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arXiv · 1601.01034

Pseudo-Newtonian equations for evolution of particles and fluids in stationary space-times

Vojtech Witzany·Claus Laemmerzahl
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Abstract

Pseudo-Newtonian potentials are a tool often used in theoretical astrophysics to capture some key features of a black-hole space-time in a Newtonian framework. As a result, one can use Newtonian numerical codes, and Newtonian formalism in general, in an effective description of important astrophysical processes such as accretion onto black holes. In this paper we develop a general pseudo-Newtonian formalism which pertains to the motion of particles, light, and fluids in stationary space-times. In return, we are able to assess the applicability of the pseudo-Newtonian scheme. The simplest and most elegant formulas are obtained in space-times without gravitomagnetic effects, such as the Schwarzschild rather than the Kerr space-time; the quantitative errors are smallest for motion with low binding energy. Included is a ready-to-use set of fluid equations in Schwarzschild space-time in Cartesian and radial coordinates.

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Vojtech Witzany, Claus Laemmerzahl. 2016-01-06. Pseudo-Newtonian equations for evolution of particles and fluids in stationary space-times. https://doi.org/10.3847/1538-4357/aa71a5

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