The Equations of Motion of Charged Test Particles in General Relativity

1954 ◽  
Vol 95 (1) ◽  
pp. 243-246 ◽  
Author(s):  
D. M. Chase
Keyword(s):  
General Relativity ◽  
Equations Of Motion ◽  
Test Particles ◽  
Charged Test

scholarly journals Non-geodesic orbital and epicyclic frequencies in vicinity of slowly rotating magnetized neutron stars

2012 ◽  
Vol 8 (S290) ◽  
pp. 185-186
Author(s):  
Pavel Bakala ◽  
Martin Urbanec ◽  
Eva Šrámková ◽  
Zdeněk Stuchlík ◽  
Gabriel Török
Keyword(s):  
Magnetic Field ◽  
Neutron Stars ◽  
Equations Of Motion ◽  
Solution Of Equations ◽  
Test Particles ◽  
Perturbative Method ◽  
Relativistic Approach ◽  
Charged Test ◽  
The Magnetic Field

AbstractWe study non-geodesic corrections to the quasicircular motion of charged test particles in the field of magnetized slowly rotating neutron stars. The gravitational field is approximated by the Lense-Thirring geometry, the magnetic field is of the standard dipole character. Using a fully-relativistic approach we determine influence of the electromagnetic interaction (both attractive and repulsive) on the quasicircular motion. We focus on the behaviour of the orbital and epicyclic frequencies of the motion. Components of the four-velocity of the orbiting charged test particles are obtained by numerical solution of equations of motion, the epicyclic frequencies are obtained by using the standard perturbative method. The role of the combined effect of the neutron star magnetic field and its rotation in the character of the orbital and epicyclic frequencies is discussed.

Spinning test-particles in general relativity. I

1951 ◽  
Vol 209 (1097) ◽  
pp. 248-258 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Equations Of Motion ◽  
Covariant Form ◽  
Test Particles

A method for the derivation of the equations of motion of test particles in a given gravitational field is developed. The equations of motion of spinning test particles are derived. The transformation properties are discussed and the equations of motion are written in a covariant form.

DELTA GRAVITY AND THE ACCELERATED EXPANSION OF THE UNIVERSE

2011 ◽  
Vol 20 (supp01) ◽  
pp. 65-72
Author(s):  
JORGE ALFARO
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Cosmological Constant ◽  
Equivalence Principle ◽  
Equations Of Motion ◽  
Accelerated Expansion ◽  
Symmetric Tensors ◽  
Test Particles ◽  
Expansion Of The Universe ◽  
The Universe

We study a model of the gravitational field based on two symmetric tensors. The equations of motion of test particles are derived. We explain how the Equivalence principle is recovered. Outside matter, the predictions of the model coincide exactly with General Relativity, so all classical tests are satisfied. In Cosmology, we get accelerated expansion without a cosmological constant.

scholarly journals Particle paths of general relativity as geodesics of an affine connection

1970 ◽  
Vol 3 (3) ◽  
pp. 325-335 ◽  
Author(s):  
R. Burman
Keyword(s):  
General Relativity ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Affine Connection ◽  
Momentum Tensor ◽  
Field Equations ◽  
Test Particles ◽  
Special Cases ◽  
Particle Paths ◽  
Arbitrary Energy

This paper deals with the motion of incoherent matter, and hence of test particles, in the presence of fields with an arbitrary energy-momentum tensor. The equations of motion are obtained from Einstein's field equations and are written in the form of geodesic equations of an affine connection. The special cases of the electromagnetic field, the Proca field and a scalar field are discussed.

The motion of charged test particles in general relativity

1985 ◽  
Vol 15 (5) ◽  
pp. 617-627 ◽  
Author(s):  
Peter A. Hogan ◽  
Ivor Robinson
Keyword(s):  
General Relativity ◽  
Test Particles ◽  
Charged Test

Conserved quantities of spinning test particles in general relativity. II

1983 ◽  
Vol 385 (1788) ◽  
pp. 229-239 ◽  
Keyword(s):  
General Relativity ◽  
Equations Of Motion ◽  
Conserved Quantities ◽  
Killing Tensor ◽  
Kerr Geometry ◽  
Change Of Variables ◽  
Test Particles ◽  
Suitable Change

In this paper, which completes earlier work on conserved quantities of spinning test particles in general relativity (Rüdiger 1981 a ), quadratic conserved quantities are considered. It is shown that by a suitable change of variables the trivial conserved quantities, which result from a reducible Killing tensor, can essentially be separated from the non-trivial quantities. If the equations of motion are linearized in the spin, it is shown that nontrivial quantities of this type can be constructed for two classes of spacetimes including the Kerr geometry and the Friedman universe.

Spinning test-particles in general relativity. II

1951 ◽  
Vol 209 (1097) ◽  
pp. 259-268 ◽  
Keyword(s):  
General Relativity ◽  
Equations Of Motion ◽  
Test Particles

The equations of motion for spinning test particles are discussed for particles characterized by the condition S i 4 ═ 0.

scholarly journals Separation of variables in Hamilton–Jacobi equation for a charged test particle in the Stackel spaces of type (2.1)

2020 ◽  
Vol 17 (14) ◽  
pp. 2050186
Author(s):  
Valeriy Obukhov
Keyword(s):  
Jacobi Equation ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Type Equation ◽  
Parabolic Type ◽  
Complete Separation ◽  
Test Particles ◽  
Charged Test Particle ◽  
Charged Test ◽  
Hamilton Jacobi Equation

We can find all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of variables in the Hamilton–Jacobi equation. Separation is carried out using the complete sets of mutually-commuting integrals of motion of type (2.1), whereby in a privileged coordinate system the Hamilton–Jacobi equation turns into a parabolic type equation.

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