We follow the original work by Oppenheimer and Snyder, starting from the general spherically symmetric metric in comoving coordinates. Further, a rederivation of the work by Chen, Adler, Bjorken and Liu shows that the same results can be obtained using the Friedmann-Robertson-Walker metric, with the curvature constant set to zero, and using Gullstrand-Painlev ́e coordinates.

For convenience, we will do this both with the Schwarzschild and GP coordinates. The reader can reinsert M by making the reverse substitution. Gullstrand-Painlevé (GP) coordinates were discovered by Allvar Gullstrand 1 [1] and Paul Painlevé [2] in 1921/1922: dτ 2 = (1 − 2M/r)dt 2 − 2 √ 2M/r dt dr − dr 2 − r 2 (dθ 2 + sin 2 (θ

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. 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.

This section also needs a reference since Wikipedia is not supposed to be original research. 24.84.125.240 10:24, 23 November 2013 (UTC) A known set of coordinates used for the Schwarzschild metric is the Painlevé-Gullstrand coordinates. They consist in performing a change from coordinate time $t$ to the proper time $T$ of radially infalling observers coming from infinity at rest. The transformation is the following $$ dT=dt+\left(\frac{2M}{r}\right)^{-1/2} f(r)^{-1}dr $$ For spherically symmetric spacetimes, we show that a Painlevé–Gullstrand synchronization only exists in the region where (dr)2 ≤ 1, r being the curvature radius of the isometry group orbits Painlevé–Gullstrand (PG) coordinates [3,4] penetrating the horizon (see [5] for a review).

By definition, the scalar Download scientific diagram | Schwarzschild black hole in Gullstrand-Painlevé coordinates, with singularity at r = 0 (red), showing constant r slices (green), and 6 Apr 2017 "Spherical spacelike geometries in static spherically symmetric spacetimes: Generalized Painleve-Gullstrand coordinates, foliation, and is equivalent to the Schwarzschild metric for any function Cprq.

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.

140 is invariant under a rescaling of the spacetime coordinates. xµ = (1 + λ)xµ. (2.34).

The continuation of the Schwarzschild metric across the event horizon is a well-understood problem discussed in most textbooks on general relativity. Among the most popular coordinate systems that are regular at the horizon are the Kruskal–Szekeres and Eddington–Finkelstein coordinates. Our first objective in this paper is to popularize another set of coordinates, the Painleve–Gullstrand

The transformation is the following $$ dT=dt+\left(\frac{2M}{r}\right)^{-1/2} f(r)^{-1}dr $$ For spherically symmetric spacetimes, we show that a Painlevé–Gullstrand synchronization only exists in the region where (dr)2 ≤ 1, r being the curvature radius of the isometry group orbits Painlevé–Gullstrand (PG) coordinates [3,4] penetrating the horizon (see [5] for a review). A chacteristic feature of PG coordinates is that the three-dimensional spatial sections of spacetimes foliated by these coordinates are ﬂat. 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 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.

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.
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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.

Among the most popular coordinate systems that are regular at the horizon are the Kruskal–Szekeres and Eddington–Finkelstein coordinates.
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Painlevé-Gullstrand coordinates, a very useful tool in spherical horizon thermodynamics, fail in anti-de Sitter space and in the inner region of Reissner-Nordström. We predict t

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.

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

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. Gullstrand coordinates” for a foliation of a spherically sym-metric spacetime with ﬂat spatial sections: this is an essen-tial feature of these coordinates that we want to preserve. Other very useful coordinates in the literature (e.g., those of [24] for the Reissner–Nordström spacetime) recast a spheri- A known set of coordinates used for the Schwarzschild metric is the Painlevé-Gullstrand coordinates. They consist in performing a change from coordinate time t to the proper time T of radially infalling observers coming from infinity at rest. The transformation is the following d T = d t + (2 M r) − 1 / 2 f (r) − 1 d r While I understand Doran coordinates and Doran form (Gullstrand-Painlevé form at a=0), I'm not entirely convinced with Gullstrand-Painlevé coordinates.

Gullstrand-Painlevé (GP) coordinates were discovered by Allvar Gullstrand 1 [1] and Paul Painlevé [2] in 1921/1922: dτ 2 = (1 − 2M/r)dt 2 − 2 √ 2M/r dt dr − dr 2 − r 2 (dθ 2 + sin 2 (θ 2007-07-12 · The isotropic coordinates have several attractive properties similar with the Painlevé–Gullstrand coordinates: There are non-singular at the horizon, the time direction is a Killing vector and the isotropic coordinates satisfy Landau's condition of the coordinate clock synchronization (1) ∂ ∂ x j (− g 0 i g 0 0) = ∂ ∂ x i (− g 0 j g 00) (i, j = 1, 2, 3). To describe the dynamics of collapse, we use ageneralized form of the Painlevé- Gullstrand coordinates in the Schwarzschildspacetime. The time coordinate of Abstract. The Painleve-Gullstrand coordinates provide a convenient framework for presenting the Schwarzschild geometry because of their flat constant-time 8 Jul 2016 Lorentz boost from. Schwarzschild to Gullstrand-. Painleve coordinates.