Is Energy Conserved in General Relativity?

In special cases, yes. In general — it depends on what you mean by “energy”, and what you mean by “conserved”.

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We will not delve into definitions of energy in general relativity such as the hamiltonian (amusingly, the energy of a closed universe always works out to zero according to this definition), various kinds of energy one hopes to obtain by “deparametrizing” Einstein’s equations, or “quasilocal energy”.  There’s quite a bit to say about this sort of thing!  Indeed, the issue of energy in general relativity has a lot to do with the notorious “problem of time” in quantum gravity. . . but that’s another can of worms.

— Original by Michael Weiss and John Baez

2013.01.26 Saturday ACHK