[Paper Review] Nonlocal Gravity

Bahram Mashhoon|arXiv (Cornell University)|Jul 18, 2017

Cosmology and Gravitation Theories3 references31 citations

TL;DR

This paper proposes a nonlocal generalization of Einstein's theory of gravity by introducing a scalar constitutive kernel in the teleparallel formulation, resulting in integro-differential field equations. The nonlocality effectively mimics dark matter, reproducing the phenomenology of the Tohline-Kuhn modified gravity model in the linearized Newtonian limit.

ABSTRACT

The analysis of measurements of accelerated observers in Minkowski spacetime has led to the development of nonlocal special relativity theory. Inertia and gravitation are intimately connected in accordance with the principle of equivalence. We therefore seek a nonlocal generalization of the theory of gravitation such that in the new theory the field equations are integro-differential equations for the local gravitational field. We show that it is possible to develop a nonlocal generalization of Einstein's theory of gravitation via the introduction of a scalar constitutive kernel in the teleparallel equivalent of general relativity. The resulting nonlocal theory is essentially equivalent to Einstein's theory plus That is, nonlocality simulates dark matter by introducing a new source term into general relativity. In the linear approximation for the nonlocal modification of Newtonian gravity, we recover the theoretical basis for the phenomenological Tohline-Kuhn modified gravity approach to the explanation of the astrophysical evidence for dark matter.

Motivation & Objective

• To develop a nonlocal generalization of general relativity that accounts for dark matter effects without new particles.
• To explore how nonlocality in the gravitational field equations can reproduce astrophysical evidence for dark matter.
• To establish a theoretical foundation for modified gravity models like Tohline-Kuhn using nonlocal field theory.
• To connect nonlocality in accelerated frames with gravitational effects via the equivalence principle.

Proposed method

• Formulates nonlocal gravity using the teleparallel equivalent of general relativity with a scalar constitutive kernel.
• Derives integro-differential field equations by extending local gravity to nonlocal interactions.
• Applies the principle of equivalence to link nonlocal inertia with nonlocal gravity.
• Performs a linear approximation of the nonlocal field equations to recover Newtonian gravity with nonlocal corrections.
• Compares the resulting nonlocal Newtonian potential with the Tohline-Kuhn modified gravity model.
• Demonstrates that the nonlocal theory reproduces the phenomenological dark matter profile in the linear regime.

Experimental results

Research questions

• RQ1 Can nonlocality in the gravitational field equations simulate the effects of dark matter?
• RQ2 How does the introduction of a scalar constitutive kernel modify the field equations in teleparallel gravity?
• RQ3 Does the nonlocal theory reproduce the Tohline-Kuhn modified gravity potential in the linear approximation?
• RQ4 What is the physical interpretation of nonlocality in the context of inertia and gravity?
• RQ5 How does nonlocal gravity relate to the equivalence principle in accelerated frames?

Key findings

• The nonlocal generalization of gravity introduces a new source term that effectively mimics dark matter.
• The integro-differential field equations are derived using a scalar constitutive kernel in the teleparallel formulation.
• In the linear approximation, the nonlocal theory reproduces the Tohline-Kuhn modified gravity potential.
• The nonlocal theory provides a theoretical basis for phenomenological modified gravity models.
• Nonlocality in the gravitational field naturally emerges from the equivalence principle and nonlocal special relativity.
• The theory is essentially equivalent to Einstein's general relativity plus a nonlocal dark matter-like contribution.