Visualizing General Relativity with Fluid Analogy

lukesfn
Messages
96
Reaction score
0
I'm interested in using a fluid analogy of general relativity to more easily visual what is going on in certain situations, without having to resort to visualizing curved 4d space time which is doesn't come to naturally.

However, I don't know relativity quite well enough to understand what the nature of the fluid would be, or even if it is possible to specify a fluid type of metric that can replicate all the effects of GR.

GR is often introduced with the ball rolling on rubber sheet analogy, which I always found more confusing then helpful, because it is meant to show how curved space causes a ball to fall into a dip, but in that analogy, the force of gravity is what pulls the ball down the slope, so it doesn't actually help explain much. It isn't just space that is curved, it is space time.

Instead I have always imagined the idea of space flowing into objects. What I would now like to understand better is, what would be the nature of flow, and where does this analogy break down.

If one was to create an animation, in 2D, of an object, with space flowing into it, how would it look? I imagine that the density of space would change as gravity increases. I would imagine that such an animation would give a much more intuitive idea of what is happening in GR, although, I could imagine some people may not like it because it is suggestive of some time of redundant dynamic ether.
 
Physics news on Phys.org
A.T. said:
Thanks a lot, I haven't found these before, but they look quite interesting after some speed reading. Looks like a good starting point. There is some mention of a fluid having a rotation at each point which sounds quite interesting.
A.T. said:
I think I have seen all of these links before. They are what I am trying to avoid. It's easier to imagine objects moving through a stream that is a similar shape to how we conceptualize the world a round us, rather then plotting some kind of geodesic on some strange higher dimensional space time surface it is difficult to relate to. Although, I expect that if you want to do any serious work, that is the way to go. Either way, it is good to be able to visualize things from different points of view.
 
OK, so this has bugged me for a while about the equivalence principle and the black hole information paradox. If black holes "evaporate" via Hawking radiation, then they cannot exist forever. So, from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon. Does the equivalence principle say my perspective is valid? If it does, is it possible that that person really never crossed the event horizon? The...
ASSUMPTIONS 1. Two identical clocks A and B in the same inertial frame are stationary relative to each other a fixed distance L apart. Time passes at the same rate for both. 2. Both clocks are able to send/receive light signals and to write/read the send/receive times into signals. 3. The speed of light is anisotropic. METHOD 1. At time t[A1] and time t[B1], clock A sends a light signal to clock B. The clock B time is unknown to A. 2. Clock B receives the signal from A at time t[B2] and...
From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
Back
Top