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Originally Posted by Nesti
What I find really interesting about gravity, it that Gravity Waves are not included within the Einstein Equation, in that on the left side we have the Einstein Tensor (consisting of the Ricci Tensor, the Metric, and then the Scalar Curvature), then on the right side we have the Energy Momentum (consisting of the 8xPi, the Gravitational Constant, and the Energy Density).
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The matter energy tensor (the right hand term) is not relevant if one wants to use black holes in the argument. This term is only applied when one is interested in external gravitational and/or electromagnetic fields acting on the field in question. It also applies to extended objects where matter is found in the field.
Gravitational waves are formed by variations of the field itself.
In other words you only need to consider the extension of the field into empty space and the propagation of gravitational waves into empty space.
The Einstein equation simply becomes Ricci Tensor=0.
Gravitational waves are derived mathematically by applying perturbation to the metric components of the Lorentzian metric. The components are time dependent indicating the field varies with time.
This is a solution to the equation.
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But gravity waves are separate, they run only within the metric tensor, and as such energy within a gravitational field cannot be conserved, unlike electric and magnetic fields.
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You have lost me. If a gravitational field varies, the energy in the field is conserved by the radiation of gravity waves. That's the basis behind the existence of gravitational waves.
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SO, this means that gravity waves slip underneath the gravitational field (geodesics) without being affected…we see this in Black Holes, where nothing can escape them, not even light, but the mass of a black hole creates gravity waves which can and do escape.
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The mass alone (density) does not create gravitational waves. A static (Schwarzchild metric) black hole doesn't generate gravitational waves. A rotating (Kerr metrc) black hole can be a different matter. Since it rotates, there is centripetal force (with a non vanishing Christoffel) that adds to the field strength. By slowing down the rotation, the loss in rotational energy is taken up by the frequency of the emitted gravitational waves.
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I've said it before, gravity (GR) is a fictitious force, it is mediated by “slippery-trickery mathematics” and is nothing like the other forces.
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There is nothing devious about the maths unlike the manipulations that occur in Quantum Field Theory.
Regards
Steven