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.

The post-Newtonian approximation

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Body Problem ◽  
Equations Of Motion ◽  
Two Body Problem ◽  
Newtonian Approximation ◽  
Actual Motion ◽  
Law Of Attraction ◽  
Universal Law ◽  
Two Bodies

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and moving slowly. It limits the discussion to corrections proportional to v2 ~ m/R, the so-called post-Newtonian or 1PN corrections to Newton’s universal law of attraction. The chapter first examines the gravitational field, that is, the metric, created by the two bodies. It then derives the equations of motion, and finally the actual motion, that is, the post-Keplerian trajectories, which generalize the post-Keplerian geodesics obtained earlier in the chapter.

Orbital dynamics of the gravitational field of stringy black holes

2014 ◽  
Vol 29 (29) ◽  
pp. 1450144 ◽  
Author(s):  
Yu Zhang ◽  
Jin-Ling Geng ◽  
En-Kun Li
Keyword(s):  
Black Holes ◽  
Angular Momentum ◽  
Gravitational Field ◽  
Phase Plane ◽  
Equations Of Motion ◽  
Orbital Dynamics ◽  
Phase Plane Analysis ◽  
Test Particles ◽  
Stable Circular Orbit ◽  
The Stability

In this paper, we study the orbital dynamics of the gravitational field of stringy black holes by analyzing the effective potential and the phase plane diagram. By solving the equation of Lagrangian, the general relativistic equations of motion in the gravitational field of stringy black holes are given. It is easy to find that the motion of test particles depends on the energy and angular momentum of the test particles. Using the phase plane analysis method and combining the conditions of the stability, we discuss different types of the test particles' orbits in the gravitational field of stringy black holes. We get the innermost stable circular orbit which occurs at r min = 5.47422 and when the angular momentum b ≤ 4.3887 the test particles will fall into the black hole.

scholarly journals Einstein’s Equation of motion for exterior test particles with spherical mass distribution having varied field, time and radial distance; Golden metric tensors approach.

2021 ◽  
Keyword(s):  
Gravitational Field ◽  
Polar Motion ◽  
Equations Of Motion ◽  
Radial Distance ◽  
Equation Of Motion ◽  
Metric Tensor ◽  
Test Particles ◽  
Einstein's Equation ◽  
Spherical Mass ◽  
Metric Tensors

Golden metric tensors exterior to hypothetical distribution of mass whose field varies with time and radial distance have been used to construct the coefficient of affine connections that invariably was used to obtained the Einstein’s equations of motion for test particles of non-zero rest masses. The expression for the variation of time on a clock moving in this gravitational field was derived using the time equation of motion. The test particles in this field under the condition of pure polar motion have an inverse square dependence velocity which depends on radial distance. Our result indicates that despite using the golden metric tensor, the inverse square dependence of the velocity on radial distance has not been changed.

ON EQUATIONS OF MOTION IN GENERAL RELATIVITY

1955 ◽  
Vol 33 (12) ◽  
pp. 824-827
Author(s):  
G. E. Tauber
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Charged Particle ◽  
Variational Principle ◽  
Classical Theory ◽  
Equations Of Motion ◽  
Field Equations

It has been shown that both the equations of motion of a charged particle in a gravitational field and the field equations can be obtained from one variational principle by suitably generalizing Dirac's classical theory of electrons.

Poincar�-invariant gravitational field and equations of motion of two pointlike objects: The postlinear approximation of general relativity

1981 ◽  
Vol 13 (10) ◽  
pp. 963-1004 ◽  
Author(s):  
Luis Bel ◽  
Thibaut Damour ◽  
Nathalie Deruelle ◽  
Jesus Ibanez ◽  
Jesus Martin
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Equations Of Motion

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.

scholarly journals Shadow of a noncommutative-inspired Einstein–Euler–Heisenberg black hole

2021 ◽  
Author(s):  
Marco Maceda ◽  
Alfredo Macias ◽  
Daniel Martinez-Carbajal
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Gravitational Field ◽  
Impact Parameter ◽  
Circular Orbits ◽  
Massless Particles ◽  
Test Particles ◽  
The Impact ◽  
Nonlinear Nature

We consider the orbits of test particles moving in the gravitational field of a noncommutative-inspired Einstein–Euler–Heisenberg black hole. Using the geometric metric, we determine the circular orbits followed by massless particles, comparing them with the circular photon orbits coming from the Plebanski pseudo-metric that takes into account the nonlinear nature of the Euler–Heisenberg electrodynamics. Using the impact parameter of the photon orbits, we define the shadow of the noncommutative-inspired black hole and discuss the constraints on the model by comparing its shadow with the prediction from General Relativity.

On The Motion of Particles in General Relativity Theory

1949 ◽  
Vol 1 (3) ◽  
pp. 209-241 ◽  
Author(s):  
A. Einstein ◽  
L. Infeld
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Equations Of Motion ◽  
Relativity Theory ◽  
Fundamental Importance ◽  
Approximation Procedure ◽  
High Approximation ◽  
Field Equations ◽  
General Relativity Theory ◽  
First Time

The gravitational field manifests itself in the motion of bodies. Therefore the problem of determining the motion of such bodies from the field equations alone is of fundamental importance. This problem was solved for the first time some ten years ago and the equations of motion for two particles were then deduced [1]. A more general and simplified version of this problem was given shortly thereafter [2].Mr. Lewison pointed out to us, that from our approximation procedure, it does not follow that the field equations can be solved up to an arbitrarily high approximation. This is indeed true.

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.

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