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In [[Theory of relativityspecial relativity]], '''lightcone coordinates''' is a special coordinate system where two of the coordinates, x<sup>+</sup> and x<sup>−</sup> are [[null (mathematics)null]] coordinates and all the other coordinates are spatial. Call them <math>x_\perp</math>.
Assume we
Instead of the standard coordinate system (using [[Einstein notation]])
A boost in the tx plane shows up as <math>x^+ \to e^{+\beta}x^+</math>, <math>x^ \to e^{\beta}x^</math>, <math>x^i \to x^i</math>. A rotation in the ijplane only affects <math>x_\perp</math>. The parabolic transformations show up as <math>x^+ \to x^+</math>, <math>x^ \to x^ + \delta_{ij}\alpha^i x^j + \frac{\alpha^2}{2} x^+</math>, <math>x^i \to x^i + \alpha^i x^+</math>. Another set of parabolic transformations show up as <math>x^+ \to x^+ + \delta_{ij}\alpha^i x^j + \frac{\alpha^2}{2} x^</math>, <math>x^ \to x^</math> and <math>x^i \to x^i + \alpha^i x^</math>.
Light cone coordinates can also be generalized to curved spacetime in general relativity. Sometimes
Light cone coordinates are sometimes used to describe relativistic collisions, especially if the relative velocity is very close to the speed of light.
== See also ==
