Final answer:
Binary system collapse in general relativity cannot be explained using Newtonian concepts of energy conservation due to the intense gravitational fields that alter spacetime curvature. Instead, we use general relativistic principles to understand these phenomena, which are consistent with energy conservation in that framework.
Step-by-step explanation:
Can we correctly invoke energy conservation to explain why binary systems do collapse in GR (General Relativity)? To answer this question, one must understand that general relativity redefines the concept of gravity from a force to a curvature of spacetime. When a massive object like a star collapses, it creates an intense gravitational field that further intensifies as the object shrinks, enlarging the curvature of spacetime around it.
Conservation of energy in the context of general relativity is a more complex concept due to the dynamic nature of spacetime. On a non-cosmological scale, energy conservation seems inviolate due to a symmetry of time, an idea brought forth by Emmy Noether. This implies that, in stable systems like the Milky Way galaxy, energy conservation holds over time.
For binary systems collapsing under general relativity, however, we cannot apply the traditional Newtonian concept of gravitational potential energy. Instead, we must use the general relativistic framework, which allows for changes in the total energy of a system under extreme gravitational fields, like those present during a collapse. As such, binary systems can evolve in ways that may seem to violate Newtonian conservation of energy, but are consistent with the conservation laws within general relativity.