Image:MinkowskiObserverRindler.png

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[edit] Summary

A Minkowski (static) observer depicted in the Rindler chart for the Minkowski vacuum (flat spacetime),

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

This observer has world line

$t=\operatorname{arccosh}(s), \; x=\sqrt{1-s^2}, \; y = 0, \; z=0, \; -1 < s < 1$

In the figure, the inessential y, z coordinates have been suppressed and the light cones are correctly scaled and boosted to agree with the motion of this observer, and are shown for proper times $s = - 1 / 2,0,1 / 2$ . Note that the world line is a the graph of sech, and at s=1 this observer has already zoomed off to $t=\infty$ in our chart! So this is an example of an incomplete timelike geodesic in the Rindler chart.

This png image was converted using eog from a jpg image made by User:Hillman using Maple.

[edit] Licensing

I, the creator of this work, hereby grant the permission to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
Subject to disclaimers.

File history

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(del) (cur) 16:43, 31 May 2006 . . Drat (Talk | contribs) . . 400×400 (917 bytes) (Cleaned up and colours reduced de-artifact, then optimised with OptiPNG.)
(del) (rev) 23:48, 4 May 2006 . . Hillman (Talk | contribs) . . 400×400 (13,180 bytes) (A Minkowski (static) observer depicted in the Rindler chart for the Minkowski vacuum (flat spacetime), :<math> ds^2 = x^2 \, dt^2 + dx^2 + dy^2 + dz^2, \; \; 0 < x < \infty, \; -\inft < t, y, z < \infty</math> This observer has world line :<math>t=\arcco)