  The framework of emergent gravity arising from Yang-Mills matrix models is
developed further, for general noncommutative branes embedded in R^D. The
effective metric on the brane turns out to have a universal form reminiscent of
the open string metric, depending on the dynamical Poisson structure and the
embedding metric in R^D. A covariant form of the tree-level equations of motion
is derived, and the Newtonian limit is discussed. This points to the necessity
of branes in higher dimensions. The quantization is discussed qualitatively,
which singles out the IKKT model as a prime candidate for a quantum theory of
gravity coupled to matter. The Planck scale is then identified with the scale
of N=4 SUSY breaking. A mechanism for avoiding the cosmological constant
problem is exhibited.
