The invariant spacelike condition is $x'^2-c^2t'^2>0$. Hence the primed-coordinate events in neither the <causal future> nor the <causal past> obey
$$
\boxed{|x'|>c|t'|.}
$$
The green regions in part <1/c> retain their shape in primed coordinates. A particular spacelike event's coordinate <time> may change sign, but it never enters either <light cone>.

Solution

Past exam of the symmetry and relativity course of the University of Oxford / 2019 / 1 / d / iii / Solution

 Solution (source code)