scholarly journals The Gravitomagnetism in the Solar System

2017 ◽  
Vol 45 ◽  
pp. 1760052
Author(s):  
Flavia Rocha ◽  
Manuel Malheiro ◽  
Rubens Marinho
Keyword(s):  
Mass Density ◽  
Slow Motion ◽  
Weak Field ◽  
Einstein Equations ◽  
Dipole Potential ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Perihelion Advance ◽  
Motion Approximation

In 1918, Joseph Lense and Hans Thirring discovered the gravitomagnetic (GM) effect of Einstein field equations in weak field and slow motion approximation. They showed that Einstein equations in this approximation can be written as in the same form as Maxwell’s equation for electromagnetism. In these equations the charge and electric current are replaced by the mass density and the mass current. Thus, the gravitomagnetism formalism in astrophysical system is used with the mass assuming the role of the charge. In this work, we present the deduction of gravitoelectromagnetic equations and the analogue of the Lorentz force in the gravitomagnetism. We also discuss the problem of Mercury’s perihelion advance orbit, we propose solutions using GM formalism using a dipole-dipole potential for the Sun-Planet interaction.

RADIATING COLLAPSE WITH VANISHING WEYL STRESSES

2005 ◽  
Vol 14 (03n04) ◽  
pp. 667-676 ◽  
Author(s):  
S. D. MAHARAJ ◽  
M. GOVENDER
Keyword(s):  
Irreversible Thermodynamics ◽  
Temperature Profiles ◽  
Junction Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Extended Irreversible Thermodynamics ◽  
Recent Approach ◽  
Dust Solution ◽  
Limiting Case

In a recent approach in modeling a radiating relativistic star undergoing gravitational collapse the role of the Weyl stresses was emphasized. It is possible to generate a model which is physically reasonable by approximately solving the junction conditions at the boundary of the star. In this paper we demonstrate that it is possible to solve the Einstein field equations and the junction conditions exactly. This exact solution contains the Friedmann dust solution as a limiting case. We briefly consider the radiative transfer within the framework of extended irreversible thermodynamics and show that relaxational effects significantly alter the temperature profiles.

scholarly journals Electron as Kerr's super-rotating black hole

2020 ◽  
Vol 3 (4) ◽  
Keyword(s):  
Black Hole ◽  
Quantum Theory ◽  
Particle Physics ◽  
Gravitational Interaction ◽  
Higgs Field ◽  
Higgs Model ◽  
Einstein Equations ◽  
Electron Charge ◽  
Field Equations

The known weakness of Gravity in particle physics is a delusion caused by underestimation of the role of spin. Spin of elementary particles is extremely high and exceeds mass on 20-22 orders (in unit’s c = G = m = k = 1). The caused by spinning gravity framedragging distorts space much stronger than mass, that shifts the usual effective scale of gravitational interaction from Planck to Compton distances. We show that compatibility between gravity and quantum theory can be achieved without modifications of the Einstein equations, by using a model of super-bag a no perturbative particle like solution to supersymmetric system of the Landau-Ginzburg (Higgs) field equations. Super-bag generates a free from gravity Compton zone for quantum theory. Shape of the bag is defined unambiguously by spinning Kerr-Newman solution. For parameters of an electron (charge e, spin J, and mass m) super-bag forms a thin superconducting disk of Compton radius coupled with circular string along its perimeter. The supersymmetric LG (Higgs) model is naturally upgraded to Wess-Zumino super-QED model, forming a bridge to perturbative formalism of conventional QED.

On the Hoyle-Narlikar theory of gravitation

1965 ◽  
Vol 286 (1406) ◽  
pp. 313-319 ◽  
Keyword(s):  
Boundary Condition ◽  
Action Principle ◽  
Einstein Equations ◽  
Expanding Universe ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Negative Mass ◽  
The World ◽  
Theory Of Gravitation ◽  
Particle Action

It is shown that the direct-particle action-principle from which Hoyle & Narlikar derive their new theory of gravitation not only yields the Einstein field-equations in the ‘smoothfluid’ approximation, but also implies that the ‘ m ’-field be given by the sum of half the retarded field and half the advanced field calculated from the world-lines of the particles. This is in effect a boundary condition for the Einstein equations, and it appears that it is incompatible with an expanding universe since the advanced field would be infinite. A possible way of overcoming this difficulty would be to allow the existence of negative mass.

scholarly journals A Note on the Gravitoelectromagnetic Analogy

Universe ◽  
2021 ◽  
Vol 7 (11) ◽  
pp. 451
Author(s):  
Matteo Luca Ruggiero
Keyword(s):  
Slow Motion ◽  
Weak Field ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Gravitational Effects ◽  
Force Equation ◽  
Test Particles ◽  
Motion Approximation ◽  
Stationary Conditions ◽  
Definition Of

We discuss the linear gravitoelectromagnetic approach used to solve Einstein’s equations in the weak-field and slow-motion approximation, which is a powerful tool to explain, by analogy with electromagnetism, several gravitational effects in the solar system, where the approximation holds true. In particular, we discuss the analogy, according to which Einstein’s equations can be written as Maxwell-like equations, and focus on the definition of the gravitoelectromagnetic fields in non-stationary conditions. Furthermore, we examine to what extent, starting from a given solution of Einstein’s equations, gravitoelectromagnetic fields can be used to describe the motion of test particles using a Lorentz-like force equation.

