scholarly journals The application of monodromy preserving deformation to the gravitational field equation

1981 ◽  
Vol 57 (4) ◽  
pp. 210-215
Author(s):  
Kimio Ueno
Keyword(s):  
Gravitational Field ◽  
Field Equation ◽  
Gravitational Field Equation

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.

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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