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Publication# Covariant formulation of relativistic mechanics

Abstract

Accretion disks surrounding compact objects, and other environmental factors, deviate satellites from geodetic motion. Unfortunately, setting up the equations of motion for such relativistic trajectories is not as simple as in Newtonian mechanics. The principle of general (or Lorentz) covariance and the mass-shell constraint make it difficult to parametrize physically adequate 4-forces. Here, we propose a solution to this old problem. We apply our framework to several conservative and dissipative forces. In particular, we propose covariant formulations for Hooke???s law and the constant force and 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, where we find that Hooke???s law corrects the deviation equation by an effective anti???de Sitter tidal force and (2) black hole infall with drag. We numerically compute some trajectories on a Schwarzschild background supporting a dustlike accretion disk.

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Relativistic mechanics

In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non-quantum mechanical description of a system of particles,

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In physics, a force is an influence that can cause an object to change its velocity, i.e., to accelerate, unless counterbalanced by other forces. The concept of force makes the everyday notion of pus

Motion

In physics, motion is the phenomenon by which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed