The Schwarzschild Solution to Einstein's Field Equations for gravity are said to be exact when outside a spherically symmetric massive body. My question is, can the Schwarzschild Solution also be used inside the massive body, such as a neutron star. In Newtonian gravity we can find the gravity potential at some position inside the body; just find the distance to the center of mass, and count the total mass enclosed by a sphere whose radius equals that distance. It is similar to Gauss' Law in electrostatics. Does a similar procedure work in general relativity? To find the gravity field at some position inside a neutron star, can I just calculate an effective Schwarzschild radius by finding the mass enclosed by a sphere passing through that position? If not, is there a correction to the Schwarzschild solution for the interior of a spherically symmetric massive body.