curved spacetime with Earth

    Caption: Einstein's general relativity (GR) shows that mass-energy causes spacetime to curve---in way that is NOT easy to perceive for relatively small mass objects like the Earth---but that can be measured.

    Features:

    1. The image illustrates the curvature vastly exaggerated with a 2-dimensional surface and the Earth as the mass-energy clump causing curvature.

      It's easy to understand curved 2-dimensional spaces like the surface of a sphere. The curvature is really in 3-dimensions which very hard for humans to visualize though mathematically it can be treated.

    2. The spacetime curvature is the cause of gravity which in turn is one of the causes of the motion of mass-energy. So GR is essentially a theory of gravity.

    3. Mass-energy is the jargon term in Relativityspeak for mass and energy which in relativistic physics are the same thing, just with different emphasis as we know from E=mc**2.

    4. It's all rather complicated to solve problems with GR since mass-energy causes gravity and gravity is one of the causes of the motion of mass-energy---so there are complicated feedback.

      One has to find a self-consistent GR solutions for physical systems dominated by gravity. This is NOT easy and, except for a few simple cases, requires masssive numerical solutions on the computer.

    5. There are a small set of exact analytic solutions in general relativity: only 6 depending on how you count them (see Wikipedia: Exact solutions in general relativity; Malcolm A. H. McCallum, 2013, Exact solutions of Einstein's equations).

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