An examination of a 'Poincaré causal diamond model of hyperbolic static spacetime'

The following is an investigation into an interesting mathematical object I stumbled upon when reading a General Relativity textbook.Defining the spacetime:A static universe in which space is hyperbolic can be described by the metric: mjx-container[jax="CHTML"] { line-height: 0; } mjx-container [space="1"] { margin-left: .111em; } mjx-container [space="2"] { margin-left: .167em; } mjx-container [space="3"] { margin-left: .222em; } mjx-container [space="4"] { margin-left: .278em; } mjx-container ...