Homogeneous Solutions of Minimal Massive 3D Gravity

Abstract

In this paper we systematically construct simply transitive homogeneous spacetime solutions of the three-dimensional Minimal Massive Gravity (MMG) model. In addition to those that have analogs in Topologically Massive Gravity, such as warped AdS and pp-waves, there are several solutions genuine to MMG. Among them, there is a stationary Lifshitz metric with the dynamical exponent z=-1 and an anisotropic Lifshitz solution where all coordinates scale differently. Moreover, we identify a homogeneous Kundt type solution at the chiral point of the theory. We also show that in a particular limit of the physical parameters in which the Cotton tensor drops out from the MMG field equation, homogeneous solutions exist only at the merger point in the parameter space if they are not conformally flat.

23 pages, v2: minor changes, references added

References in corpus (19)

• Massive Gravity in Three Dimensions
• Non-relativistic holography
• Lifshitz holography
• Warped AdS_3 black holes in new massive gravity
• Minimal Massive 3D Gravity
• Lorentzian spacetimes with constant curvature invariants in four dimensions
• Lorentzian spacetimes with constant curvature invariants in three dimensions
• Matter coupling in 3D "Minimal Massive Gravity"
• More on New Massive Gravity: Exact Solutions
• Minimal Massive Gravity: Conserved Charges, Excitations and the Chiral Gravity Limit
• Type D Solutions of 3D New Massive Gravity
• From accelerating and Poincaré coordinates to black holes in spacelike warped AdS${}_3$, and back
• On 3D Minimal Massive Gravity
• Minimal Massive 3D Gravity Unitarity Redux
• On Solutions of Minimal Massive 3D Gravity
• All stationary axi-symmetric local solutions of topologically massive gravity
• Homogeneous vacua of (generalized) new massive gravity
• Bulk and Boundary Unitary Gravity in 3D: MMG${}_2$
• Unitarity Problems in 3$D$ Gravity Theories

Cited by in corpus (7)

• Spontaneously Broken 3d Hietarinta/Maxwell Chern-Simons Theory and Minimal Massive Gravity
• Supersymmetric Solutions of N = (1,1) General Massive Supergravity
• Thermodynamic Stability of the Stationary Lifshitz Black Hole of New Massive Gravity
• Circularly symmetric solutions of Minimal Massive Gravity at its merger point
• Matter coupling in Minimal Massive 3D Gravity and spinor-matter interactions in exterior algebra formalism
• Brief Note on Thurston Geometries in 3D Quadratic Curvature Theories
• A note on the pp-wave solution of Minimal Massive 3D Gravity coupled with Maxwell-Chern-Simons theory