The Laws of Gravity and Electromagnetism

Arkady Poliakovsky is an Associate Professor at the Department of Mathematics at Ben-Gurion University of the Negev, Be'er Sheva, Israel. His main specialization is Calculus of Variations and Partial Differential Equations. However he is also interested in Physics, Mathematical Physics, Fluid Mechanics, Differential Geometry and Tensor Calculus. Prof. Poiliakovsky was born in Russia in 1978. He immigrated with his parents to Israel in 1993 and obtained all his academic degrees from the Department of Mathematics of the Technion - I.I.T., Haifa, Israel: his primary Bachelor degree (summa cum laude) in 1999, a M.Sc. degree in 2002, and a Ph.D. in 2005. During the period 2005-2012 he held Post-Doc positions at various universities: Paris VI, University of Zurich, University of Duisburg-Essen, University of Bonn, and University of Rome - Tor Vergata. He was appointed to a Tenure Track position at Ben Gurion University of the Negev (Be'er Sheva, Israel) in 2012 (Senior Lecturer till 2016, Associate Professor since 2016, tenured since 2017). He obtained secondary Bachelor degrees in Physics and Computer Science in Technion, Haifa at 2017.

Introduction.- Notations and preliminaries.- Transformations of scalar and vector elds under the change of inertial or noninertial cartesian coordinate system.- Gravity revised.-  Maxwell equations revised.- Maxwell equations in non-inertial cartesian coordinate systems.- Scalar and vectorial electromagnetic potentials.- Lagrangian of the Electromagnetic eld.- Local gravitational time and Maxwell equations in a non-rotating coordinate system.- Motion of particles in external gravitational-electromagnetic eld.- Relation between the gravitational and inertial masses and conservation laws.- Lagrangian of the unied Gravitational-Electromagnetic eld.- Covariant formulation of the physical laws in the four-dimensional non-relativistic space-time.- Relativistic-like Dirac equation.- Thermodynamics of a moving continuum medium.- Maxwell equations in the presence of Dielectrics and/or Magnetics.- Some further consequences of Maxwell equations.- Appendix.