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Gullstrand–Painlevé coordinates are a particular set of coordinates for the Schwarzschild metric – a solution to the Einstein field equations which describes a black hole. The time coordinate follows the proper time of a free-falling observer who starts from far away at zero velocity, and the spatial slices are flat. There is no coordinate singularity at the Schwarzschild radius (event horizon). The solution was proposed independently by Paul Painlevé in 1921 〔Paul Painlevé, "La mécanique classique et la théorie de la relativité", (C. R. Acad. Sci. (Paris) 173, 677–680(1921) ).〕 and Allvar Gullstrand in 1922. It was not recognized until 1933 in Lemaître's paper 〔 〕 that these solutions were simply coordinate transformations of the usual Schwarzschild solution. ==Derivation== 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 of 1. The gravitational constant has a value of 1. The metric is expressed in the +−−− sign convention. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Gullstrand–Painlevé coordinates」の詳細全文を読む スポンサード リンク
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