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Nonlocal Gravity$
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Bahram Mashhoon

Print publication date: 2017

Print ISBN-13: 9780198803805

Published to Oxford Scholarship Online: July 2017

DOI: 10.1093/oso/9780198803805.001.0001

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Field Equation of Nonlocal Gravity

Field Equation of Nonlocal Gravity

(p.98) 6 Field Equation of Nonlocal Gravity
Nonlocal Gravity

Bahram Mashhoon

Oxford University Press

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.

Keywords:   teleparallel equivalent of GR, world function, integro-differential field equation, nonlocal gravity (NLG), effective dark matter

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