The General Theory of Relativity (Continued)

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Gravitational Field ◽  
Field Equation ◽  
Reference Frames ◽  
Spectral Lines ◽  
Main Theme ◽  
Theory Of Relativity ◽  
Gravitational Field Equation ◽  
Cosmological Problem ◽  
The Masses ◽  
The Universe

This chapter shows that in the limit of weak fields and low velocities, the equation of the geodesic line reduces to Newton's equation of motion. It proceeds to derive the gravitational field equation. Next, the chapter uses the gravitational field equation to derive the three effects that served as the first tests of the theory: the bending of light by the gravitational field of the sun, the shift to the red of spectral lines emitted by atoms in a gravitational field (gravitational redshift), and the motion of the perihelion of planet Mercury. After a short remark about expressing Maxwell's equations of the electromagnetic field, the chapter turns to the “so-called cosmological problem.” Its main theme is the defense of Mach's principle, which states that all inertial phenomena, namely the fictitious forces arising in accelerated reference frames, are caused by all the masses in the universe.

scholarly journals Modification of Gravitational Field Equation due to Invariance of Light Speed and New System of Universe Evolution

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Jian Liang Yang
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Field Equation ◽  
Invariant Solution ◽  
Inertial Mass ◽  
Gravitational Field Equation ◽  
Light Speed ◽  
Planetary Orbits ◽  
Celestial Bodies ◽  
The Universe

We make a systematic examination of the basic theory of general relativity and reemphasize the meaning of coordinates. Firstly, we prove that Einsteinʼs gravitational field equation has the light speed invariant solution and black holes are not an inevitable prediction of general relativity. Second, we show that the coupling coefficient of the gravitational field equation is not unique and can be modified as 4 π G to replace the previous − 8 π G , distinguish gravitational mass from the inertial mass, and prove that dark matter and dark energy are not certain existence and the expansion and contraction of the universe are proven cyclic, and a new distance-redshift relation which is more practical is derived. After that, we show that galaxies and celestial bodies are formed by gradual growth rather than by the accumulation of existing matter and prove that new matter is generating gradually in the interior of celestial bodies. For example, the radius of the Earth increases by 0.5 mm every year, and its mass increases by 1.2 trillion tons. A more reasonable derivation of the precession of planetary orbits is given, and the evolution equation of planetary orbits in the expanding space-time is also given. In a word, an alive universe unfolds in front of readers and the current cosmological difficulties are given new interpretations.

scholarly journals Einstein-aether theory in Weyl integrable geometry

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon ◽  
John D. Barrow
Keyword(s):  
Gravitational Field ◽  
Field Equation ◽  
Scalar Field ◽  
Field Model ◽  
Affine Connection ◽  
Dynamical Evolution ◽  
Field Equations ◽  
Gravitational Field Equation ◽  
Gravitational Field Equations ◽  
Geometric Origin

AbstractWe study the Einstein-aether theory in Weyl integrable geometry. The scalar field which defines the Weyl affine connection is introduced in the gravitational field equation. We end up with an Einstein-aether scalar field model where the interaction between the scalar field and the aether field has a geometric origin. The scalar field plays a significant role in the evolution of the gravitational field equations. We focus our study on the case of homogeneous and isotropic background spacetimes and study their dynamical evolution for various cosmological models.

The General Theory of Relativity

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
General Theory ◽  
Reference Frames ◽  
Mathematical Formulation ◽  
Rotating Disk ◽  
Theory Of Relativity ◽  
Relativity Principle ◽  
Non Euclidean Geometry ◽  
Physical Laws

This chapter shows how Einstein has developed and described the mathematical apparatus that is necessary to formulate the physical contents of the general theory of gravity. It first discusses the transition from the special to the general relativity principle. According to Einstein's understanding of such a general relativity principle, physical laws are independent of the state of motion of the reference space in which they are described. The chapter argues that such a generalization of the relativity principle to include accelerated reference frames is possible because all inertial effects caused by acceleration can be alternatively attributed to the presence of a gravitational field. The model of a rotating disk is then used to show that general relativity implies non-Euclidean geometry and that the gravitational field is represented by curved spacetime. After the introduction of these basic concepts and principles, the chapter presents the mathematical formulation of the theory.

Field Equation of Nonlocal Gravity

2017 ◽  
Author(s):  
Bahram Mashhoon
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Gravitational Field ◽  
Field Equation ◽  
Abelian Group ◽  
Gravitational Field Equation ◽  
Differential Field ◽  
Einstein's Equation ◽  
Future Theory ◽  
World Function

In extended general relativity (GR), Einstein’s field equation of GR can be expressed in terms of torsion and this leads to the teleparallel equivalent of GR, namely, GR||, which turns out to be the gauge theory of the Abelian group of spacetime translations. The structure of this theory resembles Maxwell’s electrodynamics. We use this analogy and the world function to develop a nonlocal GR|| via the introduction of a causal scalar constitutive kernel. It is possible to express the nonlocal gravitational field equation as modified Einstein’s equation. In this nonlocal gravity (NLG) theory, the gravitational field is local, but satisfies a partial integro-differential field equation. The field equation of NLG can be expressed as Einstein’s field equation with an extra source that has the interpretation of the effective dark matter. It is possible that the kernel of NLG, which is largely undetermined, could be derived from a more general future theory.

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