File:MinkowskiObserverRindler.png

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This figure depicts some representative Rindler observers in a Rindler wedge ${\displaystyle 0<|T|<X}$ in a Cartesian chart for Minkowski vacuum, ${\displaystyle ds^{2}=-dT^{2}+dX^{2}+dY^{2}+dZ^{2},\;\;-\infty <T,X,Y,Z<\infty }$ The world lines of the Rindler observers are timelike hyperbolic arcs (navy color). The orthogonal hyperslices ${\displaystyle x=x_{0}}$ of the Rindler chart

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

appear as the spacelike rays in this figure, in which the Y, Z coordinates have been suppressed. The red rays correspond to the Rindler horizon x=0.

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