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Painlevé–Gullstrand coordinates for the Kerr solution

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Abstract

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-manifold. The stationary limit arises as the set of points on this manifold where the speed of the flow equals the speed of light, and the horizons as the set of points where the radial speed equals the speed of light. A deeper analysis of what is meant by the flow of space reveals that the acceleration of free-falling objects is generally not in the direction of this flow. Finally, we compare the new coordinate system with the closely related Doran coordinate system.

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  1. Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior Técnico, 1049-001, Lisboa, Portugal

    José Natário

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  1. José Natário
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Correspondence to José Natário.

Additional information

This work was partially supported by the Fundação para a Ciência e a Tecnologia through the Program POCI 2010/FEDER and by grant POCI/MAT/58549/2004.

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Natário, J. Painlevé–Gullstrand coordinates for the Kerr solution. Gen Relativ Gravit 41, 2579–2586 (2009). https://doi.org/10.1007/s10714-009-0781-2

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  • DOI: https://doi.org/10.1007/s10714-009-0781-2

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