Solutions with pure radiation and gyratons in 3D massive gravity theories

Abstract

We find exact solutions of topologically massive gravity (TMG) and new massive gravity (NMG) in $2+1$ dimensions (3D) with an arbitrary cosmological constant, pure radiation, and gyratons, i.e., with possibly non-zero $T_{uu}$ and $T_{ux}$ in canonical coordinates. Since any `reasonable' geometry in 3D (i.e., admitting a null geodesic congruence) is either expanding Robinson-Trautman ($\Theta \ne 0$) or Kundt ($\Theta =0$), we focus on these two classes. Assuming expansions $\Theta =1/r$ (`GR-like' Robinson-Trautman) or $\Theta =0$ (general Kundt), we systematically integrate the field equations of TMG and NMG and identify new classes of exact solutions. The case of NMG contains an additional assumption of $g_{ux}$ being quadratic in $r$, which is automatically enforced in TMG as well as in 3D GR. In each case, we reduce the field equations as much as possible and identify new classes of solutions. We also discuss various special subclasses and study some explicit solutions.

arXiv comment16 pages

References in corpus (32)

• Massive Gravity in Three Dimensions
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• Warped AdS_3 black holes in new massive gravity
• Minimal Massive 3D Gravity
• Bending AdS Waves with New Massive Gravity
• Classification of solutions in topologically massive gravity
• Mass and angular momentum of asymptotically AdS or flat solutions in the topologically massive gravity
• Kundt spacetimes as solutions of topologically massive gravity
• Gravitational field of a spinning radiation beam-pulse in higher dimensions
• General Kundt spacetimes in higher dimensions
• Gravitational field of relativistic gyratons
• Canonical Structure of Higher Derivative Gravity in 3D
• More on New Massive Gravity: Exact Solutions
• Relativistic gyratons in asymptotically AdS spacetime
• The General Type N Solution of New Massive Gravity
• Gyratonic pp-waves and their impulsive limit
• Some exact solutions of all f(Ricci) theories in three dimensions
• Gyratons on direct-product spacetimes
• Causality in 3D Massive Gravity Theories
• Type D Solutions of 3D New Massive Gravity
• Gravitational field of charged gyratons
• Higher-dimensional Kundt waves and gyratons
• On Exact Solutions and the Consistency of 3D Minimal Massive Gravity
• All solutions of Einstein's equations in 2+1 dimensions: $\Lambda$-vacuum, pure radiation, or gyratons
• Spinor formulation of topologically massive gravity
• Gravity Waves in Three Dimensions
• Kundt spacetimes of massive gravity in three dimensions
• Gyratons on Melvin spacetime
• Unitarity Problems in 3$D$ Gravity Theories
• Kundt solutions of Minimal Massive 3D Gravity
• Gyratons in the Robinson-Trautman and Kundt classes
• Absence of gyratons in the Robinson-Trautman class

Cited by in corpus (2)

• Robinson-Trautman spacetimes in (2+1) dimensions
• Interpreting gravitational fields of Topologically Massive Gravity using geodesic deviation