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Time dilation in de Sitter Special Relativity

  1. Feb 16, 2009 #1
    Since in the papers by Guo & Huang and Aldrovandi & Pereira I couldn't find a practical formula for time dilation in de Sitter Special Relativity, I wonder if anyone here has it (or can derive it from the high-level formulas in those papers).

    Specifically,

    let be a de Sitter spacetime with horizon R.
    Let O be the center of that spacetime.
    Let a point P be moving with velocity v with respect to O.

    When point P is at distance r with respect to O, a local event starts in P, lasting a proper time interval Delta_ts.

    In Special Relativity, Delta_t, the interval of the event as observed from the frame of reference centered in O, would be:

    Delta_t = Delta_ts / sqrt[1 - (v/c)^2]

    What is the corresponding formula in de Sitter Special Relativity? (most probably involving r/R)

    Thank you very much in advance.
     
  2. jcsd
  3. Feb 18, 2009 #2
     
  4. Feb 18, 2009 #3

    Mentz114

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    Gold Member

    Hi Parvulus,
    my guess is to divide the line element by [itex]dt^2[/itex] to get

    [tex]\frac{d\tau}{dt}=\sqrt{g_{00}-g_{11}\beta^2}[/tex]

    the ratio of this for different r gives relative clock rates.
     
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