Gradient modification of Newtonian gravity

Abstract

A second gradient generalization of Newtonian gravity is presented within the framework of gradient field theory. Weak nonlocality is introduced via first and second gradients of the gravitational field strength in the Lagrangian density. Gradient generalizations of the Poisson equation of Newtonian gravitation for the gravitational potential and of the generalized Gauss law for the gravitational field strength are presented. Such a gradient modification of Newtonian gravity provides a straightforward regularization of Newtonian gravity removing the classical Newtonian singularities. Finite gradient modifications of the gravitational potential energy and of the gravitational force law are constructed, with a possible connection to Yukawa interaction, and as suitable candidates for experimental tests of Newton's inverse-square law at short distances. In addition, nonlocal gravity of exponential type is investigated and its relation to gradient gravity theory is given.

arXiv comment9 pages, 4 figures

References in corpus (17)

• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Towards singularity and ghost free theories of gravity
• Super-renormalizable Quantum Gravity
• Sub-millimeter Tests of the Gravitational Inverse-square Law
• Particle Physics Implications of a Recent Test of the Gravitational Inverse Square Law
• New Test of the Gravitational $1/r^2$ Law at Separations down to 52 $\mu$m
• Some remarks on high derivative quantum gravity
• Superrenormalizable quantum gravity with complex ghosts
• Review of short-range gravity experiments in the LHC era
• Nonlocal Gravity Simulates Dark Matter
• Low-energy effects in a higher-derivative gravity model with real and complex massive poles
• Fat Gravitons, the Cosmological Constant and Sub-millimeter Tests
• On Newtonian singularities in higher derivative gravity models
• Nonlocal Modification of Newtonian Gravity
• On the cancellation of Newtonian singularities in higher-derivative gravity
• A non-singular continuum theory of point defects using gradient elasticity of bi-Helmholtz type
• Second gradient electromagnetostatics: electric point charge, electrostatic and magnetostatic dipoles

Cited by in corpus (2)

• Logarithmic corrections to Newtonian gravity and Large Scale Structure
• Isothermal spheres in general relativity and Horava-type gravity