1999/10/25 by Shmuel Kaniel, Kaniel, Shmuel, Yakov Itin +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #gr-qc #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.gr-qc/9910083
arxiv created 1999/10/25 · arxiv updated 2009/11/30
A scalar model of gravity is considered. We propose Lorentz invariant field equation \square f = kηabf,af,b. The aim of this model is to get, approximately, Newton's law of gravity. It is shown that f=-\frac 1kln(1-k\frac mr) is the unique spherical symmetric static solution of the field equation. f is taken to be the field of a particle at the origin, having the mass m. The field of a particle moving with a constant velocity is taken to be the appropriate Lorentz transformation of f. The field F of N particles moving on trajectories ψj(t) is taken to be, to first order, the superposition of the fields of the particles, where the instantaneous Lorentz transformation of the fields pertaining to the j-th particle is ψj(t). When this field is inserted to the field equation the outcome is singular at (ψj(t),t). The singular terms of the l.h.s. and of the r.h.s. are both O(R-2). The only way to reduce the singularity in the field equation is by postulating Newton's law of force. It is hoped that this model will be generalized to system of equations that are covariant under general diffeomorphism.