Global gravitational-optical gradient lens in expanding Universe
Pavlo DANYLCHENKO
Full
version of the article PDF
(149 kb), DOC
(54 kb).
Synopsis
Value of Schwarzschild radial coordinate of the
luminous astronomical object is connected with the difference between absolute
M and non-relativistic-corrected visible m’ its stellar magnitudes via the following relativistic photometric
dependence [1]: r=101–(M–m”)/5=(10ξ/5+H/c)–1=(1/RN+H/c)–1, where:
ξ=M–m’+5lg[(z+1)/(z’+1)]–5=–5lgRN=5lg(1/r–H/c)=5lg(H/cz’); m”=m’–5lg(z+1) – relativistic-corrected
visible stellar magnitude of this object; z and z’=Hr/(c–Hr)=HRN /c – not corrected and corrected (caused only by evolutionary process,
which is the cause of Universe expansion) values of red shift correspondingly; RN
– radial coordinate of astronomical object in background Euclidean space [2] of comoving with Universe frame of reference of
spatial coordinates and time (FR); H=c(Λ/3)–1/2
– Hubble constant; Λ – cosmological constant; с – constant of the velocity of
light.
Evolutionary process, which is the
cause of Universe expansion [3], forms in vacuum space-time continuum (STC) of
observer not only the gravitational field that force distant astronomical
objects to “run away” from the observer, but also global gravitational
lens that corresponds to this removable field. This comoving with radiation diverging lens
possesses negative Hubble lens power: ΦH=–H/c=–1/rc=1/RN–1/r
and creates virtual image of infinitely far points of background flat space
of comoving with Universe FR on the fictive spherical surface (r=rc)
of imaginary observer horizon in observer vacuum STC. The same follows from the Schwarzschild
solution in comoving with Universe.
Values of radial motion velocity v of
distant astronomical objects of expanding Universe tend to the values of
coordinate-like velocity of light vc at approaching imaginary
observer horizon and so at deepening into cosmological past. This leads to a
very big relativistic shrinkage of dimensions of these objects and of distances
between them. Also this is the formal cause of the formation of imaginary
observer horizon in comoving with matter FRs. According to Schwarzschild
solution, presence of imaginary observer horizon, which is also the horizon of
cosmological past, in vacuum STC of matter is inevitable at nonzero value of
cosmological constant. Galaxies of expanding Universe fall free on imaginary
observer horizon, but they cannot reach it in principle, because of zero value
of coordinate-like velocity of light on its fictive surface. And, therefore,
galaxies cannot hide behind the imaginary observer horizon [3].
However, rotation of observer in background Euclidean space, which
causes ellipticity of fictive surface of imaginary observer horizon, as well as
the presence of astronomical objects in its space, as well as solid filling of
the Universe with initial matter nearby this imaginary horizon, are not taken
into account by Schwarzschild solution. Therewith, given here expression for
the power of Hubble lens corresponds only to homogeneous optical medium –
hypothetical absolute vacuum, used in Schwarzschild solution. Indeed,
conventionally free space that surrounds any compact matter is filled in by
very rarefied gas-dust matter, pressure in which only gradually decreases at
distancing from compact matter and cannot be smaller than the value of pressure
of relict radiation. Therefore, it is worthwhile to examine the solution of
gravitational field equations also for non-free space that surrounds compact
matter. In commoving with Universe FR all equations, except the one that
determines the rate of matter gauge-self-contracting, come to thermodynamic
identities.
Value r at first increases at distancing from the observer until
it reaches its maximal value rmax on the singular spherical
surface of relativistic observer horizon. Then this value begins to decrease
and it tends to zero in the point of imaginary Universe Big Bang. Therefore r
should be considered not as radial coordinate, but only as Schwarzschild coordinate-like
parameter (Schwarzschild radial pseudo-coordinate). Maximal values of this
parameter are not the same in comoving with radiation FR and comoving with
compact matter FR. They corresponds to not the same moment of cosmological time
and, consequently, to not the same value of average density of Universe matter:
<μ>=(3r–2–Λ)/κc2=3(r–2–H2c–2)/κc2, where: κ – Einstein constant.
Since velocity of distancing of distant astronomical objects of
expanding Universe from observer depends on the average density of matter in
the Universe, corrected value of red shift of radiation spectrum of these
objects also depends on this density. Since
value of red shift of the frequency of radiation that comes from observer
horizon of “comoving with radiation” FR can be only infinitely big this horizon
is an imaginary observer horizon. And, consequently, its fictive surface
separates nothing from observer in infinite space of the Universe. Comoving
with radiation gravitational-optical gradient lens is formed in observer FR due
to evolutionary decrease of average density of matter in the Universe and of
refractive index of interstellar medium. Together with Hubble gravitational
lens this diverging lens, which has spatially inhomogeneous negative lens power
forms virtual image of all infinitely far points of background Euclidean space
of comoving with Universe FR on its focal surface, which is the imaginary
observer horizon.
