  Kaiser redshift-space distortion formula describes well the clustering of
galaxies in redshift surveys on small scales, but there are numerous additional
terms that arise on large scales. Some of these terms can be described using
Newtonian dynamics and have been discussed in the literature, while the others
require proper general relativistic description that was only recently
developed. Accounting for these terms in galaxy clustering is the first step
toward tests of general relativity on horizon scales. The effects can be
classified as two terms that represent the velocity and the gravitational
potential contributions. Their amplitude is determined by effects such as the
volume and luminosity distance fluctuation effects and the time evolution of
galaxy number density and Hubble parameter. We compare the Newtonian
approximation often used in the redshift-space distortion literature to the
fully general relativistic equation, and show that Newtonian approximation
accounts for most of the terms contributing to velocity effect. We perform a
Fisher matrix analysis of detectability of these terms and show that in a
single tracer survey they are completely undetectable. To detect these terms
one must resort to the recently developed methods to reduce sampling variance
and shot noise. We show that in an all-sky galaxy redshift survey at low
redshift the velocity term can be measured at a few sigma if one can utilize
halos of mass M>10^12 Msun (this can increase to 10-sigma or more in some more
optimistic scenarios), while the gravitational potential term itself can only
be marginally detected. We also demonstrate that the general relativistic
effect is not degenerate with the primordial non-Gaussian signature in galaxy
bias, and the ability to detect primordial non-Gaussianity is little
compromised.
