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- Gullstrand–Painlevé_coordinates abstract "Historical overview: Painlevé-Gullstrand (PG) metric were proposed independently by Paul Painlevé in 1921 and Allvar Gullstrand in 1922 as a solution to Einstein's equations of General Relativitiy for a spherically symmetric system. It was not recognized until 1933 in Lemaître's paper that these solutions were simply coordinate transformations of the usual Schwarzschild solution. Both Painlevé and Gulstrand used this solution to argue that Einstein's theory was incomplete in that it gave multiple solution for the gravitational field of a spherical body, and moreover gave different physics (they argued that the lengths of rods could sometimes be longer and sometimes shorter in the radial than the tangential directions). The "trick" of the Painlevé proposal was that he no longer stuck to a full quadratic (static) form but instead, allowed a cross time-space product making the metric form no longer static but stationary and no longer direction symmetric but preferentially oriented.In a second, longer paper (November 14, 1921), Painlevé explains how he derived his solution: by directly solving Einstein's equations for a generic spherically symmetric form of the metric.The result, equation (4) of his paper, depended on two arbitrary functions of the r coordinate yielding a double infinity of solutions. We now know that these simply represent a variety of choices of both the time and radial coordinates.Painlevé wrote to Einstein to introduce his solution and invited Einstein to Paris for a debate. In Einstein reply letter (December 7) Einstein apologized for not being in a position to come soon, and explained why he was not pleased with Painlevé's arguments, criticisms and solutions emphasising that the coordinates themselves have no meaning. Finally, Einstein came to Paris in early April. On the 5th of April 1922, in a debate at the "Collège de France" with Painlevé, Becquerel, Brillouin, Cartan, De Donder, Hadamard, Langevin and Nordmann on "the infinite potentials", Einstein, baffled by the non quadratic cross term in the line element, rejected the Painlevé solution. That signed the death warrant (for a long time) of the Painlevé proposal., mainly p. 34 for the debate about the horizon and penultimate paragraph for the final statement of Einstein declaring the debate void!".
- Gullstrand–Painlevé_coordinates wikiPageID "9223226".
- Gullstrand–Painlevé_coordinates wikiPageRevisionID "592179261".
- Gullstrand–Painlevé_coordinates subject Category:Black_holes.
- Gullstrand–Painlevé_coordinates subject Category:Coordinate_charts_in_general_relativity.
- Gullstrand–Painlevé_coordinates subject Category:Lorentzian_manifolds.
- Gullstrand–Painlevé_coordinates comment "Historical overview: Painlevé-Gullstrand (PG) metric were proposed independently by Paul Painlevé in 1921 and Allvar Gullstrand in 1922 as a solution to Einstein's equations of General Relativitiy for a spherically symmetric system. It was not recognized until 1933 in Lemaître's paper that these solutions were simply coordinate transformations of the usual Schwarzschild solution.".
- Gullstrand–Painlevé_coordinates label "Coordinate di Gullstrand-Painlevé".
- Gullstrand–Painlevé_coordinates label "Gullstrand–Painlevé coordinates".
- Gullstrand–Painlevé_coordinates sameAs Gullstrand%E2%80%93Painlev%C3%A9_coordinates.
- Gullstrand–Painlevé_coordinates sameAs Coordinate_di_Gullstrand-Painlevé.
- Gullstrand–Painlevé_coordinates sameAs Q5617809.
- Gullstrand–Painlevé_coordinates sameAs Q5617809.
- Gullstrand–Painlevé_coordinates wasDerivedFrom Gullstrand–Painlevé_coordinates?oldid=592179261.