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Title Behaviour of the EGR persistent vacuum field following the Lichnerowicz matching conditions
Author Patrick Marquet
Recently, the author has proposed an extension of the
General Theory of Relativity | the EGR theory, which allows for a
persistent gravity-like eld to exist as a homogeneous energy density
background. In this paper, we demonstrate the continuity of this eld
with respect to the gravitational eld of a massive body. To achieve
this goal, we make use of the Lichnerowicz 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 eld
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 e ect can be interpreted as the bare mass carrying its
subsequent gravitational eld.
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