Linearized Nonlocal Gravity

Abstract

Abstract The only known exact solution of the field equation of nonlocal gravity (NLG) is the trivial solution involving Minkowski spacetime that indicates the absence of a gravitational field. Therefore, this chapter is devoted to a thorough examination of NLG in the linear approximation beyond Minkowski spacetime. Moreover, the solutions of the linearized field equation of NLG are discussed in detail. We adopt the view that the kernel of the theory must be determined from observation. In the Newtonian regime of NLG, we recover the phenomenological Tohline-Kuhn approach to modified gravity. A simple generalization of the Kuhn kernel leads to a three-parameter modified Newtonian force law that is always attractive. Gravitational lensing is discussed. It is shown that nonlocal gravity (NLG), with a characteristic galactic lengthscale of order 1 kpc, simulates dark matter in the linear regime while preserving causality.