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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