# Null coordinates in flat spacetime

Mentor
2020 Award
There are some "standard" coordinate systems in flat spacetime, such as Minkowski (inertial), Rindler (uniform acceleration), and Born (rotation).

Is there a "standard" coordinate system in flat spacetime which has at least one null coordinate?

Bill_K
Sure, there are several. Take advanced/retarded coordinates, u = t+x, v = t-x. If you want something fancier, the coordinate system based on the null cones whose vertices lie on a straight line: u = t-r.

Mentor
2020 Award
thanks Bill_K, is there a name for the advanced retarded coordinates (I mean a person's name)?

thanks Bill_K, is there a name for the advanced retarded coordinates (I mean a person's name)?
I've seen them attributed to Brinkmann.

DrGreg
Gold Member
Not somebody's name, but I've also heard them called "light cone coordinates" or "radar coordinates". (The latter because if you imagine the observer detecting objects using radar, he transmits a pulse at time v and receives an echo at time u, in the notation of post #2.)

The basis vectors of u and v are null but not orthogonal.

There are some "standard" coordinate systems in flat spacetime, such as Minkowski (inertial), Rindler (uniform acceleration), and Born (rotation).

Is there a "standard" coordinate system in flat spacetime which has at least one null coordinate?

Barton Zwiebach uses Light-cone Coordinates in his text book, "A First Course In String Theory." The concept is introduced in Section 2.3, page 20. The Light-cone Matrix is

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