  We present a general relativistic description of galaxy clustering in a FLRW
universe. The observed redshift and position of galaxies are affected by the
matter fluctuations and the gravity waves between the source galaxies and the
observer, and the volume element constructed by using the observables differs
from the physical volume occupied by the observed galaxies. Therefore, the
observed galaxy fluctuation field contains additional contributions arising
from the distortion in observable quantities and these include tensor
contributions as well as numerous scalar contributions. We generalize the
linear bias approximation to relate the observed galaxy fluctuation field to
the underlying matter distribution in a gauge-invariant way. Our full formalism
is essential for the consistency of theoretical predictions. As our first
application, we compute the angular auto correlation of large-scale structure
and its cross correlation with CMB temperature anisotropies. We comment on the
possibility of detecting primordial gravity waves using galaxy clustering and
discuss further applications of our formalism.
