Comment on your mom falls significantly faster than g

• Sasha@lemmy.blahaj.zone ⁨2⁩ ⁨weeks⁩ ago

  Yeah it would fair point, I’ll be honest I haven’t touched Newtonian gravity in a long time now so is forgotten that was a thing.

  There’s a similar phenomenon in general relativity, but it doesn’t apply when you’ve got multiple sources because it’s non-linear.

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  • BB84@mander.xyz ⁨2⁩ ⁨weeks⁩ ago

    So if I have a spherically symmetric object in GR I can write the Schwarzschild metric that does not depend on the radial mass distribution. But once I add a second spherically symmetric object, the metric now depends on the mass distribution of both objects?

    Your point about linearity is that if GR was linear, I could’ve instead add two Schwarzschild metrics together to get a new metric that depends only on each object’s total mass?

    But even in a situation with one source, does the shell theorem work in GR? Say I put a infinitely light spherical shell around a black hole. Would it follow the same geodesic as a point particle?

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    • Sasha@lemmy.blahaj.zone ⁨2⁩ ⁨weeks⁩ ago

      Yeah, once you add in a second mass to a Schwarzschild spacetime you’ll have a new spacetime that can’t be written as a “sum” of two Schwarzschild spacetimes, depending on the specifics there could be ways to simplify it but I doubt by much.

      If GR was linear, then yeah the sum of two solutions would be another solution just like it is in electromagnetism.

      I’m actually not 100% certain how you’d treat a shell, but I don’t think it’ll necessarily follow the same geodesic as a point like test particle. You’ll have tidal forces to deal with and my intuition tells me that will give a different result, though it could be a negligible difference depending on the scenario.

      Most of my work in just GR was looking at null geodesics so I don’t really have the experience to answer that question conclusively. All that said, from what I recall it’s at least a fair approximation when the gravitational field is approximately uniform, like at some large distance from a star. The corrections to the precession of Mercury’s orbit were calculated with Mercury treated as a point like particle iirc.

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      • BB84@mander.xyz ⁨2⁩ ⁨weeks⁩ ago

        even light can stop following null geodesics because the curvature can be too big compared to the wavelength

        Very interesting! How do you study something like this? Is it classical E&M in a curved space time, or do you need to do QED in curved space time?

        Also, are there phenomena where this effect is significant? I’m assuming something like lensing is already captured very well by treating light as point particles?

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      • Sasha@lemmy.blahaj.zone ⁨2⁩ ⁨weeks⁩ ago

        On that first point, calculating spacetime metrics is such a horrible task most of the time that I avoided it at all costs. When I was working with novel spacetimes I was literally just writing down metrics and calculating certain features of the mass distribution from that.

        For example I wrote down this way to have a solid disk of rotating spacetime by modifying the Alcubierre warp drive metric, and you can then calculate the mass distribution along the radius. I did that calculation to show that such a spacetime requires negative mass to exist.

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