  We revise general relativity (GR) from the perspective of calculus for moving
surfaces (CMS). While GR is intrinsically constructed in pseudo-Riemannian
geometry, a complete understanding of moving manifolds requires embedding in a
higher dimension. It can only be defined by extrinsic Gaussian differential
geometry and its extension to moving surfaces, known as CMS. Following the
recent developments in CMS, we present a new derivation for the Einstein field
equation and demonstrate the fundamental limitations of GR. Explicitly, we show
that GR is an approximation of moving manifold equations and only stands for
dominantly compressible space-time. While GR, with a cosmological constant,
predicts an expanding universe, CMS shows fluctuation between inflation and
collapse. We also show that the specific solution to GR with cosmological
constant is constant mean curvature shapes. In the end, by presenting
calculations for incompressible but deforming two-dimensional spheres, we
indicate that material points moving with constant spherical velocities move
like waves, strongly suggesting a resolution of the wave-corpuscular dualism
problem.
