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

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.

Published in ApJ

References in corpus (4)

• The Jacobi-metric for timelike geodesics in static spacetimes
• Generalized pseudo-Newtonian potential for studying accretion disk dynamics in off-equatorial planes around rotating black holes: Description of a vector potential
• Newtonian analogue of corresponding spacetime dynamics of rotating black holes: Implication on black hole accretion
• Newtonian analogue of Schwarzschild de-Sitter spacetime: Influence on the local kinematics in galaxies

Cited by in corpus (5)

• Orbit classification in an equal-mass non-spinning binary black hole pseudo-Newtonian system
• Logarithmic potential for the gravitational field of Schwarzschild black holes
• Orbit classification in a pseudo-Newtonian Copenhagen problem with Schwarzschild-like primaries
• Bondi Accretion in the Spherically Symmetric Johannsen-Psaltis Spacetime
• Spherical accretion in the Schwarzschild spacetime in the Newtonian analogous construct