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Parvulus

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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.