  We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the
IKKT or IIB matrix model. Gauge fields and metric fluctuations are identified
among the excitation modes with lowest spin, supplemented by a tower of
higher-spin fields. They arise from an internal structure which can be viewed
as a twisted bundle over $S^4$, leading to a covariant noncommutative geometry.
The linearized 4-dimensional Einstein equations are obtained from the classical
matrix model action under certain conditions, modified by an IR cutoff. Some
one-loop contributions to the effective action are computed using the formalism
of string states.
