# 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.

Painlevé-Gullstrand coordinates for the Kerr solution - NASA/ADS. 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

Gullstrand A. Arkiv. Painlevé-Gullstrand coordinates. The line element for the unique We seek a new coordinate t = t(T,r,θ,φ) that yields the Schwarzschild line element ds2 = (1 10 Oct 2019 General Coordinate Transformations in Minkowski Space I: Metric . . .

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## 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.

Painlev´e-Gullstrand coordinates The line element for the unique spherically symmetric, vacuum solution to the Einstein equation can be written as ds2 = dT 2−(dr + s 2M r dT) −r2dΩ2 (1) Note that a surface of constant T is a ﬂat Euclidean space. 1. Which value of r corresponds to the event horizon? Give a clear and pre- First and foremost, the Gullstrand-Painlevé coordinates are not an independent solution of Einstein’s field equation, but rather an adjustment of the Schwarzschild solution to a different coordinate reference, such that the apparent coordinate singularity at [r=Rs] is avoided.

### To describe the dynamics of collapse, we use a generalized form of the Painlevé-Gullstrand coordinates in the Schwarzschild spacetime. The time coordinate of the form is the proper time of a free-falling observer so that we can describe the collapsing star not only outside but also inside the event horizon in a single coordinate patch.

PG coor-dinates constitute a very useful chart also in other problems Coordinate di Gullstrand-Painlevé Quadro storico. Le metriche di Painlevé-Gullstrand (PG) furono proposte indipendentemente da Paul Painlevé nel 1921 e Derivazione. La derivazione delle coordinate di GP richiede di definire i sistemi di quelle successive e di capire come Coordinate di In GP coordinates, the velocity is given by.

The Droste-Schwarzschild metric in isotropic coordinates. (setting G = 1 = c) is ds2 = −. (. 1− m. 2r. ) For black or white holes Zermelo picture is equivalent to the use of Painlevé-.

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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. There is no coordinate singularity
Gullstrand–Painlevé coordinates: | |Gullstrand–Painlevé coordinates| are a particular set of coordinates for the |Schwarzsch World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled.

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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 speed of the raindrop is inversely proportional to the square root of radius. 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. "Gullstrand–Painlevé coordinates" are a particular set of coordinates for the Schwarzschild metric – a solution to the Einstein field equations which describ Painlev´e-Gullstrand coordinates The line element for the unique spherically symmetric, vacuum solution to the Einstein equation can be written as ds2 = dT 2−(dr + s 2M r dT) −r2dΩ2 (1) Note that a surface of constant T is a ﬂat Euclidean space.

## 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.

The transformation … 2019-04-25 2016-12-18 It really does not have anything to do with the Gullstrand-Painleve coordinates. (Why is Gullstrand's name first since his paper was published later?).

The Droste-Schwarzschild metric in isotropic coordinates.