Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-11-20
J.Math.Phys.53:042501,2012
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
27 pages, 4 figures; v2: minor improvements, accepted for publication in J. Math. Phys
Scientific paper
The recent nonlocal generalization of Einstein's theory of gravitation reduces in the Newtonian regime to a nonlocal and nonlinear modification of Poisson's equation of Newtonian gravity. The nonlocally modified Poisson equation implies that nonlocality can simulate dark matter. Observational data regarding dark matter provide limited information about the functional form of the reciprocal kernel, from which the original nonlocal kernel of the theory must be determined. We study this inverse problem of nonlocal gravity in the linear domain, where the applicability of the Fourier transform method is critically examined and the conditions for the existence of the nonlocal kernel are discussed. This approach is illustrated via simple explicit examples for which the kernels are numerically evaluated. We then turn to a general discussion of the modified Poisson equation and present a formal solution of this equation via a successive approximation scheme. The treatment is specialized to the gravitational potential of a point mass, where in the linear regime we recover the Tohline-Kuhn approach to modified gravity.
Chicone Carmen
Mashhoon Bahram
No associations
LandOfFree
Nonlocal Gravity: Modified Poisson's Equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nonlocal Gravity: Modified Poisson's Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonlocal Gravity: Modified Poisson's Equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-375590