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Coordinate change in de Sitter spacetime

  1. Feb 11, 2009 #1
    Hello folks. Just registered, first post (moved here from the Physics forum).

    Let there be a de Sitter metric in static coordinates:

    ds^2 = - [1 - (r/R)^2] c^2 dt^2 + dr^2 / [1 - (r/R)^2] + r^2 d(omega)^2


    r is the radial coordinate
    R is the cosmological horizon
    coordinate time t is as observed from r = 0, the "origin", which we will call point O.

    Let rP be the radial coordinate (i.e. as observed from the origin O) of a static point P.

    Let's change now to a static frame of reference centered in said point P, and call r' the radial coordinate in that frame of reference.

    What is r'O, that is the distance from P to O as observed from the frame of reference centered in P?

    If you prefer to give the general equation for r' as a function of r, rP and R, that's fine.

    Thank you in advance for your help.
  2. jcsd
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