A covariant formulation of Relativistic Mechanics [CL]

http://arxiv.org/abs/2202.04658


Accretion disks surrounding compact objects, and other environmental factors, deviate satellites from geodesic motion. Unfortunately, setting up the equations of motion for such relativistic trajectories is not as simple as in Newtonian mechanics. Here, we propose a simple method aimed at generating physically accurate covariant 4-forces. We apply this method to several conservative and dissipative forces. In particular, we compute the drag due to gravitational and hard-sphere collisions in dust, gas and radiation media. We recover and covariantly extend known forces such as Epstein drag, Chandrasekhar’s dynamical friction and Poynting-Robertson drag. Variable-mass effects are also considered, namely Hoyle-Lyttleton accretion and the variable-mass rocket. We conclude with two applications: 1. The free-falling spring. We find that Hooke’s law amounts to an effective Anti-de Sitter tidal force; 2. Black hole infall with drag. We numerically compute some trajectories on a Schwarzschild background supporting a dust-like accretion disk.

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M. Correia
Fri, 11 Feb 22
63/71

Comments: 17 pages + appendices