${\displaystyle 0<{!}T{!}<X}$

${\displaystyle ds^{2}=-dT^{2}+dX^{2}+dY^{2}+dZ^{2},\;\;-\infty <T,X,Y,Z<\infty }$ The world lines of the Rindler observers are timelike hyperbolic arcs (navy color). The orthogonal hyperslices ${\displaystyle x=x_{0}}$ of the Rindler chart

${\displaystyle ds^{2}=-x^{2}\,dt^{2}+dx^{2}+dy^{2}+dz^{2},0<x<\infty ,-\infty <t,y,z<\infty }$