  Forthcoming radio continuum surveys will cover large volumes of the
observable Universe and will reach to high redshifts, making them potentially
powerful probes of dark energy, modified gravity and non-Gaussianity. Here we
extend recent works by analyzing the general relativistic (GR) corrections to
the angular power spectrum. These GR corrections to the standard Newtonian
analysis of the power spectrum become significant on scales near and beyond the
Hubble scale at each redshift. We consider the continuum surveys with LOFAR,
WSRT and ASKAP, and examples of continuum surveys with the SKA. We find that
the GR corrections are at most percent-level in LOFAR, WODAN and EMU surveys,
but they can produce $O(10%)$ changes for high enough sensitivity SKA continuum
surveys. The signal is however dominated by cosmic variance, and
multiple-tracer observations will be needed to overcome this problem. The GR
corrections are suppressed in continuum surveys because of the integration over
redshift -- we expect that GR corrections will be enhanced for future SKA HI
surveys in which the source redshifts will be known. We also provide
predictions for the angular power spectra in the case where the primordial
perturbations have local non-Gaussianity. We find that non-Gaussianity
dominates over GR corrections, and rises above cosmic variance when $f_{\rm
NL}\gtrsim5$ for SKA continuum surveys.
