  Firstly, we present a reformulation of the standard canonical approach to
spherically symmetric systems in which the radial gauge is imposed. This is
done via the gauge unfixing technique, which serves as the exposition in the
context of the radial gauge. Secondly, we apply the same techniques to the full
theory, without assuming spherical symmetry, resulting in a reduced phase space
description of general relativity. The canonical structure of the theory is
analyzed.
