general relativity - Is the curvature of space-time a smooth function everywhere ? (except at black holes)

Is the curvature of space-time a smooth function everywhere (except at black holes) in view of General relativity. By 'smooth' it is meant that it possesses derivatives of all order at a given point.

Answer

No, not at the boundary of a solid object like a planet. There's a step function in the stres-energy tensor, and so you'll have a step function in the Riemann tensor.