Lorentz-Poincaré type aspects of the matter Lagrangian in General Relativity Theory

It is well known that the solution to the Einstein Field Equation, gµ, can be either interpreted as the metric tensor itself or the mere gravitational field, their geochronometric correspondence being assured by the Equivalence Principle (e.g. Brown 2005). Within the field interpretation, which allows emphasis on physical effects of gravitation on microphysical constituents of matter, we expose gravitational Lorentz-Poincaré type properties of the relativistic gravitational matter Lagrangian. The Weierstrass parametrization (Johns 2005) of the matter Lagrangian LM in the explicit Lorentz-Poincaré type gravitation model is shown to render it equal to the standard matter Lagrangian --which can be reduced to the proper time invariant (g_{\mu\nu} dx^\mu / d \lambda dx^\nu / d\lambda)^{1/2} for the geodesic motion (Stephani 2004)-- in GRT. As such the GRT matter Lagrangian can be interpreted to result --following a Legendre transformation-- from the energy of the matter fields obtained from Gravitationally Modified Lorentz Transformations (Broekaert 2005).The resultant correspondence between matter Lagrangians exposes explicitly the Lorentz-Poincaré type features such as (coordinate) spatially-variable speed of light, $ c(r) = c' \Phi^2$, partial Machian mass induction $m(r, \nu) =m_0' \gamma \Phi^{_3}$ and gravitational affecting of space and time observations in local coordinates in GRT. These features are only apparent relative to the coordinative manifold, while locally and in physical coordinates the effects all vanish in concordance with the local Minkowski metric. ©2007 American Institute of Physics