= Solution
Introduce
$$
T=t\cosh\chi,\qquad R=t\sinh\chi.
$$
Then
$$
-dT^2+dR^2+R^2d\Omega^2
=-dt^2+t^2(d\chi^2+\sinh^2\chi\,d\Omega^2),
$$
which is the <Minkowski metric>. Since $t>0$,
$$
T^2-R^2=t^2>0,\qquad T>0,
$$
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 transformation>[Lorentz transformations] of Minkowski spacetime that fix $p$.
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