A solution of the Mitra Paradox

Abstract

The “Mitra paradox” refers to the fact that while the de Sitter spacetime appears non-static in a freely falling reference frame, it looks static with reference to a fixed reference frame. The coordinate-independent nature of the paradox may be gauged from the fact that the relevant expansion scalar, θ=3Λ−−√ , is finite if Λ>0 . The trivial resolution of the paradox would obviously be to set Λ=0 . However, here it is assumed that Λ>0 , and the paradox is resolved by invoking the concept of “expansion of space”. This is a reference-dependent concept, and it is pointed out that the solution of the Mitra paradox is obtained by taking into account the properties of the reference frame in which the coordinates are co-moving.