Rindler wedge ($X>|T|$)

The right Rindler wedge is the open region $X>|T|$ of Minkowski spacetime. Coordinates $T=\rho \sinh \tau$, $X=\rho \cosh \tau$, $\rho >0$, give metric $-{\rho }^{2}d{\tau }^2+d{\rho }^2+d{Y}^2+d{Z}^2$. The wedge extends into Minkowski spacetime and is geodesically incomplete, while its constant-$\tau$ slices are Cauchy surfaces for the wedge itself.