equations: PHYSICAL REVIEW D 91, 046012 (2015) 112 -2 u3 -u2, 2 2 113 = u2 --u 2 --u2u2. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) Eliminating u3 then gives an equation for u2 alone «2 = ~\ u2 -^(u 2 u '2y. (3.15) This equation is known as the Boussinesq equation [31], which has been studied in the context of propagation of waves.…”

“…The operator L is now of fourth order and contains three fields uh i -2 ,3 .4 , L = d4 + u2d2 + u3d + u4. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) From this we can evaluate L i/4 = 0 + ^ 0 -i + 1 d~2 + " 4 ~ l "3 + ^ m2 ~ §2 U3) ° 3 + °(9~^- (3.18) The Lax operator is given by…”

“…In the following we will focus on the asymptotically Lifshitz solutions following the approach developed in [13]. On the field theory side, systems with Lifshitz scaling, i.e.…”

About the phase space of SL(3) black holes

“…Higher spin theories [2][3][4][5][6] in 3D, have been of great interest recently, and specifically, the study of higher spin black holes in the Chern-Simons formulation has been one of the most active lines of research [1,[7][8][9][10][11][12][13][14][15][16][17][18].…”