The weak field approximation

2019 ◽  
pp. 66-71
Author(s):  
Steven Carlip
Keyword(s):  
Field Approximation ◽  
Weak Field ◽  
Gravitational Energy ◽  
Newtonian Gravity ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Frame Dragging ◽  
Coupled Partial Differential Equations ◽  
Flat Spacetime ◽  
Weak Fields

The Einstein field equations are a complicated set of coupled partial differential equations, which are usually too complicated to find exact solutions. This chapter introduces a simple approximation for weak fields. It discusses the lowest order solution, which gives back Newtonian gravity, and the next order, which includes “gravitomagnetic” or “frame-dragging” effects. The chapter briefly discusses higher order approximations, expansions around a curved background, and the evidence that gravitational energy itself gravitates. It concludes with a brief description of an alternative derivation of the Einstein field equations, starting from flat spacetime and “bootstrapping” the gravitational self-interaction.

scholarly journals A GRAVITOMAGNETIC EFFECT ON THE ORBIT OF A TEST BODY DUE TO THE EARTH'S VARIABLE ANGULAR MOMENTUM

2002 ◽  
Vol 11 (05) ◽  
pp. 781-787 ◽  
Author(s):  
LORENZO IORIO
Keyword(s):  
Angular Momentum ◽  
Test Particle ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Slow Motion ◽  
Weak Field ◽  
Test Body ◽  
Angular Velocity Vector ◽  
Motion Approximation ◽  
General Relativistic

The well known general relativistic Lense–Thirring drag of the orbit of a test particle in the stationary field of a central slowly rotating body is generated, in the weak-field and slow-motion approximation of General Relativity, by a gravitomagnetic Lorentz-like acceleration in the equations of motion of the test particle. In it the gravitomagnetic field is due to the central body's angular momentum supposed to be constant. In the context of the gravitational analogue of the Larmor theorem, such acceleration looks like a Coriolis inertial term in an accelerated frame. In this paper the effect of the variation in time of the central body's angular momentum on the orbit of a test mass is considered. It can be shown that it is analogue to the inertial acceleration due to the time derivative of the angular velocity vector of an accelerated frame. The possibility of detecting such effect in the gravitational field of the Earth with LAGEOS-like satellites is investigated. It turns out that the orbital effects are far too small to be measured.

scholarly journals Analytic approximations in GR and gravitational waves

2019 ◽  
Vol 28 (06) ◽  
pp. 1930011 ◽  
Author(s):  
Luc Blanchet
Keyword(s):  
Binary Systems ◽  
State Of The Art ◽  
Equations Of Motion ◽  
Slow Motion ◽  
Weak Field ◽  
Analytic Approximation ◽  
Compact Binary ◽  
Recent Developments ◽  
Motion Approximation ◽  
Self Force

Analytic approximation methods in general relativity play a very important role when analyzing the gravitational wave signals recently discovered by the LIGO and Virgo detectors. In this contribution, we present the state of the art and some recent developments in the famous post-Newtonian (PN) or slow-motion approximation, which has successfully computed the equations of motion and the early inspiral phase of compact binary systems. We discuss also some interesting interfaces between the PN and the gravitational self-force (GSF) approach based on black-hole perturbation theory, and between PN and the post-Minkowskian (PM) approximation, namely a nonlinearity expansion valid for weak field and possibly fast-moving sources.

Symmetries and conservation laws of some asymptotically symmetric spacetimes of interest in gravitational waves

2019 ◽  
Vol 16 (10) ◽  
pp. 1950152 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
A. H. Kara ◽  
B. B. I. Gadjagboui ◽  
Ghulam Shabbir
Keyword(s):  
Conservation Laws ◽  
Gravitational Waves ◽  
Flat Space ◽  
Einstein Equations ◽  
Necessary Condition ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Symmetric Spacetimes ◽  
Flat Spacetimes

In this paper, we discuss symmetries and the corresponding conservation laws of certain exact solutions of the Einstein field equations (EFEs) representing a Schwarzschild black hole and gravitational waves in asymptotically flat space times. Of particular interest are symmetries of asymptotically flat spacetimes because they admit a property that identifies them for the existence of gravitational waves there. In the light of this fact, we discuss symmetry algebras of a few recently published solutions of Einstein equations in asymptotically flat metrics. Given the fact that gravitational waves are of great interest in relativity, we focus in this paper on finding the type of symmetries they admit and their corresponding conservation laws. We also show how these symmetries are radically different from the other well-known symmetries and present necessary condition that distinguishes them.

A Method for Numerical Integration of Time-Dependent Einstein Equations

1973 ◽  
Vol 51 (7) ◽  
pp. 743-750 ◽  
Author(s):  
J. Pachner ◽  
R. Teshima
Keyword(s):  
Initial Data ◽  
Numerical Integration ◽  
Numerical Computation ◽  
Axial Symmetry ◽  
Einstein Equations ◽  
Time Dependent ◽  
Einstein Field Equations ◽  
Field Equations

A method for the numerical computation of the initial data and for the numerical integration of the exact Einstein field equations is described for the case of a rotating incoherent matter with axial symmetry. The results of the integration show that the method gives reliable results.

Some special solutions in Bianchi type VI0 cosmological models with modified chaplygin gas in general relativity

2015 ◽  
Vol 24 (02) ◽  
pp. 1550017 ◽  
Author(s):  
S. D. Katore ◽  
S. P. Hatkar ◽  
S. N. Bayaskar
Keyword(s):  
Cold Dark Matter ◽  
Bianchi Type ◽  
Complete Solution ◽  
Chaplygin Gas ◽  
Modified Chaplygin Gas ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Modified Model ◽  
Geometrical Properties

In the present paper, the role of modified chaplygin gas models in relation with the Bianchi type VI0 universe is examined. For obtaining complete solution of Einstein field equations, it is assumed that expansion scalar in the model is proportional to shear scalar and equation of state of this modified model is valid from the radiation era to the Lambda cold dark matter (ΛCDM) model. State finder and various physical, geometrical properties have also been discussed.

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