Null coordinates in flat spacetime

  • Thread starter Dale
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  • #1
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Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
Bill_K
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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.
 
  • #3
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thanks Bill_K, is there a name for the advanced retarded coordinates (I mean a person's name)?
 
  • #4
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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.
 
  • #5
DrGreg
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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.)
 
  • #6
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The basis vectors of u and v are null but not orthogonal.
 
  • #7
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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
LightCone_Matrix2.jpg
 
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