…Energy Is Not Conserved

Einstein tells us that space and time are dynamical, and in particular that they can evolve with time. When the space through which particles move is changing, the total energy of those particles is not conserved.

Don’t look for a free lunch. There are still rules:

….energy and momentum evolve in a precisely specified way in response to the behavior of spacetime around them. If that spacetime is standing completely still, the total energy is constant; if it’s evolving, the energy changes in a completely unambiguous way.

This has been known since the 1920’s, and I learned about it when I first seriously studied GR at Stanford in 1973. However, scientists now need to pay more attention to it. In recent decades astronomical observations have have revealed many more situations where the effects of general relativity are significant.

Mathematical details at Is Energy Conserved in General Relativity?