  We study the spontaneous emission of a dipole emitter imbedded into a layered
metal-dielectric metamaterial. We demonstrate ultra-high values of the Purcell
factor in such structures due to a high density of states with hyperbolic
isofrequency surfaces. We reveal that the traditional effective-medium approach
greatly underestimates the value of the Purcell factor due to the presence of
an effective nonlocality, and we present an analytical model which agrees well
with numerical calculations.
