Yes, that's correct. A singularity is a point in space-time where the known laws of physics, specifically those described by the standard model of particle physics and general relativity, break down or become insufficient to describe the physical processes occurring there.
In the context of the Big Bang, the singularity refers to the initial state of the universe, where it is believed to have been infinitely hot and dense. At this point, our current understanding of physics, including the standard model, cannot accurately describe the conditions or predict the behavior of matter and energy.
Similarly, in the context of black holes, a singularity is thought to exist at the center, beyond the event horizon. The singularity is a point of infinite density and curvature, where the laws of physics as we currently understand them cease to apply. It represents a breakdown of our current theories, including the standard model and general relativity, and implies the existence of physics beyond our current understanding.
The presence of singularities in the Big Bang and black holes is one of the reasons why scientists seek a theory of quantum gravity. A theory of quantum gravity is expected to provide a more complete and unified framework that can describe the behavior of matter and energy under extreme conditions, including at singularities. However, developing such a theory is an ongoing challenge in theoretical physics, and it remains an active area of research.