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For the benefit of brevity I'll give a straight answer: the second Weyl scalar is not related to electromagnetic radiation in any way. As per my previous comment, a simple proof is the Schwarzschild (or Kerr) spacetime. It describes a stationary black hole, without electromagnetic (or even gravitational) radiation, yet there is a basis in which all Weyl ...


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If you are asking about the mechanism that causes gravitation, it's mass. And energy. Why? General relativity doesn't say why. It says what happens. If you are asking why Einstein chose to use the equivalence principle as a guiding concept in his development of general relativity, in a very real sense he had no other choice. There's a general concept that ...


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I learned my GR from Landau and Lifshitz Classical Theory of Fields, 2nd edition. Even at 402 (4th Edition) pages it is kind of breathless. The interesting thing about it is the first half is special relativity and electrodynamics which dovetails into the 2nd half which is GR. One has to persivere because it's terse but not too terse. Like Weinberg it has a ...


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This is a statement about a congruence of null geodesics. We are looking for a conjugate point, which is just a place where the null geodesics cross each other. The theorem is putting a bound on how far you can advance the affine parameter $\nu$ along the geodesics before the conjugate point occurs (this is what is meant by affine parameter distance). ...


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As photons have energy, gravity affects light rays, turning their path from straight to curved, and changing their energy (frequency/color). In classical relativity light always travels in a straight zero-lenght line, with phase speed = $c$. If you include gravity in your relativistic model you this is not true anymore. As this is an important property of ...


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In general relativity the fundamental equation is roughly $$\textrm{Curvature} = \textrm{Matter content}$$ .In the context of general relativity it does not make sense to ask "why" matter curves spacetime, because this is the most basic assumption in the theory. It makes more sense to ask why one would try to construct a theory where gravitation is a ...


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For a stationary massive object like Earth or the Sun, the gravity well does not change from the expansion of space. The gravity well at one time is the same as the gravity well at future times for the same mass. Any minute force imposed by the expansion of space does not constitute a change in the gravity well itself. The well is not stretched or ...


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Duration is certainly a more physical concept than time. Duration is something you may measure between timelike separated events while time is always something you compute by adding up duration measurements + an arbitrary constant to fix the origin. Duration is experimental and relational while time (e.g. GPS time) is an abstract a posteriori ...


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Okay, I am going to try and give this a shot, but this is most probably not going to be a decisive answer. Let us operate with the term event time and duration and consider only special relativity (SR). The conclusions of general relativity should be the same for reasonable space-times. (e.g. without closed time-like curves etc.) We expect event time to ...


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General Relativity allows black holes of any size (though making a small one might be hard or worse than hard). So as a thought experiment that means that you can consider a small black hole that curves spacetime exactly as much as the sun does. This black hole would be much smaller than the sun, but to us out here spacetime would look the same (except we ...



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