The Gravitational Equations and the Problem of Motion. II

1940 ◽  
Vol 41 (2) ◽  
pp. 455 ◽  
Author(s):  
A. Einstein ◽  
L. Infeld
Keyword(s):  
Gravitational Equations

scholarly journals Post-Newtonian limit: second-order Jefimenko equations

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
David Pérez Carlos ◽  
Augusto Espinoza ◽  
Andrew Chubykalo
Keyword(s):  
Linear Equations ◽  
Space Time ◽  
Second Order ◽  
Field Equations ◽  
Gravitational Fields ◽  
Mass Distributions ◽  
Minkowski Space Time ◽  
Theory Of Gravitation ◽  
Gravity Probe ◽  
Gravitational Equations

Abstract The purpose of this paper is to get second-order gravitational equations, a correction made to Jefimenko’s linear gravitational equations. These linear equations were first proposed by Oliver Heaviside in [1], making an analogy between the laws of electromagnetism and gravitation. To achieve our goal, we will use perturbation methods on Einstein field equations. It should be emphasized that the resulting system of equations can also be derived from Logunov’s non-linear gravitational equations, but with different physical interpretation, for while in the former gravitation is considered as a deformation of space-time as we can see in [2–5], in the latter gravitation is considered as a physical tensor field in the Minkowski space-time (as in [6–8]). In Jefimenko’s theory of gravitation, exposed in [9, 10], there are two kinds of gravitational fields, the ordinary gravitational field, due to the presence of masses, at rest, or in motion and other field called Heaviside field due to and acts only on moving masses. The Heaviside field is known in general relativity as Lense-Thirring effect or gravitomagnetism (The Heaviside field is the gravitational analogous of the magnetic field in the electromagnetic theory, its existence was proved employing the Gravity Probe B launched by NASA (See, for example, [11, 12]). It is a type of gravitational induction), interpreted as a distortion of space-time due to the motion of mass distributions, (see, for example [13, 14]). Here, we will present our second-order Jefimenko equations for gravitation and its solutions.

scholarly journals Some solutions of Einstein's gravitational equations for systems with axial symmetry

1930 ◽  
Vol 126 (803) ◽  
pp. 592-602 ◽  
Keyword(s):  
Angular Velocity ◽  
Axial Symmetry ◽  
Second Order ◽  
Newtonian Potential ◽  
Static Distribution ◽  
Gravitational Equations

§1. In this paper we find solutions of Einstein’s gravitational equations G μν = 0 which give the field due to any static distribution of matter sym­metrical about an axis; in the later part of the paper an angular velocity about the axis is introduced. We take the ground form ds 2 = - e λ ( dx 2 + dr 2 ) - e -ρ r 2 d θ 2 + e ρ dt 2 , (1) where λ, ρ are functions of x and r . Further we take ρ to be the Newtonian potential of an auxiliary distribution of matter of density σ ( x, r ), the potential being calculated as though our co-ordinates were Euclidean. We find that it is then possible to determine λ, so that the equations G μν = 0 are exactly satisfied everywhere outside the auxiliary body. λ is nearly equal to —ρ, the quantity μ = λ + ρ being of the second order in terms of σ.

IRREVERSIBILITY OF THE COSMOLOGICAL EXPANSION

1987 ◽  
Vol 02 (01) ◽  
pp. 133-163 ◽  
Author(s):  
GEORGE MARX ◽  
HUMITAKA SATO
Keyword(s):  
Microwave Radiation ◽  
Closed System ◽  
Thermal Equilibrium ◽  
Mechanical Instability ◽  
The Past ◽  
Cosmological Expansion ◽  
The Universe ◽  
Gravitational Equations

The spectrum and isotropy of the relic microwave radiation indicates that the universe was in a state of thermal equilibrium in the past. The question arises: how could it happen that a closed system dropped out of its equilibrium? According to the models presented here this was the outcome of an interplay between the mechanical instability in the gravitational equations and the different scaling behaviors of differentiated materials.

scholarly journals Marginal stability and chaos in the solar system

1996 ◽  
Vol 172 ◽  
pp. 75-88
Author(s):  
Jacques Laskar
Keyword(s):  
Solar System ◽  
Marginal Stability ◽  
Gravitational Equations

The motion of the planets is one of the best modelized problems in physics, and its study can be practically reduced to the study of the behavior of the solutions of the well known gravitational equations, neglecting all dissipation, and treating the planets as mass points. In fact, the mathematical complexity of this problem, despites its apparent simplicity is daunting and has been a challenge for mathematicians and astronomers since its formulation three centuries ago.

scholarly journals Quintessence in low-energy effective theory

2018 ◽  
Vol 168 ◽  
pp. 08004
Author(s):  
Tae Hoon Lee
Keyword(s):  
Scalar Field ◽  
Effective Potential ◽  
Cosmological Solution ◽  
Low Energy ◽  
Effective Theory ◽  
Late Time ◽  
Inverse Power Law ◽  
Virtual Interactions ◽  
The Universe ◽  
Gravitational Equations

Considering a theory of Brans-Dicke gravity with general couplings of a heavy field, we derive the low-energy effective theory action in the universe of temperature much lower than the heavy field mass. Gravitational equations and the Brans-Dicke scalar field equation including an effective potential of the scalar field are obtained, which is induced through virtual interactions of the heavy field in the late-time universe. We find a deSitter cosmological solution stemming from the inverse power law effective potential of the scalar field and discuss the possibility that the late time acceleration of our universe can be described by means of the solution.

A non-static source of the Taub solution of Einstein's gravitational equations

1977 ◽  
Vol 63 (2) ◽  
pp. 79-80 ◽  
Author(s):  
J. Horský ◽  
P. Lorenc ◽  
J. Novotný
Keyword(s):  
Static Source ◽  
Gravitational Equations
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