Searching for AdS_3 waves and Asymptotically Lifshitz black holes in R^3-NMG

Abstract

In this paper we consider the structure of the $Ad{S}_3$ vacua in $R^3$ expansion of the New Massive Gravity ($R^3$-NMG). We obtain the degeneracies of the $Ad{S}_3$ vacua at several points of the parametric space. Additionally, following a specific analysis we show that $Ad{S}_3$ wave solutions are present. Using these wave solutions, we single out two special points of the parametric space for which logarithmic terms appear in the solutions. The first one is a point at which the effective mass of the wave profile which is interpreted as a scalar mode, completely saturates the Breitenlohner-Freedman bound of the $Ad{S}_3$ space in which the wave is propagating. The second special point is a point at which the central charge of the theory vanishes. Furthermore, we investigate the possibility of asymptotically Lifshitz black solutions to be present in the three-dimensional $R^3$-NMG. We derive analytically the Lifshitz vacua considering specific relations between the mass parameters of $R^3$-NMG. A certain polynomial equation arises at the first special point where solutions with logarithmic fall-off in the $Ad{S}_3$ space appear. Solving this polynomial equation, we obtain the values of the dynamical exponent $z$ which correspond to possible asymptotically Lifshitz black hole solutions. However, it is shown that asymptotically Lifshitz black solutions do not exist in the three-dimensional $R^3$-NMG for a specific ansatz of the black hole metric.

18 pages, LaTeX, no figures, to appear in Phys. Rev. D

References in corpus (14)

• Massive Gravity in Three Dimensions
• More on Massive 3D Gravity
• On the new massive gravity and AdS/CFT
• Warped AdS_3 black holes in new massive gravity
• Analytic Lifshitz black holes in higher dimensions
• Born-Infeld extension of new massive gravity
• Asymptotically anti-de Sitter spacetimes in topologically massive gravity
• A boundary stress tensor for higher-derivative gravity in AdS and Lifshitz backgrounds
• AdS_3/LCFT_2 - Correlators in New Massive Gravity
• Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes
• AdS_3/LCFT_2 - Correlators in Cosmological Topologically Massive Gravity
• AdS Black Hole Solutions in the Extended New Massive Gravity
• Boundary stress tensor and counterterms for weakened AdS_3 asymptotic in New Massive Gravity
• Deeper discussion of Schrödinger invariant and Logarithmic sectors of higher-curvature gravity

Cited by in corpus (5)

• Ricci cubic gravity in d dimensions, gravitons and SAdS/Lifshitz black holes
• Hyperscaling-violating Lifshitz Solutions in Cubic Gravity
• Thin-Shells and Thin-Shell Wormholes in New Massive Gravity
• Non-linear regime of the Generalized Minimal Massive Gravity in critical points
• Exact Solutions in Weyl-Cubed Gravity