Gaussian curvature of spherical shells: a geometric measure of complexity

In this paper we consider a semitetrad covariant decomposition of spherically symmetric spacetimes and find governing hyperbolic equation the Gaussian curvature two dimensional spherical shells, that emerges due to decomposition. The restoration factor travelling wave allows us construct geometric measure complexity. This depends critically on curvature, demonstrate connection complexity for first time. We illustrate utility by classifying well known metrics with different matter distributions. also define an order structure set all spacetimes, according their physical properties.