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  2. Derivation of the Schwarzschild solution - Wikipedia

    en.wikipedia.org/wiki/Derivation_of_the...

    This is unfounded because that law has relativistic corrections. For example, the meaning of "r" is physical distance in that classical law, and merely a coordinate in General Relativity.] The Schwarzschild metric can also be derived using the known physics for a circular orbit and a temporarily stationary point mass. [1]

  3. Schwarzschild metric - Wikipedia

    en.wikipedia.org/wiki/Schwarzschild_metric

    In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero.

  4. Karl Schwarzschild - Wikipedia

    en.wikipedia.org/wiki/Karl_Schwarzschild

    Karl Schwarzschild (German: [kaʁl ˈʃvaʁtsʃɪlt] ⓘ; 9 October 1873 – 11 May 1916) was a German physicist and astronomer.. Schwarzschild provided the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical non-rotating mass, which he accomplished in 1915, the same year that Einstein first introduced general relativity.

  5. Metric tensor (general relativity) - Wikipedia

    en.wikipedia.org/wiki/Metric_tensor_(general...

    Its derivation can be found here. The Schwarzschild metric approaches the Minkowski metric as M {\displaystyle M} approaches zero (except at the origin where it is undefined). Similarly, when r {\displaystyle r} goes to infinity, the Schwarzschild metric approaches the Minkowski metric.

  6. Kruskal–Szekeres coordinates - Wikipedia

    en.wikipedia.org/wiki/Kruskal–Szekeres_coordinates

    The paler hyperbolas represent contours of the Schwarzschild r coordinate, and the straight lines through the origin represent contours of the Schwarzschild t coordinate. In general relativity , Kruskal–Szekeres coordinates , named after Martin Kruskal and George Szekeres , are a coordinate system for the Schwarzschild geometry for a black hole .

  7. Gullstrand–Painlevé coordinates - Wikipedia

    en.wikipedia.org/wiki/Gullstrand–Painlevé...

    The derivation of GP coordinates requires defining the following coordinate systems and understanding how data measured for events in one coordinate system is interpreted in another coordinate system. Convention: The units for the variables are all geometrized. Time and mass have units in meters. The speed of light in flat spacetime has a value ...

  8. Schwarzschild radius - Wikipedia

    en.wikipedia.org/wiki/Schwarzschild_radius

    The Schwarzschild radius was named after the German astronomer Karl Schwarzschild, who calculated this exact solution for the theory of general relativity in 1916. The Schwarzschild radius is given as =, where G is the gravitational constant, M is the object mass, and c is the speed of light.

  9. Schwarzschild coordinates - Wikipedia

    en.wikipedia.org/wiki/Schwarzschild_coordinates

    See Deriving the Schwarzschild solution for a more detailed derivation of this expression. Depending on context, it may be appropriate to regard a and b as undetermined functions of the radial coordinate (for example, in deriving an exact static spherically symmetric solution of the Einstein field equation). Alternatively, we can plug in ...