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 ( Θ≠0 ) or Kundt ( Θ=0 ), we focus on these two classes. Assuming expansions Θ=1/r (‘GR-like’ Robinson–Trautman) or Θ=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.

中文翻译：

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3D 重力理论中的纯辐射和回旋子解

我们找到了具有任意宇宙常数、纯辐射和回旋子的 2 + 1 维 (3D) 拓扑质量引力 (TMG) 和新质量引力 (NMG) 的精确解，即可能为非零时间 _呃 和时间 _用户体验 在规范坐标中。由于 3D 中的任何“合理”几何（即承认零测地线同余）要么是展开 Robinson–Trautman（ θ≠0 ）或昆特（ θ=0 ），我们重点关注这两类。假设扩张 θ=1/r （'GR-like' Robinson–Trautman）或 θ=0 （通用 Kundt），我们系统地积分了 TMG 和 NMG 的场方程，并确定了新类别的精确解。 NMG 的情况包含一个额外的假设G _用户体验 是二次方r，这在 TMG 和 3D GR 中自动强制执行。在每种情况下，我们都尽可能地减少场方程并确定新类别的解决方案。我们还讨论了各种特殊子类并研究了一些显式解决方案。