cavediver writes:
Ok, curvature as a source of curvature doesn't involve T and doesn't require dynamic solutions. All of my favourite solutions are vacuum: T=0. So G=8(pi)T reduces to just R=0... so much nicer and gets rid of all that nasty physics side of the equation. You're just left with maths.
Pure Schwarzschild is a vacuum solution and is static but as you know has considerable curvature. What is the source of this curavture? Itself. That is just a result of the non-linearity of the equations. (of course you can generate a non-vacuum Schwarzschild with a non-zero T... As you know, it is the solution outside an uncharged, non-rotating spherical mass)
The stress-energy (or in the case of the Schwartzchild solution, the mass) is the source of the curvature. Just as the electric charge is not the same thing as the electromagnetic field, but is the source of the electromagnetic field, the stress-energy/mass is not the curvature, but is the source of the curvature.
As for myself, I kind of like the Friedman solutions.
cavediver writes:
If we move to quantum gravity, this means the graviton self-interacts, like the gluons and the Weak bosons. The photon is the quantum of the LINEAR Maxwell equations, so photons don't self-interact. It's a good job as otherwise there would be such thing as sight!
The Linearity relates to EM being an Abelian gauge theory, where-as Gravity, Strong and Weak are non-Abelian gauge theories.
Yet the strong and the weak forces have been integrated, whereas we have yet been unable to cancel out the infinities in the case of gravity. I forget exactly what the difference is.
However, gravitational waves are generated only in the case of dynamic solutions. For example, the Kerr solution is the solution for a black hole with angular momentum, but in the Kerr solution, nothing actually changes, therefore no gravitational waves are produced, whereas with two neutron stars revolving around one-another, gravitational waves are produced, and therefore energy is lost from the system in the form of gravitational waves, resulting in the death spiral where they will ultimately collide.
See the following:
Binary pulsar PSR B1913+16
compiled by Wm. Robert Johnston
last updated 30 August 2004
Binary pulsar PSR B1913+16
No gravitons are emitted in the case of the non-dynamic solution, but when the solution is dynamic, gravitational waves are produced, in which case gravitons are produced which result in the loss of energy. The gravitons are the energy, just as photons are energy, and the energy will be equivilent to mass, resulting in additional spacetime curvature.