Gravity and Particle Cosmology Group, Division of Particle and Astrophysical Science, Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan and Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan.
Phys Rev Lett. 2013 Oct 18;111(16):161102. doi: 10.1103/PhysRevLett.111.161102. Epub 2013 Oct 14.
Time evolution of a black hole lattice toy model universe is simulated. The vacuum Einstein equations in a cubic box with a black hole at the origin are numerically solved with periodic boundary conditions on all pairs of faces opposite to each other. Defining effective scale factors by using the area of a surface and the length of an edge of the cubic box, we compare them with that in the Einstein-de Sitter universe. It is found that the behavior of the effective scale factors is well approximated by that in the Einstein-de Sitter universe. In our model, if the box size is sufficiently larger than the horizon radius, local inhomogeneities do not significantly affect the global expansion law of the Universe even though the inhomogeneity is extremely nonlinear.
模拟了黑洞晶格玩具模型宇宙的时间演化。通过在原点处有一个黑洞的立方盒中的真空爱因斯坦方程，并使用相对的每对面的周期性边界条件进行数值求解。通过使用立方盒的表面面积和边的长度来定义有效标度因子，并将其与爱因斯坦-德西特宇宙中的进行比较。发现有效标度因子的行为很好地近似于爱因斯坦-德西特宇宙中的行为。在我们的模型中，如果盒子尺寸足够大于视界半径，则局部非均匀性不会显著影响宇宙的全局膨胀规律，即使非均匀性极其非线性。
