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If the gravity well of a non-rotating heavy object is in roughly the same inertial frame as an observer, its spacetime geometry (as measured e.g. by photon lensing) will present as spherically symmetric.

If the same object is passes near the observer at a linear velocity close to c, special relativity would seem to require that its gravity well present itself (e.g. through photon lensing) as both deeper and asymmetrically compressed in the direction of motion.

Is that correct? Does SR transform the shape of spacetime around fast-moving heavy objects, and does it do so in a fashion that is experimentally measurable using photons and other particles as probes?

[Note to readers: I stupidly used the phrase "rubber sheet model" in my first try at this question, so the first comments you will see below are referring to that version.]

Terry Bollinger
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    Note that the rubber-sheet model kind of sucks – rob Dec 15 '17 at 16:32
  • Related: http://physics.stackexchange.com/a/13839/2451 and links therein. – Qmechanic Dec 15 '17 at 16:37
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    @Rob, No disagreement, but as with all those 2D surface videos of massive pairs, correct visusl subsets can help engage the analytically powerful visual components of human cognition. Those are never a substitute for the math, but they can be unexpectedly useful for navigating the often very large configuration spaces implied by the math. – Terry Bollinger Dec 15 '17 at 17:01
  • The main problem with the rubber-sheet model is that it has NOTHING to do with general relativity. It works on completely different principle and is popular for the sole reason that it easily fools people into thinking that they understand how curved spacetime works. – OON Dec 15 '17 at 17:29
  • That 2D surfaces cannot possibly explain GR is trivially obvious, so I'm trying to understand what you mean. Are you asserting that it is flatly impossible to create a formal mechanism for down-projecting a topologically meaningful subset of complete GR model data onto a 3D embedded 2D surface? If so, I'll of course retract this question. But I must say that does not sound right, given the frequency with which such projections are used in papers, including all those recent neutron star collision papers. – Terry Bollinger Dec 15 '17 at 17:45
  • https://physics.stackexchange.com/questions/256521/does-an-object-creates-gravitational-waves-when-only-accelerating-in-one-directi –  Dec 16 '17 at 06:50
  • Terry, rubber sheet model seems to annoy some people .What you probably mean is a computer graphics simulation/visualization . I am just not sure what is it that you want to visualise. Is it a massive, extended object in an otherwise empty background? – magma Dec 16 '17 at 10:06
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    Trying to apply SR to the gravitational fields around objects is a canonical example of something that won't work. For instance you talk about a gravity well 'being in an inertial frame' as if that makes sense, but it doesn't. –  Dec 16 '17 at 13:45
  • @tfb thanks that is why I'm asking! Something must transform in the situation I just described, if nothing else because the probe photons if the observer cannot possibly return a spherically symmetric result. Surely there is some mature subset of GR papers that accurately describes what does happen in this situation? – Terry Bollinger Dec 16 '17 at 15:32

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