We investigate the influence of the chimney topology $T\times T\times R$ of the Universe on the gravitational potential and force that are generated by point-like massive bodies. We obtain three distinct expressions for the solutions. One follows from Fourier expansion of delta functions into series using periodicity in two toroidal dimensions. The second one is the summation of solutions of the Helmholtz equation, for a source mass and its infinitely many images, which are in the form of Yukawa potentials. The third alternative solution for the potential is formulated via the Ewald sums method applied to Yukawa-type potentials. We show that, for the present Universe, the formulas involving plain summation of Yukawa potentials are preferable for computational purposes, as they require a smaller number of terms in the series to reach adequate precision.

中文翻译：

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烟囱格子宇宙中的引力相互作用

我们研究了烟囱形拓扑的影响 $Ť\times Ť\times \mathrm{[R}$点状块状体产生的引力和力。对于解决方案，我们获得了三种不同的表达式。一个是从使用二维环面的周期性的三角函数的傅立叶展开成级数开始的。第二个是源质量及其无限多图像的汤姆势势形式的亥姆霍兹方程解的总和。电位的第三个替代解决方案是通过适用于Yukawa型电位的Ewald sums方法制定的。我们表明，对于当前的宇宙，涉及汤川势的简单求和的公式出于计算目的是更可取的，因为它们需要级数更少的项才能达到足够的精度。