# What,s the energy of the gravitational field?

1. May 12, 2006

### eljose

What,s the "energy" of the gravitational field?..

If we can define for the Electro-Magnetic field an "energy"...

$$Energy= \alpha \int_{V} (E^{2}+B^{2})dv$$

where E and B are the electric and magnetic field..but my question is...¿why can not define an "energy" for the gravitational field so H=Energy where H is the Hamiltonian?..

2. May 12, 2006

### pervect

Staff Emeritus
The very short answer is "Noether's theorem".

http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html
gives some of the history

"Local" here is a rather ambibuous word - basically, when the author says that GR doesn't conserve energy "locally", he really means that we can't write the intergal you write above.

Basically, Noether's theorem says that the symmetry group of GR is too large (it's infinte, as the theory is diffemorphism invariant) to have a conserved energy in the sense above.

Last edited by a moderator: Apr 22, 2017
3. May 12, 2006

### Garth

Remember that energy is a frame dependent concept whereas energy-momentum is not.

Thus in GR it is energy-momentum that is conserved (in all frames) not generally energy.

There is one theory that also includes the local conservation of energy, but that is not "mainstream" (although published and about to be tested).

Garth