# Famous quotes containing the words speeds and/or light: “ An honest tale speeds best being plainly told. —William Shakespeare (1564–1616) “ Erasmus was the light of his century; others were its strength: he lighted the way; others knew how to walk on it while he himself remained in the shadow as the source of light always does. But he who points the way into a new era is no less worthy

in Doran-Cartesian coordinates, of the river field, essentially defines what we Gullstrand-Painlevé-Cartesian coordinate system xµ. By definition, the scalar

41. While I understand Doran coordinates and Doran form (Gullstrand-Painlevé form at a=0), I'm not entirely convinced with Gullstrand-Painlevé coordinates. While the Doran time coordinate ( t ¯) is expressed-. d t ¯ = d t + β 1 − β 2 d r. where. At the end of part 1, we looked at the form the metric of the Schwarzschild geometry takes in Gullstrand-Painleve coordinates: ds^2 = – \left( 1 – \frac{2M}{r} \right) dT^2 + 2 \sqrt{\frac{2M}{r}} dT dr + dr^2 + r^2 \left( d\theta^2 + \sin^2 \theta d\phi^2 \right) It really does not have anything to do with the Gullstrand-Painleve coordinates.

. . . 10.3 Kerr coordinates and extension of the spacetime manifold through ∆=0 . 266.

## • The original Gullstrand-Painleve coordinates are for “rain”, e=1 • (Bonus: generalised Lemaitre coordinates) Generalised Gullstrand-Painlevé coordinates

We predict t example, consider a situation where a metric is independent of a certain coordinate in a certain coordinate system, say q. Then, we claim that ξα = ∂/∂q is a Killing vector on that spacetime.3 To see this, let us assume ξα = ∂q and consider ∇αξ β +∇βξ α = ∇αξ β +gβµg αν∇µξ ν = Γβ αλξ λ+gβµg ανΓ ν λ The continuation of the Schwarzschild metric across the event horizon is a well-understood problem discussed in most textbooks on general relativity.

### The importance of choosing an appropriate time coordinate when describing physical processes in the vicinity of Painlevé P. C.R. Acad. Gullstrand A. Arkiv.

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. These were first introduced in the 1920s, and have 15 feb 2021 Finally, we extend this to the case of nonzero curvature constant, again using Gullstrand-Painlevé coordinates.

De inngående koordinatene er slik at tidskoordinaten følger riktig tid for en fritt fallende observatør som starter langt borte med null hastighet, og de romlige skivene er flate. We derive the exact equations of motion (in Newtonian, F = ma, form) for test masses in Schwarzschild and Gullstrand–Painlevé coordinates. These equations of motion are simpler than the usual geodesic equations obtained from Christoffel tensors, in that the affine parameter is eliminated. A Painlev´e–Gullstrand synchronization is a slicing of the spacetime by a family of ﬂat space-like 3-surfaces. For spherically symmetric spacetimes, we show that a Painleve–Gullstrand synchronization only exists in the region where´ (dr)2 1, r being the curvature radius of the isometry group orbits (2-spheres). Likewise, the outgoing Eddington–Finkelstein coordinates are obtained by replacing t with the null coordinate . The metric is then given by In both these coordinate systems the metric is explicitly non-singular at the Schwarzschild radius (even though one component vanishes at this radius, the determinant of the metric is still non-vanishing and the inverse metric has no terms which diverge
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.

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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. These were first introduced in the 1920s, and have 15 feb 2021 Finally, we extend this to the case of nonzero curvature constant, again using Gullstrand-Painlevé coordinates.

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
example, consider a situation where a metric is independent of a certain coordinate in a certain coordinate system, say q.

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### Gold Member. 748. 41. While I understand Doran coordinates and Doran form (Gullstrand-Painlevé form at a=0), I'm not entirely convinced with Gullstrand-Painlevé coordinates. While the Doran time coordinate ( t ¯) is expressed-. d t ¯ = d t + β 1 − β 2 d r. where.

PACS numbers: 04.20.Cv, 04.20.−q 1. Introduction 2009-02-02 2011-05-01 gravitational collapse, gravitation, general relativity, black hole, Schwarzschild coordinates, Gullstrand-Painleve coordinates, Friedmann-Robertson-Walker metric, finite-time collapse other publication id LU-TP 21-02 language English id 9040456 date added to LUP … 2007-07-12 And inside the horizon, the velocity exceeds the speed of light. Technically, the Gullstrand-Painlevé metric encodes not only a metric, but also a complete orthonormal tetrad, a set of four locally inertial axes at each point of the spacetime. The Gullstrand-Painlevé tetrad free-falls through the coordinates at the Newtonian escape velocity. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We derive the exact equations of motion (in Newtonian, F = ma, form) for test masses in Schwarzschild and Gullstrand-Painlevé coordinates. These equations of motion are simpler than the usual geodesic equations obtained from Christoffel tensors in that the affine parameter is eliminated.