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.

16 pages

References in corpus (12)

• Massive Gravity in Three Dimensions
• Warped AdS_3 black holes in new massive gravity
• Minimal Massive 3D Gravity
• General Kundt spacetimes in higher dimensions
• More on New Massive Gravity: Exact Solutions
• Canonical Structure of Higher Derivative Gravity in 3D
• Gyratonic pp-waves and their impulsive limit
• Gyratons on direct-product spacetimes
• Type D Solutions of 3D New Massive Gravity
• Kundt spacetimes of massive gravity in three dimensions
• Gyratons on Melvin spacetime
• Gyratons in the Robinson-Trautman and Kundt classes

Cited by in corpus (2)

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