WebAug 25, 2024 · After a quick introduction to the Schwarzschild metric solution, it is now time to derive it. According to his letter from 22 december 1915, Schwarzschild started out from the approximate solution in … WebIn particular, the force produced by a gravitational field which source is spherically symmetrical (Schwarzschild’s spacetime) is obtained. Such expression uses a redefinition of the classical reduced mass, in the limit case it can be reduced to Newton’s Universal Law of Gravitation and it produces two different orbital velocities for test ...
A Mathematical Derivation of the - East Tennessee State …
The Schwarzschild solution is named in honour of Karl Schwarzschild, who found the exact solution in 1915 and published it in January 1916, a little more than a month after the publication of Einstein's theory of general relativity. It was the first exact solution of the Einstein field equations other than the trivial flat space solution. Schwarzschild died shortly after his paper was published, as a result of a disease he developed while serving in the German army during World War I. The Schwarzschild solution describes spacetime under the influence of a massive, non-rotating, spherically symmetric object. It is considered by some to be one of the simplest and most useful solutions to the Einstein field equations . See more On each hypersurface of constant $${\displaystyle t}$$, constant $${\displaystyle \theta }$$ and constant $${\displaystyle \phi }$$ (i.e., on each radial line), $${\displaystyle g_{11}}$$ should only depend on See more Using the metric above, we find the Christoffel symbols, where the indices are $${\displaystyle (1,2,3,4)=(r,\theta ,\phi ,t)}$$. The sign $${\displaystyle '}$$ denotes a total … See more The geodesics of the metric (obtained where $${\displaystyle ds}$$ is extremised) must, in some limit (e.g., toward infinite speed of light), … See more In deriving the Schwarzschild metric, it was assumed that the metric was vacuum, spherically symmetric and static. The static assumption is unneeded, as Birkhoff's theorem states that any spherically symmetric vacuum solution of Einstein's field equations See more To determine $${\displaystyle A}$$ and $${\displaystyle B}$$, the vacuum field equations are employed: See more The Schwarzschild metric can also be derived using the known physics for a circular orbit and a temporarily stationary point mass. Start … See more • Karl Schwarzschild • Kerr metric • Reissner–Nordström metric See more imsc s3
Physics:Derivation of the Schwarzschild solution - HandWiki
WebMar 5, 2024 · The Schwarzschild solution describes spacetime under the influence of a massive, non-rotating, spherically symmetric object. It is considered by some to be … WebJan 4, 2024 · Abstract This paper presents a derivation of the temporally static and spatially isotropic solution of the Einstein's Field Equations for a non-rotating body in vacuum … WebThe Schwarzschild Solution 8.1 Cartan’s structure equations 8.1.1 Curvature forms This section deals with a generalisation of the connection coefficients, and the torsion and … ims crushers