Recent results show that important singularities in General Relativity can be
naturally described in terms of finite and invariant canonical geometric
objects. Consequently, one can write field equations which are equivalent to
Einstein's at non-singular points, but in addition remain well-defined and
smooth at singularities. The black hole singularities appear to be less
undesirable than it was thought, especially after we remove the part of the
singularity due to the coordinate system. Black hole singularities are then
compatible with global hyperbolicity, and don't make the evolution equations
break down, when these are expressed in terms of the appropriate variables. The
charged black holes turn out to have smooth potential and electromagnetic
fields in the new atlas. Classical charged particles can be modeled, in General
Relativity, as charged black hole solutions. Since black hole singularities are
accompanied by dimensional reduction, this should affect Feynman's path
integrals. Therefore, it is expected that singularities induce dimensional
reduction effects in Quantum Gravity. These dimensional reduction effects are
very similar to those postulated in some approaches to making Quantum Gravity
perturbatively renormalizable. This may provide a way to test indirectly the
effects of singularities, otherwise inaccessible.Comment: To appear in Advances in High Energy Physic
