We have made high-resolution radio images, using the Very Large Array
(VLA), of a sample of radio galaxies at z > 2 selected from the MRC/1
Jy complete sample. These are also the first detailed observations of
radio galaxies at the high rest-frame frequencies of 15-30 GHz. Compac
t (<0.2 arcsec) cores at the mJy and sub-mJy level were detected in mo
st of the objects, coincident with the optical galaxies. In sharp cont
rast to the flat spectra of radio cores in galaxies at low redshift, w
e find that most of the cores at high redshift have a steep spectral i
ndex (alpha > 0.5) between 4.7 and 8.3 GHz (observed). We identify thi
s steepening with the optically thin part of a synchrotron self-absorb
ed spectrum at frequencies above the turnover. Both core- and lobe-dom
inated quasars have also been reported to show such a turnover from fl
at to steep spectra but at much higher observed frequencies. We sugges
t that the cores in galaxies and quasars are intrinsically similar (in
the rest frame of the emitting plasma) and that the observed differen
ces can be explained in terms of Doppler shifting by different amounts
in quasar and galaxy cores. This model is consistent with the unifica
tion scheme for radio galaxies and quasars. Using the theory of synchr
otron self-absorption we estimate sizes of similar to 1 pc, magnetic f
ields of similar to 1 G and electron densities of similar to 1000 cm(-
3) for the cores of both quasars and radio galaxies. The similar value
s are perhaps an indication of similar physical processes and paramete
rs in their cores. The spectrum at turnover provides information on sc
ales much smaller than the telescope resolution. It is therefore a use
ful tool for probing the cores of galaxies which are usually too weak
for very long-baseline interferometry studies.