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Covariant formulation of relativistic mechanics
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...
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Lenguaje: | eng |
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2022
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Acceso en línea: | https://dx.doi.org/10.1103/PhysRevD.105.084041 http://cds.cern.ch/record/2812678 |
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author | Correia, Miguel |
author_facet | Correia, Miguel |
author_sort | Correia, Miguel |
collection | CERN |
description | 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. |
id | cern-2812678 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2022 |
record_format | invenio |
spelling | cern-28126782023-10-04T08:49:02Zdoi:10.1103/PhysRevD.105.084041http://cds.cern.ch/record/2812678engCorreia, MiguelCovariant formulation of relativistic mechanicsastro-ph.HEAstrophysics and Astronomygr-qcGeneral Relativity and CosmologyAccretion 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.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. We find that Hooke's law corrects the deviation equation by 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.arXiv:2202.04658oai:cds.cern.ch:28126782022-02-09 |
spellingShingle | astro-ph.HE Astrophysics and Astronomy gr-qc General Relativity and Cosmology Correia, Miguel Covariant formulation of relativistic mechanics |
title | Covariant formulation of relativistic mechanics |
title_full | Covariant formulation of relativistic mechanics |
title_fullStr | Covariant formulation of relativistic mechanics |
title_full_unstemmed | Covariant formulation of relativistic mechanics |
title_short | Covariant formulation of relativistic mechanics |
title_sort | covariant formulation of relativistic mechanics |
topic | astro-ph.HE Astrophysics and Astronomy gr-qc General Relativity and Cosmology |
url | https://dx.doi.org/10.1103/PhysRevD.105.084041 http://cds.cern.ch/record/2812678 |
work_keys_str_mv | AT correiamiguel covariantformulationofrelativisticmechanics |