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Figure 2
A 2D real Minkowski spacetime depicts hyperbolas given by [{x^2} - ({ct} )^2 = x'^2 - (ct')^2 = \pm {\xi ^2}], where the purple pair of hyperbolas correspond to [ - {\xi ^2}] (time-like events) and the black pair of hyperbolas to [ + {\xi ^2}] (space-like events). An arbitrary time-like event is shown by a blue line from the origin to the event (the blue bird), and the projection of its coordinates (x,ct) = [(\xi \sinh\beta, \xi \cosh\beta)] and [({x}',ct')] = [[\xi \sinh(\beta -\alpha ), \xi \cosh(\beta -\alpha )]] is depicted by broken lines on to the ground (GF, black) and the train (TF, red) frames. The diagonal yellow lines are the light lines given by [\xi = 0]; their poles [ + ({\infty, \pm \infty } )] and [ - ({\infty, \pm \infty } )] are indicated. The four hyperbola branches are labeled F, P, U and T. See the Mathematica script in the Mathematica notebook in the supporting information to generate this plot.

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ISSN: 2053-2733
Volume 77| Part 4| July 2021| Pages 242-256
https://doi.org/10.1107/S2053273321003259
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