Caption: A conceptual animation of both (3-dimensional physical) space distortions and time distortions (i.e., the spacetime) near a general spherically symmetric mass distribution (e.g., star or black hole outside of the event horizon).

The spacetime geometry is that of the Schwarzschild solution (1916) to general relativity (1915) for a spherically symmetric mass distribution. Karl Schwarzschild (1873--1916) discovered his eponymous solution while serving in the Imperial German Army at the Russian front in 1915: he was soon invalided home to die. The Schwarzschild solution was the first exact analytic solution to general relativity. Albert Einstein (1879--1955) himself only ever found one exact analytic solution and it was NOT a top-level solution. For more information on exact analytic solutions to general relativity, see Relativity file: general_relativity_exact_solutions.html.

Features:

1. The animation is a visualization tool. You CANNOT completely represent 3-dimensional curved spaces in 2-dimensional flat space imagery.

   The animation can only show certain aspects of 3-dimensional curved space of the Schwarzschild solution.

2. The rotation in the animation is just for viewing: the system is NOT rotating.

3. Note the transverse distances getter shorter compared to the radial distances as you go deeper into the gravitational well due to (3-dimensional physical) space distortions.

4. Note the clocks run slower compared to those of outside observers the deeper you go into the gravitational well due gravitational time dilation.

5. Yours truly thinks this animation is qualitatively accurate, but will NOT swear to it.

6. As a historical tidbit, it is sad to say, Schwarzschild and Alexander Friedmann (1888--1925) were on the opposite sides of the line on the Russian front during World War I (1914--1918).

   Friedmann was the discoverer of the Friedmann equation (1922), another exact analytic solution to general relativity and the key equation of modern general relativistic cosmology. For more on Friedmann, see Astronomer file: alexander_friedmann.html.