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  A pseudo-Newtonian limit for test motion in arbitrary space-times

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Referee this paper: arXiv:1601.01034 by Vojtech Witzany

Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)

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We present a particular low-energy limit of the Hamiltonian of free test particle motion in arbitrary relativistic space-times. As it turns out, this limit gives insight into the general Newtonian limit by providing an intermediate, "pseudo-Newtonian" step, which encompasses some pseudo-Newtonian formulas already present in the literature.

If the metric is expressed so as to be diagonal in the coordinate-time components, we are able to derive a description exactly reproducing the spatial shapes of geodesics. In fully general space-times where dragging ("time non-diagonal") terms appear in the metric, the limit at least yields a previously unknown Hamiltonian reproducing exact shapes of null geodesics. Furthermore, if the space-time is stationary, the exact shapes of null geodesics can be also correctly parametrized by coordinate-time, the limit thus provides an alternative Hamiltonian for computations in gravitational lensing.

Relevant astrophysical superpositions of gravitating sources, the addition of electromagnetic fields, and fluid dynamics in the pseudo-Newtonian limit are discussed. Additionally, the method is demonstrated in the case of the Kerr space-time and massive-particle circular orbits, and analogies with respect to the recent pseudo-Kerr Lagrangian by Ghosh et al. (2014) is commented upon.

requested Jan 8, 2016 by Void (1645 points)
summarized by Void
paper authored Jan 5, 2016 to class-gr by Void
  • [ revision history ]
    retagged Jan 14, 2016 by dimension10.admin

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