# Spherically Symmetric Gravitational Collapse

TRYCK - Essays.se

Our first objective in this paper is to popularize another set of coordinates, the Painleve–Gullstrand These include: Kruskal-Szekeres [@kruskal1960;@szekeres1960], Eddington-Finkelstein [@eddington1924;@finkelstein1958], Gullstrand-Painleve [@painleve1921; @gullstrand1922], Lemaitre [@lemaitre1933], and various Penrose transforms with or without a black hole [@hawking1973]. Painlevé–Gullstrand coordinates for the Kerr solution Painlevé–Gullstrand coordinates for the Kerr solution Natário, José 2009-03-08 00:00:00 We construct a coordinate system for the Kerr solution, based on the zero angular momentum observers dropped from infinity, which generalizes the Painlevé–Gullstrand coordinate system for the Schwarzschild solution. For an explanation of the equations of motion, see The Force of Gravity in Schwarzschild and Gullstrand-Painleve Coordinates, Carl Brannen, (2009, 6 pages LaTeX). Source code: GravSim.java HTML made with Bluefish HTML editor. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We construct a coordinate system for the Kerr solution, based on the zero angular momentum observers dropped from infinity, which generalizes the Painlevé-Gullstrand coordinate system for the Schwarzschild solution. The Kerr metric can then be interpreted as describing space flowing on a (curved) Riemannian 3-manifod.

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At places very far away from the black hole, the speed is extremely small. As the raindrop plunges toward the black hold, the speed increases. At the event horizon, the speed has the value 1, same as the speed of light. It is known that Painlev ´ e, Gullstrand and (some years later) Lema ˆ ıtre used a non-orthogonal curvature coordinate system which allows to extend the Sc hwarzsc hild solution inside its horizon, The boundary and gauge fixing conditions are chosen to be consistent with generalized Painleve-Gullstrand coordinates, in which the metric is regular across the black hole future horizon. For convenience, we will do this both with the Schwarzschild and GP coordinates.

## TRYCK - Essays.se

There is no coordinate singularity 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 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. 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.

### TILL GULLSTRAND - Uppsatser.se

2r. ) For black or white holes Zermelo picture is equivalent to the use of Painlevé-. Gullstrand coordinates. Here is a low-tech exampl 1 Aug 2019 formation [11]) in the Painlevé–Gullstrand coordinates, which are naturally adapted to a freely-falling observer. Given that the RSET. There are a few choices of these types of coordinates with the most common being the Gullstrand-Painleve coordinates. If we take the Schwarzschild metric.

relativity; black hole; Schwarzschild coordinates; Gullstrand-Painleve coordinates; from the general spherically symmetric metric in comoving coordinates. "The metric in*Kruskal–Szekeres coordinates*covers all of the have some similarity to the*Gullstrand–Painlevé coordinates*in that both are
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. 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.

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To describe the dynamics of collapse, we use ageneralized form of the Painlevé-Gullstrand coordinates in the Schwarzschildspacetime. The time coordinate of the form is the proper time of a free-fallingobserver so that we can describe the collapsing star not only outside but alsoinside the event horizon in a single coordinate patch. For convenience, we will do this both with the Schwarzschild and GP coordinates. The reader can reinsert M by making the reverse substitution.

19 Jul 2010 Painlevé–Gullstrand (PG) coordinate system, the metric is not diagonal, but recovers the extended Schwarzschild metric in PG coordinates,
Gullstrand–Painlevé coordinates are a particular set of coordinates for the Schwarzschild metric – a solution to the Einstein field equations which describes a
The importance of choosing an appropriate time coordinate when describing physical processes in the vicinity of Painlevé P. C.R. Acad. Gullstrand A. Arkiv.

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### Paradox då man faller in i svart hål. - Sidan 2 - Flashback Forum

There are a few choices of these types of coordinates with the most common being the Gullstrand-Painleve coordinates. If we take the Schwarzschild metric. 16 Oct 2019 Gullstrand-Painlevé coordinates [45,52,53]. Having worked out the general case, we now study a special case with u as a constant, φ = 0, and 6 Oct 2018 The corresponding coordinate system is called Painleve - Gullstrand 1: Charged non - rotated black hole in Painleve Gullstrand reference The Schwarzschild metric: It's the coordinates, stupid! One such system, introduced by Painleve and Gullstrand in the 1920's, is especially simple and pe. first objective in this paper is to popularize another set of coordinates, the Painlevé–Gullstrand coordinates.