singularity:
The center of a black hole, where the curvature of spacetime is maximum. At the singularity, the gravitational tides diverge; no solid object can even theoretically survive hitting the singularity. Generally even though singularities predict inconsistencies in theory, singularities inside black holes do not essentially imply that general relativity is incomplete so long as singularities are surrounded by event horizons always.
A proper formulation of quantum gravity might well ignore the classical singularity at the centers of black holes.