The relativistic galaxy number counts in the weak field approximation
  We present a novel approach to compute systematically the relativistic
projection effects at any order in perturbation theory within the weak field
approximation. In this derivation the galaxy number counts is written
completely in terms of the redshift perturbation. The relativistic effects
break the symmetry along the line-of-sight and they source, contrarily to the
standard perturbation theory, the odd multipoles of the matter power spectrum
or 2-point correlation function, providing a unique signature for their
detection in Large Scale Structure surveys. We show that our approach agrees
with previous derivations (up to third order) of relativistic effects and, for
the first time, we derive a model for the transverse Doppler effect. Moreover,
we show that in the Newtonian limit this approach is consistent with standard
perturbation theory at any order.
