Download Fiziev

P. P. Fiziev
Department of
Theoretical Physics
University of Sofia
GAS@BS
Kiten, 12-20 June, 2005
The Beginning
and
the End of
the Black Hole Myth
The
Black Hole
Story
Black Holes

Born on: 29 December 1967,
West Ballroom, NY Hilton, John Wheeler

Death on: 21 July 2004,
GR17, Dublin, Stephen Hawking
A PERSONAL VIEW
It seems to me that
at present
we are witnessing
a revolution
in this area !
Gravitational Condensate Stars:
An Alternative to Black Holes
G. Chapline, E. Hohlfeld, R.B. Laughlin, D. Santiago, Phil.
Mag. D 81, 235 (2001).
P.Masur, E.Mottola, gr-qc/0109035.
E. Mottola, P. Mazur, Proc. Nat. Acad. Sci., 111, 9546
(2004)
J. Barbierii, G. Chapline, Phys. Lett. B 590, 8 (2004)
Black holes 'do not exist'
“These mysterious objects
are dark-energy stars”,
physicist claims.
George Chapline
31 March 2005
The Main Question is:



What we are really seen?
The correct answer:
Very Compact Objects
Which Are Black (Dark)
With a Very Big Mass
No
one has never
seen the very hole!

It is
“non-observable”
by definition
How it could be?

Since 1916 to 1967 all respectable
physicist (Edington, Brillouin, Einstein,
Pauli, Dirac, Feynman, …) were thinking
that BH are nonphysical objects.

Since 1967 to 2004 all respectable
physicist were thinking that BH may be
real physical objects.
The original Schwarzschild Solution
(February 1916) – NO BH:
ds = (1 - 2m / r (r ) )dt + (1 - 2m / r (r ) ) dr
2
2
+ r (r )2 d W2
r (r ) = (r + (2m ) )
3
3 1/ 3
Þ r ( 0) = 2m
- 1
2
Hilbert gauge (1917):
r (r ) = r
Hilbert form of Schwarzschild
solution (1917):
ds = (1 - 2m / r )dt + (1 - 2m / r ) dr + r d W
2
r horizon = 2m
2
-1
2
2
2
Marcel Brillouin:
Le Journal De Phys. et Le Radium, 23 , 43 (1923).
“This discontinuity is by far sharper than
all the ones that have been
encountered up to now in the
problems of mathematical physics”
Albert Einstein:
Ann. Math., 40, 922 (1939)
 “The essential result of this
investigation is a clear understanding
as to why the “Schwarzschild
singularities” do not exist in the
physical reality…for the reason that
matter cannot be concentrated
arbitrary. … otherwise the constituting
particles would reach the velocity of
light. “
A modern version of Einstein conclusion:
A.A. Logunov, M.A. Mestverischvili, V.V. Kiselev:
gr-qc/0412058
“We argue for black holes do not represent a strict
consequence of general relativity…
… The Schwarzschild singularity of metric coefficients at
the sphere r=2m is formally canceled by the Kruskal
transformation. Nevertheless the solution of Hilbert-Einstein
equations does not become physical, since in accordance to
this solution the physical velocity become equal to the
speed of light at infinity which is unacceptable. … the
singularity can be removed from the metric coefficients, but
not from the interval. Thus we see that the notion of “black
holes” is based on presence of Schwarzschild singularity,
which is in contradiction of the basics of general relativity…”
P. A. M. Dirac:
Proc. Roy. Soc. London, 270, 354 (1962)
“The mathematicians can go beyond this
Schwarzschild radius, and get inside, but
I would maintain that this inside region is
not a physical space, because to send a
signal inside and get it out again would
take an infinite time, so I feel that the
space inside the Schwarzschild radius
must belong to a different universe and
should not be taken into account in any
physical theory. …
… I tried for some time to work with particle
with radius equal to Schwarzschild radius, but I
found great difficulties, because the field at the
Schwarzschild radius is so strongly
singular, and it seems that more profitable
line of investigations is to take a particle
bigger than the Schwarzschild radius and
to try to construct a theory for such
particle interacting with gravitational field.”
Leonard Abrams:
Can. J. Phys., 67, 919 (1988).
Title:
Black holes: the legacy of Hilbert’s error
“…the Kruscal-Fronsdal black hole is
merely an artifact of Hilbert’s error…”
…
 Dozens of articles in the same
direction, which have been usually
ignored up to recently, being outside
the main BH stream (thousands of
articles ) during the last 37 years.
 Many of these articles contain
technical mistakes,
together with the right results.
Where are placed
the horizon
singularities ?
Subtle is God:
(A. Einstein)
 Trajectories:
j
= lò
 Time integral:
 Action integral:
e2 + v(g)
1
dg
2
2
g
(1
g
)
e + v (g )
t = 2m e ò
dg
e + v(g)
g(1 - g)2
W r = 2mM ò
2
dg
2
2
v(g) = g(1 - l (1 - g) )
The Phase Portrait
The Phase Portrait: 1/Pg
1/
Martin Veltman
hep-ph/9404358 & Acta Phys. Polonca.
 “Why then, if the description in momentum space is
equivalent, do we not introduce a metric in momentum
space? Is that space flat by definition? Putting this issue
this way the basic conflict between gravitation and
quantum mechanics becomes obvious. Gravitation is
particular to space-time.
 We can not, on the one hand, do gauge theories and
renormalizable field theory in momentum space, and on
other hand solve classical equations of motion and play
with BH in coordinate space… we must realize that these
descriptions may not be equivalent, and that
we may have to make a choice depending
on the agreement with observed physics.
The theory of gravitation can be formulated as a gauge
theory…The trouble is that the theory is not renormalazible…
For Schwarzschild BH with radius R the special components of
gravitational tensor are
hjk
=
xj x k R
r r- R
The Fourier transform of this is non-existent, and also cannot
be defined as a function of R in some region and then
continued to the region of positive real R…
…the remarkable absence of BH outside the domain of
astrophysical speculation tends to support the idea of relative
space and the perturbative approach.”
Stephen Hawking
GR17, Dublin, 21 July, 2004
“The Euclidean path integral over all
topological trivial metrics can be done by time
slicing and so is unitary when analytically
continued to the Lorentzian. On the other
hand, the path integral over all topologically
non-trivial metrics is asymptotically
independent on the initial state. Thus the total
path integral is unitary and information is not
lost in formation and evaporation of BH.
The way the information gets out seems to be
that a true event horizon never forms, just an
apparent horizon.”
George Chapline
Texas Conference on Relativistic Astrophysics,
gr-qc/0503200
 “The fundamental reason for the tension
between quantum mechanics and GR is the
lack of universal time in GR. …
 One thing, that is wrong with BH vis a vie
QM is the existence of space-time
singularity which destroys quantum
information.
 A more profound difficulty, though, is the
presence of an infinite red-shift surface,
i.e., an event horizon, whose existence
precludes being able to establish a
universal time based on synchronization of
atomic clocks…”
BH = ?
Too many different definitions:






Analytical GR
Numerical GR
Mathematical Physics
String Theory
Astrophysics (CDO, M>3-5 solar masses)
Ashtekar & Krishnan (gr-qc/0407042)
The only general feature: the people, involved
in BH business believe that the situation can be
improved.
Let us remind the
Columbus Story
More then 500 years ago

America was discovered
(for Europeans)
by Christopher Columbus
(a well educated and very active
man of that epoch).

Have you ask yourself:
Why America
was not called
Columbia?
May be because of
Cabal of the
Non Euclidean Geometry:
Earth
is
Round
a quite perfect
statement !
An absolutely right conclusion:
One can reach India
going to the WEST,
not only to the EAST
One of the results of Columbus
expedition:
We are still speaking about
(American)
Indians
who have never seen
India
BH:
Fictions and
Observations
Observational Evidences for BH
Candidates (not undisputed):




X-ray binary systems (Cygnus X-1 +
some 10 more candidates:
~ 4-20 solar masses)
Intermediate mass BH (several
candidates already observed:
~ 50-100 solar masses)
AGN (more then 29 candidates:
~ 10-1000 million solar masses)
Quasars ???
The
Galactic
Center
How to observe
the unobservable hole?
A Critical
Experiment
demonstration:
MARCH 2005
P.P.F, T.L. Bojadjiev, D.A. Georgieva
Novel Properties of Bound States of KleinGordon Equation in Gravitational Field of
Massive Point
JCPTP, 45(3), p. 526 (2005)
gr-qc/040636



We are considering for the first time the solutions
of Klein-Gordon equation in gravitational field of a
massive point source in GR.
We examine numerically the basic bounded
quantum state and the next few states in the
discrete spectrum for different values of the
principal number n and of the orbital momentum l.
A novel feature of the solutions is the essential
dependence if their physical properties on the
gravitational mass defect of the point source,
even not introduced up to recently.
It yields a repulsion or an attraction of the
quantum levels and to their quasi-crossing with
varying of the mass defect.
The potential w(g)
wl (g)



g







BASIC NUMERICAL RESULTS:
The function P0l(u) for l=2,3,4,5,6,7,8.




