P. P. FizievP. P. Fiziev

Department of Department of Theoretical Physics Theoretical Physics University of SofiaUniversity 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:Gravitational Condensate Stars:An Alternative An Alternative toto Black HolesBlack 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)

“These mysterious objects are dark-energy stars”, physicist claims.

George Chapline

31 March 2005

Black holes 'do not exist'

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:

2 2 1 2

3 3 1/

2 2

3

1 2 / ( ) 1 2 / (

(

)

) ( (2 ) ) 0) 2

(

(

)

) )( (ds m r dt m r d

r r m m

r

r d

r r

r

r r

-= - + -

+

= + Þ =

W

Hilbert gauge (1917):

( )r rr =

Hilbert form of Schwarzschild solution (1917):

2 2 1 2 2 21 2 / 1 2 /

2

) )( (horizon

ds m dt m dr d

m

r r r

r

-= - + - + W

=

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:

Time integral:

Action integral:22

12

(1 )( )

dgt m

g gv ge

e=

-+ò

2 ( )

dgl

v gj

e=

+ò

222 ( )

(1 )r

dgW mM v g

g ge= +

-ò2 2( ) (1 (1 ) )v g g l g= - -

The Phase Portrait

The Phase Portrait: 1/Pg

1/

Martin Veltmanhep-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

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.”

j kjk

xx Rh

r r R=

-

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 ChaplineTexas 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 America was discovered (for Europeans)(for Europeans) by by Christopher Columbus Christopher Columbus (a well educated and very active (a well educated and very active

man of that epoch)man of that epoch).. Have you ask yourself:Have you ask yourself:

Why America Why America was not called was not called

Columbia? Columbia?

May be because of May be because of

Cabal of theCabal of the

Non Euclidean Geometry:Non Euclidean Geometry:

Earth is Round-a quite perfect statement !

An absolutely right conclusion:An absolutely right conclusion:

One can reachOne can reach IndiaIndia going to thegoing to the WEST,WEST,not only to thenot only to the EASTEAST

One of the results of ColumbusOne of the results of Columbusexpedition:expedition:

We are still speaking aboutWe are still speaking about (American)(American) IndiansIndians

who have never seenwho have never seen IndiaIndia

BH: BH: Fictions and Fictions and ObservationsObservations

Observational Evidences for BH Observational Evidences for BH CandidatesCandidates (not undisputed):(not undisputed):

X-ray binary systemsX-ray binary systems (Cygnus X-1 + (Cygnus X-1 + some 10 more candidates: some 10 more candidates: ~~ 4-20 solar masses4-20 solar masses))

Intermediate mass BHIntermediate mass BH (several (several candidates already observed: candidates already observed: ~~ 50-100 solar masses50-100 solar masses))

AGNAGN (more then 29 candidates: (more then 29 candidates: ~~ 10-1000 10-1000 millionmillion solar masses solar masses))

QuasarsQuasars ??? ???

The The Galactic Galactic CenterCenter

How to observe How to observe the unobservable hole?the unobservable hole?

A Critical Experiment demonstration:

Novel Properties of Bound States of Klein-Novel Properties of Bound States of Klein-Gordon Equation in Gravitational Field of Gordon Equation in Gravitational Field of

Massive PointMassive Point

JCPTP, JCPTP, 4545(3), p. 526 (2005)(3), p. 526 (2005)gr-qc/040636gr-qc/040636

MARCH 2005MARCH 2005

P.P.F, T.L. Bojadjiev, D.A. GeorgievaP.P.F, T.L. Bojadjiev, D.A. Georgieva

We are considering for the first time the solutions We are considering for the first time the solutions of Klein-Gordon equation in gravitational field of a of Klein-Gordon equation in gravitational field of a massive point sourcemassive point source in GR in GR..

We examine numerically the basic bounded We examine numerically the basic bounded quantum state and the next few states in the quantum state and the next few states in the discrete spectrumdiscrete spectrum for different values of the for different values of the principal number principal number nn and of the orbital momentum and of the orbital momentum ll..

A novel feature of the solutions is the essential A novel feature of the solutions is the essential dependence if their physical properties on thedependence if their physical properties on the gravitational gravitational mass defectmass defect of the point source, of the point source, even not introduced up to recently.even not introduced up to recently.

