In recent years, a new class of exact solutions of the Einstein field
equations of general relativity in the presence of matter, in the static
and spherically symmetric case, was discovered and analyzed by analytical
and numerical means. In this talk, these new solutions are described in the
case of the polytropic equations of state, and their main conceptual
consequences for the structure of the theory are discussed.

As a consequence of the development of these solutions, new aspects of the
concept of spacetime singularity were uncovered, namely that there exist
previously unsuspected repulsive singularities, as well as new facts about
the existence and character of the gravitational field within spherically
symmetric vacuous cavities. The existence of these new solutions also led
to new and radically different conclusions about the concept of
gravitational collapse, as well as about the internal geometry and
structure of black holes.

The analysis of limits of sequences of shell solutions that approach the
exterior geometries of black holes and the formation of event horizons led
to a completely unexpected connection with the quantum aspects of
physics. We were able to reproduce, by purely classical means, the two
main conclusions of the study of quantum mechanics in the background
geometry of the exterior Schwarzschild solution, representing a naked
black hole. This led to the conclusion that general relativity seems to
contain remnants of some underlying quantum structure.

There is some ongoing work further exploring this connection of general
relativity with quantum field theory, for which it is necessary to use the
Euclidean lattice formulation of this theory. This connection is
made directly with the standard model of particle physics through the
spontaneous symmetry breaking mechanism involving the Higgs field. This
can be qualitatively commented on if there is time and interest.