**Schwarzschild solved the Einstein equations under the assumption of spherical symmetry in 1915**,
two years after their publication.
This in itself is a good indication that the equations of General Relativity are a good deal more complicated than Electromagnetism.

The most obvious spherically symmetric problem is that of a
**point mass**.
The mass curves space-time and thus affects the particles moving nearby.
The metric tensor in Schwarzschild (spherical coordinates becomes

This goes to the normal flat Minkowski space-time interval (in spherical coordinates) for or for zero mass .

The
**Schwarzschild radius for normal planets and stars is much smaller than the actual size of the object** so the
Schwarzschild solution is only valid outside the object.
For black holes, the Schwarzschild radius is the horizon inside of which nothing can escape the black hole.

Jim Branson 2012-10-21