Logarithmic potential for the gravitational field of Schwarzschild black holes

Abstract

Approximate gravitational potentials are often used to describe analytically the motion of particles near black holes (BHs), as well as to study the structure of an accretion disk. Such 'pseudo-Newtonian' potentials are used with the flat-metric equations. Here we consider the motion of a free particle near a non-rotating BH in the context of an exact `logarithmic' gravitational potential. We show how the logarithmic potential gives an exact solution for a mechanical problem and present the relativistic Bernoulli equation for the fluid in the Schwarzschild metric.

5 pages, 2 figures, 1 table; accepted for publication in MNRAS

References in corpus (2)

• A Global Three Dimensional Radiation Magneto-hydrodynamic Simulation of Super-Eddington Accretion Disks
• Pseudo-Newtonian equations for evolution of particles and fluids in stationary space-times

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• Possible evidence from the flaring activity of Sgr A* for a star at a distance of ~3.3 Schwarzscild radii from the blackhole
• On the desert between neutron star and black hole remnants