We analyze the motion of both massive and massless particles in a model with space-time of 3D Einstein gravity with torsion. We consider the spinor field and the massless scalar field as the source of torsion respectively. Following the Hamilton–Jacobi formalism, we investigate the effective potential of radial motion for test particles in a homogeneous and isotropic space-time with torsion. We show that there are no stable circular orbits for massive and massless particles in the Einstein gravity with torsion induced by the spinor field, in a space-time with two spatial and one time dimensions. In the case of massive particles, we show that stable orbits exist in 3D Einstein gravity with torsion induced by the scalar field.

我们分析了具有扭转的 3D 爱因斯坦引力时空模型中的大质量和无质量粒子的运动。我们分别考虑自旋场和无质量标量场作为扭转源。遵循 Hamilton-Jacobi 形式主义，我们研究了测试粒子在具有扭转的均匀和各向同性时空中的径向运动的有效潜力。我们表明，在具有两个空间维度和一个时间维度的时空中，爱因斯坦引力中存在由自旋场引起的扭转的有质量和无质量粒子的稳定圆形轨道。在大质量粒子的情况下，我们表明在标量场引起的扭曲的 3D 爱因斯坦引力中存在稳定的轨道。