Graduate Is There a Proper Way to Define Energy in General Relativity?

[bhobba]

In another thread Peter Donis mentioned there may be a way to define energy properly GR.

I always thought it highly problematical because you don't have time transnational symmetry so Nother can be applied.

John Baez wrote an interesting article about it:
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

Has the situation changed since then or are we still stuck with the same issues - or am I missing something? The second option is most likely

Thanks
Bill

 

[PAllen]

Baez article remains a good summary, so far as I know. It would help to link to the thread you implicitly reference. Note that Baez does briefly refers to approaches that some physicists believe provide general solutions, but such beliefs have never reached consensus (e.g. Hamiltonian formulations, quasilocal energy, or the various pseudotensors; I would call Philip Gibbs approach as being a variant of Hamiltonian formulation with exactly zero total energy for closed universes). There are claims that pseudotensors meet all reasonable physical expectations when harmonic coordinates are used, and you should accept this coordinate preference for this specific purpose. So I would say 'stuck with the same issues' is a remains a good summary.

 

[PeterDonis]

In another thread Peter Donis mentioned there may be a way to define energy properly GR.

Can you give a specific quote?

 

[bhobba]

Can you give a specific quote?

then there is in fact a way to define "energy stored in the gravitational field" in an invariant way--it's just the GR analogue of the Newtonian gravitational potential energy (defined using the norm of the timelike KVF). But this energy is not a tensor; it's a scalar.

As I said - I may be missing something - but I am sure Peter can clarify.

Thanks
Bill

 

[PeterDonis]

I may be missing something

You are. I said that in a stationary spacetime there is an invariant way to define energy stored in the gravitational field. You left out the rest of my post where I made the qualifier clear.

I always thought it highly problematical because you don't have time transnational symmetry so Nother can be applied.

A stationary spacetime does have time translation symmetry; it has a timelike Killing vector field, by definition.

(Note that the Baez article @PAllen linked to says "static" when it should really say "stationary". A static spacetime is a stationary spacetime whose timelike KVF is hypersurface orthogonal; heuristically, that means the source of gravity is not rotating. But you don't need that extra condition to define gravitational potential energy; just the timelike KVF is enough.)

 

[Dale]

heuristically, that means the source of gravity is not rotating. But you don't need that extra condition to define gravitational potential energy; just the timelike KVF is enough.)

Which makes sense by Noether’s theorem.