A theory of gravitation

Abstract

The paper presents a theory of gravitation as a continuum dynamical theory, i.e. the equations of motion are first order in the time derivatives. The theory satisfies the laws of conservation of total energy, momentum and mass in the standard sense, i.e. as applications of Stokes’ theorem. A model in this theory is defined by the specification of an energy density function that accounts for the total mechanical and gravitational energy of the system and which in turn defines an action function. The derivation of the equations of motion is based on Hamilton’s principle of least action with the “same” action function as used for the derivation of the Einstein equation of the theory of general relativity, however, not with respect to variations of the metric but with respect to variations induced by local displacements of space, i.e. variations of the conjugate variable of the momentum and variations of the momentum density. Entropy density is introduced as a variable. This makes it possible to determine the thermodynamic equilibrium conditions for a model. Solutions of the equilibrium conditions are the Schwarzschild and Minkowski metrics on space-time, and the metrics defining the spherical and hyper spherical spaces.