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.

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.

scholarly journals Emergence of a cosmological constant in anisotropic fluid cosmology

2021 ◽  
pp. 2150156
Author(s):  
M. Cadoni ◽  
A. P. Sanna
Keyword(s):  
Cosmological Constant ◽  
Large Scale ◽  
Spatial Scales ◽  
Time Dependent ◽  
Anisotropic Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Coincidence Problem ◽  
Order Of Magnitude ◽  
Natural Way

In this paper, we investigate anisotropic fluid cosmology in a situation where the space–time metric back-reacts in a local, time-dependent way to the presence of inhomogeneities. We derive exact solutions to the Einstein field equations describing Friedmann–Lemaítre–Robertson–Walker (FLRW) large-scale cosmological evolution in the presence of local inhomogeneities and time-dependent backreaction. We use our derivation to tackle the cosmological constant problem. A cosmological constant emerges by averaging the backreaction term on spatial scales of the order of 100 Mpc, at which our universe begins to appear homogeneous and isotropic. We find that the order of magnitude of the “emerged” cosmological constant agrees with astrophysical observations and is related in a natural way to baryonic matter density. Thus, there is no coincidence problem in our framework.

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 ON TIME-DEPENDENT BLACK HOLES AND COSMOLOGICAL MODELS FROM A KALUZA–KLEIN MECHANISM

2009 ◽  
Vol 24 (07) ◽  
pp. 1383-1415
Author(s):  
C. CASTRO ◽  
J. A. NIETO ◽  
L. RUIZ ◽  
J. SILVAS
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cosmological Model ◽  
Black Hole Entropy ◽  
Time Dependent ◽  
Einstein Field Equations ◽  
Schwarzschild Black Hole ◽  
Field Equations ◽  
Newman Black Hole ◽  
Kaluza Klein

Novel static, time-dependent and spatial–temporal solutions to Einstein field equations, displaying singularities, with and without horizons, and in several dimensions, are found based on a dimensional reduction procedure widely used in Kaluza–Klein-type theories. The Kerr–Newman black hole entropy as well as the Reissner–Nordstrom, Kerr and Schwarzschild black hole entropy are derived from the corresponding Euclideanized actions. A very special cosmological model based on the dynamical interior geometry of a black hole is found that has no singularities at t = 0 due to the smoothing of the mass distribution. We conclude with another cosmological model equipped also with a dynamical horizon and which is related to Vaidya's metric (associated with the Hawking radiation of black holes) by interchanging t ↔ r, which might render our universe a dynamical black hole.

scholarly journals Relativistic models of thin disks immersed in a Robertson-Walker type spacetime

2013 ◽  
Vol 9 (18) ◽  
pp. 131-140
Author(s):  
Gonzalo García Reyes ◽  
Edwin García-Quintero
Keyword(s):  
Perfect Fluid ◽  
Time Dependent ◽  
Energy Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Ricci Collineations ◽  
Walker Metric ◽  
Relativistic Models ◽  
Thin Disks

Using the well known “displace, cut and reflect” method used to generate disks from given solutions of Einstein field equations, we construct somerelativistic models of time dependent thin disks of infinite extension made of a perfect fluid based on the Robertson-Walker metric. Two simple families of models of disks based on Robertson-Walker solutions admitting Matter and Ricci collineations are presented. We obtain disks that are inagreement with all the energy conditions.

CONSTRAINTS OF INITIAL DATA FOR A DISCRETE UNIVERSE

2012 ◽  
Vol 12 ◽  
pp. 213-223
Author(s):  
KJELL ROSQUIST ◽  
LARS SAMUELSSON
Keyword(s):  
Initial Data ◽  
Clusters Of Galaxies ◽  
Einstein Field Equations ◽  
Matter Distribution ◽  
Field Equations ◽  
And Topology ◽  
Discrete Nature ◽  
The Universe

The matter distribution of the universe is observed to be discrete in the form of stars, galaxies and clusters of galaxies. Due to the non-linearities of the Einstein field equations, the discrete nature of the matter implies modifications of the standard Friedmann cosmology paradigm. The modifications affect both the dynamics and the possible cosmological initial data. We discuss properties and restrictions for the intial data of a universe with a discrete matter distribution, in particular possible implications for the curvature and topology.

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 SOLUTION OF THE EINSTEIN FIELD EQUATIONS

1960 ◽  
Vol 38 (12) ◽  
pp. 1661-1664
Author(s):  
Peter Rastall
Keyword(s):  
Empty Space ◽  
Time Dependent ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Cylindrically Symmetric ◽  
Gravitational Field Equations ◽  
Axis Of Symmetry ◽  
Time Dependent Solution ◽  
Empty Universe ◽  
Number Of Particles

An exact, cylindrically symmetric, time-dependent solution of the Einstein gravitational field equations for empty space is derived. A particular case of the solution has singularities only on the axis of symmetry and may represent a number of particles in an otherwise empty universe.

TIME-DEPENDENT SOLUTIONS OF 5D VACUUM EINSTEIN EQUATIONS WITH COSMOLOGICAL CONSTANT

2011 ◽  
Vol 26 (22) ◽  
pp. 1673-1679 ◽  
Author(s):  
TAE HOON LEE
Keyword(s):  
Cosmological Constant ◽  
Time Dependence ◽  
Scale Factor ◽  
Einstein Equations ◽  
Time Dependent ◽  
Vacuum Field ◽  
Field Equations ◽  
Vacuum Einstein Equations ◽  
Dimensional Gravity

We solve vacuum field equations in five-dimensional gravity with cosmological constant to determine the time-dependence of the Robertson–Walker scale factor. We discuss its cosmological implications.

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