MOND: An Approximation of a Particular Solution of Linearized General Relativity

It has been demonstrated that dark matter (DM) can theoretically be completely explained by a natural effect of General Relativity (GR) without exotic matter, the Lense-Thirring effect that exists exclusively in GR and that would be due to the clusters of galaxies. In this study, we show that this explanation of DM leads to a modelization that can be interpreted as MOND-based theories. More concretely, we retrieve from GR the value of MOND parameter a₀~10^-8cm·s^-2 and deep MOND and AQUAL parameters G'~1.37G. It means that MOND-based theories could be interpreted as an approximation of the linearized GR (i.e. GR in a weak gravitational field or small acceleration) in a particular physical case of a uniform gravitic field (2nd component of GR in its linearized form, similar to magnetic field of Electromagnetism). A publication has recently observed deviations from Newtonian acceleration with a 10σ significance for wide binary stars at weak gravitational acceleration. The author demonstrates that these deviations can be explained by MOND theory with the previous parameters’ values. This situation leads to a difficulty. On one hand, the traditional DM hypothesis can’t explain these deviations and on the other hand, empirical MOND theories are difficult to justify compared to the success of GR. With our result, no more difficulty, these deviations do not need to be explained by MOND theory but by linearized GR with the uniform gravitic field explaining the DM component (Lense-Thirring effect of the clusters of galaxies).