4

I was wondering-how do you visualise curvature in the context of general relativity. The gravity well and trampoline analogies are quite wrong, so I want a more realistic approach to it (say, the way Einstein himself might have visualised it). Mathematically, it all makes sense, but I am not really sure how does this really looks like. More specifically:

  1. How do you visualise Riemann tensor?
  2. Ricci tensor?
  3. Weyl Tensor?

ANY DIFFERENCE IN THE VISUALISATIONS?

Qmechanic
  • 220,844
GRrocks
  • 2,818

1 Answers1

1

No actual diagrams, but this paper looks like it could be helpful: Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature. And there's also this course outline on John Baez's site, and Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes which does have a bunch of diagrams.

Also, you say "The gravity well and trampoline analogies are quite wrong"--it's true that the "rubber sheet diagrams" you often see cannot really be thought of as "gravity wells", but they can be defined in such a way as to accurately depict proper distances in a 2D subsection of a curved 3D hypersurface of simultaneity from a larger 4D spacetime, see my answer here. It's also possible to similarly "embed" a 1+1 dimensional cross-section (with one spacelike dimension and one timelike) of a larger 3+1 curved spacetime in a 2+1 flat (Minkowski) spacetime, see here.

Community
  • 1
Hypnosifl
  • 6,240