P0, l

Case: varrho , n








u






The function Pl(u) for different varrho
Case: l , n 
2

The Potential Wl
1
2
1  varrho 

P0,2
2
2  varrho 
3

2
4
3  varrho 
3
4  varrho 
2
1, 2




u




The radial functions P0,2(u;\ r ) are different for
different values of the gravitational mass defect,
described by the variable \ r .
Depending on the values of the mass ratio \ r of the
point source, the wave function of the test particle in its
gravitational field is located:
• in the inner potential well (for small \ r ), or
• in the exterior potential well (for big \ r ).
• In the narrow intermediate domain of values of \ r
a transition regime take place.
• It's clear that in our approach the basic new
physical phenomena are related with the
gravitational mass defect for the point source of
gravitational field.
• Such mass defect was not considered and
studied correctly until now, because for the
standard Hilbert form of the Schwarzschild
solution
“the bare rest-mass density is never even
introduced"
R.Arnowitt, S.Deser, C.W.Misner, Phys. Rev. Lett., 4 (7),
375 (1960).
The function P02(u,varrho)
Such nontrivial behavior of the eigenvalues
nl ( r ) of the Klein-Gordon equation in a
gravitational field of a point particle is due to
the existence of two finite potential wells:
e
1) An inner one which in general case of macroscopic orbital
moments is very deep and has a size of order of the
Schwarzschild radius and
2) An exterior one, which is extremely thin in comparison
with the inner well.
The normal world with almost Newton gravity "lives" in the
exterior well.
The both wells are separated typically by a huge
potential barrier which looks like a centrifugal
barrier from outside, and as a suspensory barrier
of the type of a spherical potential wall from
inside.
Our calculations describe the quantum
penetration under this barrier. The quantum
result depends strongly on the mass defect of the
point source.
The eigenvalues for different principal quantum number
n=0,1,2,3 and orbital quantum number l = 2

Case: l , n 




varrho






First Eigenvalue
Minimal Eigenvalue


Case: l , n 



varrho





2



Third Eigenvalue
Second Eigenvalue


Case: l , n 


varrho









varrho


Case: l , n 






2

A typical steep-like dependence of the discrete
eigenvalues nnl on the variable \ r is seen.
e
For each value of the principle quantum number n
the number of the jumps of en l ( \ r ) depends on
the number of the maxima of the corresponding
wave function which are moved from the inner
well to the exterior one during the
transition regime which develops with the
increase of the values of the mass ratio \ r .
It is easy to observe one more astonishing phenomena in the
discrete spectrum of a test quantum particle in gravitational
field of point source. It is related, too, with the mass defect of
the source.
If one puts in the same figure the dependence of all discrete
eigenvalues n l on the squared mass ratio
, one can observe a repulsion
\ r 2 = gtt (0)
and
an attraction (up to a quasi-crossing) of the levels.
Such type of behavior of quantum discrete levels is well
known in the laser physics, in the neutrino oscillations and
in other branches of quantum physics.
e
To the best of our knowledge we are observing such behavior of quantum
levels in the fundamental gravitational physics for the first time.
Eigenvalues

Case: l = 2








varrho
    




The obtained in this article behavior of a quantum test particles
in the gravitational field of point source of gravity seems to us
to be much more physical then the one in the wide spread
models of black holes. Clearly, in contrast to such space-time
holes with nonphysical infinitely deep well in them, in our case
the finite inner well plays the role of a trap for the test particles.
It is not excluded that this way one may be able to construct a
model of very compact matter object
s with an arbitrary large mass and a size of order of
Schwarzschild radius. It's possible that such type of objects
may explain the observed in the Nature compact dark objects
and may be the final product of the stellar evolution, instead of
the quite formal and sophisticated constructions like black
holes.
Of course, at present these possibilities are an open problem
which deserves further careful study.
Regge-Wheeler potential for waves
with different spin s:
v
=
2
2
g (1 + l(l + 1)(1 - g ) + (1 - s )(1 - g)
u- 1
W (e )
g = g(u ) =
u- 1
W (e ) + 1
u – the tortoise coordinate
Lambert W
function
3
)
The Regge-Wheeler potential
for gravitational waves (s=2)
for l=0 and l=1
Gravitational waves with l=0:
The basic wave function and the basic eigenvalue
ñ
ñ
ñ
ñ
How about the Columbus Story?
It was Americo Vispuchi who first has
recognized that they have discovered
not India, but
SOMETHING MUCH MORE INTERSTING:
A NEW CONTINENT
AMERICA
Is it not possible
that the BH story
will have the same
END
?
Thank You