# Energy density of grav. field - analagous to EM

1. Nov 19, 2009

### ringerha

The electromagnetic energy density is well-defined through the square of the Maxwell Field tensor. Why cannot such a quantity be defined for the grav. field?

2. Nov 19, 2009

### atyy

3. Nov 19, 2009

### Noja888

I heard a report on NPR that this idea is being explored and so far it seems possible to describe as a field at this time without violating measured observations. Not much detail was in the NPR report as to why.

4. Nov 19, 2009

### ringerha

5. Nov 19, 2009

### Jonathan Scott

It can't be defined as a true tensor mainly because one person's gravitational field is another one's free fall.

Landau and Lifgarbagez derive a specific unique symmetrical pseudotensor which is supposed to have all the right properties for gravitational energy density. I've not studied the LL pseudotensor in detail, but I think that in a weak field approximation the result is very similar to the Maxwell energy density and Poynting vector.

If you take a Newtonian model of gravity and combine it with the GR idea that the potential energy decreases the rest mass, you find that when you bring two masses together, the total energy of the masses decreases by twice the potential energy change. A simple explanation of this is that within this approximate model the gravitational field has a positive energy density $g^2/(8\pi G)$ where $g$ is the magnitude of the Newtonian acceleration. This expression is closely analogous to the Maxwell energy density in electromagnetism. When integrated over all space this accounts for the missing energy exactly. This value for the field can be shown to add up correctly for any static distribution of sources, except that it doesn't allow for the gravitational effect of the energy of the field itself (which is of course negligible anyway in the weak field approximation).

6. Nov 19, 2009

### Bob_for_short

Because the gravity in GR is not of a field nature but of geometric one. It is an effect of the curved space-time. That is why they introduce pseudo-tensors.

In the Logunov's RTG (in a flat space-time) the gravity is of a field nature and its energy-momentum density is well defined.

7. Nov 19, 2009

### ringerha

I like that... The analogy is complete because radiated electromagnetic energy also goes as the square of the acceleration.

8. Nov 19, 2009

### ringerha

The grav field would be represented by the geometric object - the Connection - which is not a tensor as you state. So the square of the connection could be a measure of energy. Didn't Einstein do someting like that early -on?