View Full Version : Gravitational Energy in general relativity

iniaes

2010-Apr-17, 08:40 PM

I was wandering (given e=mc^2) does gravitational energy (or the enrgy of the strong or weak force) contribute to the curvature of space-time, or is it only mass and electromagnetic energy that affects space-time to cause the curvature we experience as gravity/accelleration?

Thanks in advance for your time and answers :)

Hornblower

2010-Apr-17, 10:27 PM

I was wandering (given e=mc^2) does gravitational energy (or the enrgy of the strong or weak force) contribute to the curvature of space-time, or is it only mass and electromagnetic energy that affects space-time to cause the curvature we experience as gravity/accelleration?

Thanks in advance for your time and answers :)

If I am not mistaken, all forms of energy contribute to that curvature. For example, a star that has fused most of its original hydrogen into helium is less massive than it was in the beginning. The hydrogen had nuclear potential energy that was released when the strong nuclear force overpowered the electrostatic repulsion of like charges and bound the particles together.

publius

2010-Apr-21, 12:36 AM

I was wandering (given e=mc^2) does gravitational energy (or the enrgy of the strong or weak force) contribute to the curvature of space-time, or is it only mass and electromagnetic energy that affects space-time to cause the curvature we experience as gravity/accelleration?

Thanks in advance for your time and answers :)

Actually, this is a very involved subject. The meaning of gravitational energy in General Relativity is a very complex subject. In GR, the Newtonian notion of gravitational energy doesn't exist, although there is what can be called, or seems it should be called a type of gravitational energy.

The source of space-time curvature in GR is the source term of the EFE, the dreaded Einstein Field Equation. The right hand side of that is known as the stress-energy tensor and contains all "non gravitational' forms of energy (and momentum and the flow of both). Now, the EFE is a complicated non-linear humdinger of a tensor mess. Those complex operations can be broken out and in certain circumstances, one can move terms to the right hand side along with the stress-energy tensor, and come up with something conceptually thus:

Simpler_differential_equation = Stress_energy + (high order non-linear terms).

One can think of the higher order non-linear stuff as being gravitational contributions to a simpler equation for gravity on the left-hand side. But that's just a way of thinking of it.

And then there enters gravitational radiation, and the complicated dynamic space-times that go along with it. Gravitaitonal radiation can take energy and momentum away from a system (or bring it in). The trouble is, that "missing energy" can't be made invariant in a sastifactory global way in the general case.

-Richard

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