论文标题
牛顿近似（1 + 1）维度
Newtonian approximation in (1 + 1) dimensions
论文作者
论文摘要
我们研究了牛顿重力制度的可能存在，即$ 1+1 $尺寸，考虑到Kerr-Schild和Sonformal形式的指标。在前一种情况下，度量标准给出了泊松方程在平坦空间中的精确溶液，但是溶液的弱场极限和地球运动的非相关状态并不小。我们表明，使用谐波坐标，度量标准是合成平坦的，弱场膨胀很简单。对地球运动非相关主义制度的分析仍然非平凡，而弱场电位仅满足平坦的泊松方程。
We study the possible existence of a Newtonian regime of gravity in $1+1$ dimensions, considering metrics in both the Kerr-Schild and conformal forms. In the former case, the metric gives the exact solution of the Poisson equation in flat space, but the weak-field limit of the solutions and the non-relativistic regime of geodesic motion are not trivial. We show that using harmonic coordinates, the metric is conformally flat and a weak-field expansion is straightforward. An analysis of the non-relativistic regime of geodesic motion remains non-trivial and the weak-field potential only satisfies the flat space Poisson equation approximately.
