Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 38D / c / Solution

IntroduceThenwhich is the Minkowski metric. Since $t>0$,so these coordinates cover exactly the interior of the future light cone of its vertex $p$. The $t=\text{constant}$ slices are future hyperboloids. Their spatial isometries are precisely the proper orthochronous Lorentz transformations of Minkowski spacetime that fix $p$.