Time dilation in de Sitter Special Relativity

[Parvulus]

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.

 

[JANm]

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./QUOTE]
The starting point seen will be t=t_0+r/c and the ending point will be t'=t_o+delta_ts+(r+delta_ts*v)/c.
difference = delta_ts(1+v/c).
I Know about the Sitter and how he rejected emission theorie, for images would get blurred if light would get superluminous with aproaching lamps and subluminous with receding lamps, so: lightvelocity is independent of velocity of the source, c. But I do know that the time of the local event which starts a P of endurance delta_ts is strectched by a factor (1+v/c), assumed that v is the radial velocity.
greetings jm

 

[Mentz114]

Hi Parvulus,
my guess is to divide the line element by $dt^2$ to get

$$\frac{d\tau}{dt}=\sqrt{g_{00}-g_{11}\beta^2}$$

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