TITLE:
Minkowskian Solution of General Relativity with Cosmological Constant and the Accelerating Universe
AUTHORS:
Yves Pierseaux
KEYWORDS:
General Relativity, Minkowskian Fluid, Cosmological Constant, Accelerating Universe
JOURNAL NAME:
Journal of Modern Physics,
Vol.5 No.16,
October
30,
2014
ABSTRACT: A
Minkowskian solution of the equation of General Relativity (as written by
Einstein in 1915) is trivial because it simply means that both members of the
equation are equal to zero. However, if alternatively, one considers the
complete equation with a non-zero constant Λ (Einstein
1917), a Minkowskian solution is no longer trivial because it amounts to impose
a constraint on the right hand side of the equation (i.e. a non-null
stress-energy tensor). If furthermore one identifies (as usual) this tensor to
the one of a perfect fluid, one finds that this fluid has a positive energy
density and a negative pressure that depend on the three constants of the
equation (i.e. gravitational constant G,
cosmological constant Λ and velocity of light c). When doing that (§1), one has
to consider the “Minkowskian Vacuum” as a physical object of GR (an enigmatic
non-baryonic Minkowskian fluid). Can one build a model of this object on the
basis of a dynamical equilibrium between the effective gravitational attraction
due to the positive energy density versus the negative pressure repulsion? We
propose to study such a model, where the (enigmatic) fluid is assumed to exist
only in a limited sphere whose surface acts like a “test body” sensitive to the
gravitational field created by the fluid. No static equilibrium exists, but a
pseudoNewtonian “dynamical equilibrium” (§2) can be reached if the
pseudoEuclidean fluid is in state of expansion. Up to there, we have simply
constructed a model of an “abstract Universe” (i.e. the limited sphere: There is no fluid outside this sphere!) that
gives to a (purely mathematical) constant Λ a concrete physical meaning. We
discover finally that our expanding fluid has not only dynamical
(gravitational) properties (§3) but also optical properties that are connected
with Doppler Redshift (§4). Remembering that recent observations in Cosmology
indicate that the “real Universe” seems to be “Flat” and in “Accelerated
Expansion”; remembering also (after all) that the archetypal Flat Universe is
simply a Minkowskian Universe, we logically wonder if the unexpected
Minkowskian global solution, could not be also a significant cosmological model
(conclusion).