基于Wolfram模型对数值相对论的研究
Research on Numerical Relativity Based on Wolfram Model

在数值相对论研究方面，侧重于将爱因斯坦场方程转化为3 + 1维的柯西问题。在3维空间超曲面上给出初始柯西条件，随时间演化。而Wolfram模型也把爱因斯坦场方程作为先验柯西问题，在单个空间超图上指定初始柯西数据，然后通过超图重写规则进行演化，得到的因果网络结构对应时空的共形不变性结构。侧重研究Jonathan Gorard如何使用Wolfram模型提供广义相对论的数值解法，对Jonathan Gorard对Berger和Colella提出的自适应网格细化进行数值验证(包括史瓦西黑洞、克尔黑洞、史瓦西黑洞极限)。将该代码的结果和没有PDE系统的Wolfram模型演化结果进行比较，发现会在相同极限收敛，继而说明Wolfram模型的可靠性。
In the research of numerical relativity, he focuses on transforming the Einstein field equations into the 3 + 1-dimensional Cauchy problem, and gives the initial Cauchy conditions on the 3-dimensional space hypersurface, which evolves with time. The Wolfram model takes the Einstein field equations as a priori Cauchy problem, specifies the initial Cauchy data on a single space hypergraph, and then evolves through the hypergraph rewriting rules, and the resulting causal network structure corresponds to the conformal invariant structure of space and time. This article describes how Jonathan Gorard uses the Wolfram Model to provide a numerical solution to General Relativity. Jonathan Gorard numerically validates the adaptive mesh refinement proposed by Berger and Colella (including Schwarzschild black hole, Kerr black hole, Schwarzschild black hole limit). Comparing the results of this code with the evolution of the Wolfram model without the PDE system shows that it converges at the same limit, thus illustrating the reliability of the Wolfram model.