General relativistic effects in the galaxy bias at second order
  The local galaxy bias formalism relies on the energy constraint equation at
the formation time to relate the metric perturbation to the matter density
contrast. In the Newtonian approximation, this relationship is linear, which
allows us to specify the initial galaxy density as a function of local physical
operators. In general relativity however, the relationship is intrinsically
nonlinear and a modulation of the short-wavelength mode by the long-wavelength
mode might be expected. We describe in detail how to obtain local coordinates
where the coupling of the long- to the short-wavelength modes is removed
through a change of coordinates (in the absence of the primordial
non-Gaussianity). We derive the general-relativistic correction to the galaxy
bias expansion at second order. The correction does not come from the
modulation of small-scale clustering by the long-wavelength mode; instead, it
arises from distortions of the volume element by the long-wavelength mode and
it does not lead to new bias parameters.
