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Deriving the Schwarzschild Solution to Einstein's Field Equations

http://gmjacksonphysics.blogspot.de/2017/04/deriving-schwarzschild-solution-to.htm

Deriving the Schwarzschild Solution to Einstein's Field Equations

by Grandmaster Jackson

Excerpts

Each dimension in space is a hypotenuse of a right triangle with two other dimensions which can replace the hypotenuse. We make a final substitution and we get the Schwarzschild metric (equation 32). Schwarzschild used spherical coordinates. For clarity and to help you visualize this type of coordinate system, I provide the diagrams below. The first two diagrams show the front and side view of a sphere of spacetime with a mass in the center. The position in spacetime is given by the radius (r), the first angle (top diagram), and a shorter radius (rsin[first angle]) and the second angle (bottom diagram).

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We can solve for R44--the spacetime curvature--by plugging in the mass (m) of a star, planet or black hole; the volume (V) of the space, mass and energy within an imaginary sphere with radius (r); and radius (r).

http://gmjacksonphysics.blogspot.de/2017/04/deriving-schwarzschild-solution-to.html