Gravitational deflection in relativistic Newtonian dynamics
Abstract
In a recent series of papers, the authors introduced a new Relativistic Newtonian Dynamics (RND) and tested its validity by the accurate prediction of the gravitational time dilation, the anomalous precession of Mercury, the periastron advance of any binary and the Shapiro time delay. This dynamics incorporates the influence of potential energy on spacetime in Newtonian dynamics and, unlike Einstein's General Relativity, treats gravity as a force without the need to curve spacetime. In this paper, this dynamics is applied to derive the gravitational deflection of both objects with nonzero mass and of massless particles passing the strong gravitating field of a massive body. Equations for the trajectory and the resulting analytical expressions for the deflection angle, in terms of the distance and velocity at the point of closest approach to the massive object, were derived in both cases. It is shown that with a carefully defined limit, the trajectory of a massless particle is the limiting case of that of an object with nonzero mass. In the “weak” deflection limit, the derived expression for the deflection angle of a massless particle (photon) reproduces the experimentally tested Einstein's formula for weak gravitational lensing of a light ray, thereby providing another test for the validity of the RND.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 March 2017
 DOI:
 10.1209/02955075/117/59001
 arXiv:
 arXiv:1705.06967
 Bibcode:
 2017EL....11759001F
 Keywords:

 Physics  General Physics
 EPrint:
 4 pages, 1 figure