Weak Field Limit of Infinite Derivative Gravity

Abstract

A form of infinite derivative gravity is free from ghost-like instabilities with improved small scale behavior. In this theory, we calculate the tree-level scattering amplitude and the corresponding weak field potential energy between two localized covariantly conserved spinning point-like sources that also have velocities and orbital motion. We show that the spin-spin and spin-orbit interactions take the same form as in Einstein's gravity at large separations, whereas at small separations, the results are different. We find that not only the usual Newtonian potential energy but also the spin-spin and spin-orbit interaction terms in the potential energy are non-singular as one approaches r->0.

11 pages, references added, version accepted for publication in PRD

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• Nonlocal gravity with worldline inversion symmetry
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• Ghost-free modification of the Polyakov action and Hawking radiation
• Perturbations in higher derivative gravity beyond maximally symmetric spacetimes
• Light bending by a slowly rotating source in quadratic theories of gravity
• Gravitational memory effects in Brans-Dicke theory
• Graviton Mass and Memory
• Linearized modified gravity theories and gravitational waves physics in the GBD theory
• On effective models of regular black holes inspired by higher-derivative and nonlocal gravity
• Junction conditions in infinite derivative gravity
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• Gravitational field of scalar lumps in higher-derivative gravity
• Kerr-Schild perturbations in higher derivative gravity theories in $D$ dimensions
• New effective theories of gravitation and their phenomenological consequences