The Hořava theory in \(2+1\) dimensions can be formulated at a critical point in the space of coupling constants where it has no local degrees of freedom. This suggests that this critical case could share many features with \(2+1\) general relativity, in particular its large-distance effective action that is of second order in derivatives. To deepen on this relationship, we study the asymptotically flat solutions of the effective action. We take the general definition of asymptotic flatness from \(2+1\) general relativity, where an asymptotically flat region with a nonfixed conical angle is approached. We show that a class of regular asymptotically flat solutions are totally flat. The class is characterized by having nonnegative energy (when the coupling constant of the Ricci scalar is positive). We present a detailed canonical analysis on the effective action showing that the dynamics of the theory forbids local degrees of freedom. Another similarity with \(2+1\) general relativity is the absence of a Newtonian force. In contrast to these results, we find evidence against the similarity with \(2+1\) general relativity: we find an exact nonflat solution of the same effective theory. This solution is out of the set of asymptotically flat solutions.

\（2 + 1 \）维的Hořava理论可以在耦合常数空间中没有局部自由度的临界点上提出。这表明该临界情况可以具有\（2 + 1 \）广义相对论的许多特征，特别是其在导数中为二阶的大距离有效作用。为了加深这种关系，我们研究了有效动作的渐近平坦解。我们从\（2 + 1 \）得出渐近平坦度的一般定义广义相对论，其中逼近具有非固定圆锥角的渐近平坦区域。我们证明了一类规则渐近平的解是完全平的。该类的特征是具有非负能量（当Ricci标量的耦合常数为正时）。我们对有效动作进行了详细的规范分析，表明该理论的动力学禁止局部自由度。与\（2 + 1 \）广义相对论的另一个相似之处是缺少牛顿力。与这些结果相反，我们找到了与\（2 + 1 \）广义相对论相似的证据：我们找到了同一有效理论的精确非平坦解。该解不在渐近平解的集合之内。