It yields a It yields a repulsionrepulsion or an or an attractionattraction of the of the quantumquantum levels and to their quasi-crossing with levels and to their quasi-crossing with varying of the mass defect.varying of the mass defect.

The potential w(g)

(g)

l

g

w

BASIC NUMERICAL RESULTS:BASIC NUMERICAL RESULTS:

The function P0l(u) for l=2,3,4,5,6,7,8.

u

Case: varrho , n

P0, l

The function Pl(u) for different varrho

3

1, 2

43

2

1

1 varrho2 2 varrho2 3 varrho2 4 varrho2

The Potential Wl

Case: l , n

P0,2

u

The radial functions P0,2(u; ) are different fordifferent values of the gravitational mass defect, described by the variable .

Depending on the values of the mass ratio of the point source, the wave function of the test particle in itsgravitational field is located:

• in the inner potential well (for small ), or

• in the exterior potential well (for big ).

• In the narrow intermediate domain of values of a transition regime take place.

\ r

\ r

\ r

\ r

\ r

\ r

• 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 PThe function P0202(u,varrho)(u,varrho)

Such nontrivial behavior of the eigenvalues Such nontrivial behavior of the eigenvalues of the Klein-Gordon equation in a of the Klein-Gordon equation in a gravitational field of a point particle is due to gravitational field of a point particle is due to

the existence of the existence of two finite potential wellstwo finite potential wells: :

1) An inner one which in general case of macroscopic orbital 1) An inner one which in general case of macroscopic orbital moments is very deep and has a size of order of the moments is very deep and has a size of order of the Schwarzschild radius and Schwarzschild radius and

2) An exterior one, which is extremely thin in comparison with 2) An exterior one, which is extremely thin in comparison with the inner well. the inner well.

The normal world with almost Newton gravity "lives" in the The normal world with almost Newton gravity "lives" in the exterior wellexterior well. .

The both wells are separated typically by a The both wells are separated typically by a huge huge potential barrierpotential barrier which looks like which looks like a centrifugal a centrifugal barrier from outsidebarrier from outside, and as a suspensory barrier of , and as a suspensory barrier of the type of a spherical the type of a spherical potential wall from insidepotential wall from inside. .

Our calculations describe the quantum penetration Our calculations describe the quantum penetration under this barrier. The quantum result depends under this barrier. The quantum result depends strongly on the mass defect of the point source.strongly on the mass defect of the point source.

)(nl re

The eigenvalues for different principal quantum number n=0,1,2,3 and orbital quantum number l = 2

Case: l , n

varrhoMin

imal

Eig

enva

lue

Case: l , n

varrhoSeco

nd E

igen

valu

e

Case: l , n

varrho2Thi

rd E

igen

valu

e

Case: l , n

varrho2Fir

st E

igen

valu

e

A typical steep-like dependence of the discrete eigenvalues on the variable is seen.

For each value of the principle quantum number n the number of the jumps of ( ) depends on the number of the maxima of the corresponding wave function which are moved from the inner well to the exterior one during thetransition regime which develops with the increase of the values of the mass ratio .

lne

lne \ r

\ r

\ r

lne

It is easy to observe one more astonishing phenomena in thediscrete spectrum of a test quantum particle in gravitationalfield of point source. It is related, too, with the mass defect ofthe source.

If one puts in the same figure the dependence of all discrete eigenvalues on the squared mass ratio

, one can observe a repulsion 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.

To the best of our knowledge we are observing such behavior of quantum levels in the fundamental gravitational physics for the first time.

2 (0)\ ttgr =lne

Case: l = 2

varrhoEige

nval

ues

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 objects 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 Regge-Wheeler potential for waves with different spinwith different spin ss::

( )2 2 31 ( 1)(1 ) (1 )(1 )g l l g gsv = + + - + - -

1

1

( )( )

( ) 1

u

u

W eg gu

W e

-

-= =+

Lambert W function

– the tortoise coordinateu

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

ññ

ñ

How about the Columbus Story?How about the Columbus Story?

It was It was AmericoAmerico VispuchiVispuchi who first has who first has recognized that they have discoveredrecognized that they have discovered

not India, butnot India, but

SOMETHING MUCH MORE INTERSTING:SOMETHING MUCH MORE INTERSTING:

A NEW CONTINENTA NEW CONTINENT

AMERICA AMERICA

Is it not possible Is it not possible that the BH story that the BH story will have the samewill have the same

END END

??

Thank YouThank You