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Null coordinates in flat spacetime

  1. Jun 9, 2012 #1


    Staff: Mentor

    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?
  2. jcsd
  3. Jun 9, 2012 #2


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    Science Advisor

    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.
  4. Jun 9, 2012 #3


    Staff: Mentor

    thanks Bill_K, is there a name for the advanced retarded coordinates (I mean a person's name)?
  5. Jun 9, 2012 #4


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    Gold Member

    I've seen them attributed to Brinkmann.
  6. Jun 9, 2012 #5


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    Science Advisor
    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.)
  7. Jun 10, 2012 #6
    The basis vectors of u and v are null but not orthogonal.
  8. Jun 10, 2012 #7
    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
    Last edited: Jun 10, 2012
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