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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

where:

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 Oas 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.

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# Homework Help: Coordinate change in de Sitter spacetime

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