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Note on motion in the Schwarzschild field. Collapsing objects and the background emission of light. Master thesis, Eberhard–Karls Universität Tübingen (2004) Grave, F.: Visualisierungen zum Gravitationskollaps und Wellenfronten in der Allgemeinen Relativitätstheorie (in german). Past–future asymmetry of the gravitational field of a point particle. On the behavior of radiation near massive bodies. A comparison of Whitehead’s and Einstein’s formulas. Optical appearances of distant objects to observers near and inside a Schwarzschild black hole. Generalized observers and velocity measurements in general relativity. (arXiv: astro-ph/0709.4274)Ĭarter, B.: Half century of black-hole theory: from physicists “purgatory to mathematicians” paradise. 151: 659īakala, P., Čermák, P., Hledík, S., Stuchlík, Z., Truparová, K.: Extreme gravitational lensing in the vicinity of Schwarzschild-de Sitter black holes.
The optical appearance of a star that is collapsing through its gravitational radius. He can find meaningful information from these data.Abramowitz M. Thus, the physicist can compare and interpret the data intelligently. The numbers in the reports are translated into data in Schwarzschild coordinates, which provide a systematic means of evaluating and describing the events globally. The bookkeeper gathers and combines the reports from various places. Observers local to the events are enlisted to make measurements and send the results to him. Instead, he is far away from the black hole and the events. He does not directly make measurements of events that occur in different places. The metric is expressed in the +−−− sign convention.įree falling worldlines in classic Schwarzschild-Droste coordinatesĪ Schwarzschild observer is a far observer or a bookkeeper. The gravitational constant has a value of 1. The speed of light in flat spacetime has a value of 1. 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.Ĭonvention: The units for the variables are all geometrized. That these solutions were simply coordinate transformations of the usual Schwarzschild solution, although Einstein immediately believed that to be true. It was not explicitly shown until 1933 in Lemaître's paper The solution was proposed independently by Paul Painlevé in 1921 and Allvar Gullstrand in 1922. The outgoing ones are simply the time reverse of ingoing coordinates (the time is the proper time along outgoing particles that reach infinity with zero velocity). There is no coordinate singularity at the Schwarzschild radius (event horizon). The ingoing coordinates are such that 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. 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. Coordinates suitable for following a free-falling observer of a Schwarzchild black hole
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