The Abraham Zelmanov Journal
The journal for General Relativity, gravitation and cosmology
Behaviour of the EGR Persistent Vacuum Field Following the Lichnérowicz Matching Conditions
Recently, the author has proposed an extension of the General Theory of Relativity — the EGR theory, which allows for a persistent gravity-like field to exist as a homogeneous energy density background. In this paper, we demonstrate the continuity of this field with respect to the gravitational field of a massive body. To achieve this goal, we make use of the Lichnérowicz conjecture which formulates the conditions required to match a hyperbolic 4-metric characterized by a material-energy tensor, with a similar type of vacuum-solution metric. This is herein applied to a spherically symmetric class of the general relativistic solutions compatible with the Schwarzschild exterior metric. The EGR covariant derivatives of the metric are then only radial and time-dependent functions: the radial persistent field tensor component vanishes on a hypersurface separating the vacuum from the matter state. As a consequence, when this hypersurface is narrowed down to the size of a particle, it follows a non-Riemannian geodesic describing the trajectory of the particle whose mass slightly increased: this effect can be interpreted as the bare mass carrying its subsequent gravitational field.
Ref: The Abraham Zelmanov Journal, 2010, volume 3, pages 71-89
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The Abraham Zelmanov Journal is an annually issue scientific journal registered with the Royal National Library of Sweden.