Relativistic observer horizon of comoving with compact matter FR is not
an imaginary. World points of its singular surface are not connected by light
signals to observer. Coordinate-like velocity of light on its surface is equal
to zero in the moment of registration of radiation that has come from it, but
not in the moment of its generation. Therefore, this horizon determines only
the configuration of intrinsic space of compact matter and this horizon is the
true event horizon of the past. Since Universe is expanding, events, which are
simultaneous in observer FR but take place in different points, are not
simultaneous in cosmological time of comoving with Universe FR. Therefore,
world point of imaginary Big Bang of the Universe is present in intrinsic space
of the observer in every moment of observer intrinsic time. This point and the
point, where observer is, are opposite poles of four-dimensional hypersurface
of observer space. Schwarzschild radial pseudo-coordinates are only the
radiuses of latitudinal cross-sections of this hypersurface. If gradient lens
was not taken into account, then lens power of global gravitational lens would
be spatially homogeneous and, therefore, red shift of radiation spectrum of
astronomical objects would linearly depend on the distances to these objects.
If gradient lens is taken into account, then this dependence becomes nonlinear.
And if correct (this distribution is compatible with the law of evolutionary
change of global gravithermodynamic state of matter in the Universe) spatial
distribution of non Doppler ratio of identical emission radiations frequencies
in observer intrinsic space is used, then it corresponds to accelerated
Universe expansion. In this case imaginary observer horizon (pseudo-horizon of
cosmological past), which corresponds to infinitely far points of background
flat space of the Universe, degenerates at the transition from ideal to real
intrinsic FR of astronomical body and transforms into the point of imaginary
Big Bang of the Universe. This fact is an analogy to degeneration of the
horizon of cosmological future (Schwarzschild sphere) in internal solution of
gravitational field equations.
So, imaginary observer horizon in the Universe
is an attribute of only ideal intrinsic FRs of the bodies and of corresponding
to them STCs. Singular surface, which maybe corresponds to time moment of origination
of free radiation in the Universe, takes the maximum value of photometric
radius in real intrinsic observer FR, as it is shown on the picture below.
Behind this surface photometric radius (Schwarzschild radial pseudo-coordinate)
of world space of astronomical body begins to decrease at deepening into
cosmological past [1]. And, consequently, additional decreasing of the value of
photometric radius of astronomical objects, takes place. This additional
decreasing is caused by the presence of irremovable gravitational field in real
observer FR and additional lens power of global gravitational-optical gradient
lens that corresponds to this field.
Pic. Intrinsic space of astronomical
body in its real FR in the concrete moment of its intrinsic time.
1 – intrinsic
space of the body (one from the set of radial directions in this space); 2 –
world point of body center; 3 – world point of imaginary Big Bang of the
Universe that does not belong to body space; 4 – points of world surface of the
Universe with maximal value of photometric radius r (Schwarzschild
radial pseudo-coordinate); 5 – exponential scale, by which cosmological time is
counted; r –
radius-vector of observed object in nonlinearly transformed fundamental world
space of comoving with Universe.
Full
version of the article PDF
(149 kb), DOC
(54 kb).
Reference
list
1. P. Danylchenko, in
Introduction to relativistic gravithermodynamics (IRG), Nova knyga, Vinnytsia Ukraine (2008),
p. 106
(in Russian); in
Abstracts of RUSGRAV-13, June
23-28, 2008. PFUR, Moscow, Russia (2008), p. 109; E-print: http://pavlo-danylchenko.narod.ru/docs/RelativisticValues.html.
2. Ya. B. Zel’dovich, L. P. Grishchuk, UFN 155, 517 (1988).
3. P.
Danylchenko, in Gauge-evolutional interpretation of
special and general relativities, О. Vlasuk, Vinnytsia Ukraine (2004), p.
33, E-print archives, http://pavlo-danylchenko.narod.ru/docs/Possibilities_Eng.html;
Nova knyga, Vinnytsia Ukraine (2008), p. 45 (in Russian); E-print: http://pavlo-danylchenko.narod.ru/docs/Possibilities_Rus.html.
4. P.
Danylchenko, in IRG, p. 19 (in Russian); in
Abstracts of RUSGRAV-13, June
23-28, 2008. PFUR, Moscow, Russia (2008), p. 109; E-print: http://pavlo-danylchenko.narod.ru/docs/UnitedNature.html.