As discussed in a previous blog, the noted scholar and researcher on gravitation, Prof. Thanu Padmanabhan, noted way back in 1988
that the concept of Black Holes (BH) not only leads to various inconsistencies but is unphysical too in certain ways. The following paper coauthored by him
1. “The Schwarzschild Solution:Some Conceptual Difficulties’‘ by J.V. Narlikar & T. Padmanabhan published in Foundations of Physics, Vol. 18, pp.659-668 (1988)
“Nevertheless there are several conceptual difficulties associated with this simple and elegant solution that are usually ignored because of its manifest usefulness. Our purpose in this article is to highlight these problems since we feel that their eventual resolution will advance our understanding of the complex basic interaction of gravitation.”
Even before this the ABSTRACT of the paper may be recalled:
“It is shown that inconsistencies arise when we look upon the Schwarzschild solution as the space-time arising from a localized point singularity. The notion of black holes is critically examined, and it is argued that, since black hole formation never takes place within the past light cone of a typical external observer, the discussion of physical behavior of black holes, classical or quantum, is only of academic interest. It is suggested that problems related to the source could be avoided if the event horizon did not form and that the universe only contained quasi-black holes.”
About continued gravitational collapse to a point, these authors wrote that
“Thus we have arrived at an inconsistency at R = 0. It could be argued that a point source at R= 0 is unrealistic and that the Schwarzschild solution works for a distributed source only. This way out is unfortunately ruled out by the phenomenon of gravitational collapse that inevitably results in all the matter converging to R=0 in finite
Accordingly, this paper repeatedly stressed so-called “Black Hole Candidates” could be just Quasi Black Holes rather than true BHs. Also in principle, a true BH cannot be observed directly. ”
Later in the following paper:
2.“Phase volume occupied by a test particle around an incipient black hole”
T. Padmanabhan, Physics Letters A, Volume 136, p. 203(1989)
he wrote that
“The volume of phase space g(E) available for a system with a definite energy E plays an important role in statistical mechanics. We compute g(E) for a test particle in Schwarzschild geometry and show that it diverges as the source evolves to form a black hole.”
The consequence of the DIVERGENCE of g(E) is that Entropy of the ideal gas too would diverge in case an Event Horizon (EH) would form. Note that when ever unphysical or singular properties of the EH become manifest BH proponents shout “Oh! This must be a coordinate singularity”. But Padmanabhan correctly emphasized that blowing up of g(E) or entropy was not all any coordinate effect, on the other hand such a divergence shows true singular property of the EH. In fact one can easily trace the reason for the divergence of Entropy to the singular properties of the metric coefficients of the Schwarzschild Metric at the EH:
So as per the research carried out by Padmanabhan during the 1980s, atleast as far as General Relativity (GR) is concerned,
(i) The singularity of the Schwarzschild Metric at the EH can lead to genuine physical singularities, i.e., EH does not correspond to a mere “Coordinate Singularity”, and
(ii) The concept of BH is unphysical, and the so-called BH Candidates should be “Quasi- BHs” which to a far away observer look almost as compact and BLACK as theoretical BHs.
Following this ,a logical and honest future course of his Black Hole research could have been to explore the subtleties and nuances of the complex topic of General Relativistic Gravitational Collapse to see how continued collapse must prevent formation of Theoretical BHs, and on the other hand lead to only Quasi-BHs.
But This Was Not To Be
However, Padmanabhan did not pursue any such uncertain, un-trodden and tortuous path of research. Instead, after a hibernation in BH research; he went on writing papers after papers which assumed that (iii) Gravitational Collapse Must Produce Black Holes and Event Horizons and (iv) Black Holes and Event Horizons are one of the most important concepts in not only gravitation but physics as a whole IN DIRECT CONTRADICTION to his own previous ideas (i) and (ii).
In particular, the idea of Event Horizons became the basis of his future research in Gravitation which won him all accolades and awards. Recall his later papers:
3. “Quantum Structure of Spacetime and Entropy of Schwarschild Black Holes” : Physical Review Letters, Volume 81, pp.4297 (1988)
4. “Event horizon of a Schwarzschild black hole: Magnifying glass for Planck length physics”: Physical Review D, Volume 59, id. 124012 (1999)
5. “Classical and quantum thermodynamics of horizons in spherically symmetric spacetimes”: Classical and Quantum Gravity, Volume 19, pp. 5387 (2002)
6. “Thermodynamics of Horizons”: Modern Physics Letters A, Volume 17, pp. 923-942 (2002)
7. “Why Gravity Has No Choice: Bulk Spacetime Dynamics Is Dictated by Information Entanglement Across Horizons”: General Relativity and Gravitation, v. 35, p. 2097-2103 (2003)
8. “Entropy of Horizons, Complex Paths and Quantum Tunnelling”: Modern Physics Letters A, Volume 19, pp. 2637, (2004)
9. “Gravity and the thermodynamics of horizons”: Physics Reports, Volume 406, p. 49-125 (2005)
10. “Entropy of null surfaces and dynamics of spacetime”: Physical Review D, vol. 75, id. 064004 (2007) (Note: Null Surface is a surface similar to an “Event Horizon”).
11. “Einstein’s equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons”: Physics Letters B, Volume 652, p. 338-342 (2007)
12. “Gravity as AN Emergent Phenomenon”: International Journal of Modern Physics D, Volume 17, pp. 591-596 (2008)
13. “Ideal gas in a strong gravitational field: Area dependence of entropy”: Physical Review D, vol. 83, Issue 6, id. 064034 (2011)
14. “Structure of the gravitational action and its relation with horizon thermodynamics and emergent gravity paradigm”: Physical Review D, vol. 87, id. 124011 (2013)
Let us not first debate “Which of the two Self-contradictory phases of research of Padmanabhan is scientifically correct?”
Note that even if one would consider Quantum Gravity BHs, the latter must yield GR results for large quantum numbers or for macroscopic cases. Thus even QG BH research must be organically related to classical GR results. And let the latter phase, Papers 3-14 be correct. Note there is no harm if an honest researcher would change his course of research as new arguments, new facts would emerge . In fact, up to 1996, I was a strong believer in the Black Hole paradigm, but I took a U-turn by 1998, as my research showed that my earlier belief was incorrect.
If Padmanabhan were an honest researcher and committed to scientific truths alone, he should have offered due explanation as to how his initial research which showed that GR should not allow BHs and EHs was incorrect. But he made no such attempts. In fact in a very mysterious manner, he never cited his own papers 1 & 2 in almost 100 papers, articles, books authored by him which involved the concept of “Black Holes” and “Horizons” or “Null Surfaces”!!!!!!
Now let us quickly adjudge which phase of his research is the physically and scientifically correct. In a series of peer reviewed papers by the present author, it has been shown that Black Holes and Event Horizons Indeed Correspond to Genuine Physical Singularities and Hence They Are Unphysical & Must Not Form. To cut a long story short, it has been shown that
- A Radially Falling Material Test Particle Would Behave Like a Photon If It would Reach The Event Horizon Irrespective of the Coordinate System Used; and this is not allowed by GR.
- The Coordinate Independent Scalar Acceleration Felt By An Observer At the EH is INFINITE indicating EH is a PHYSICAL SINGULARITY. In fact this is the reason that “nothing not even light can escape the Event Horizon”.
- There are indeed scalars made out of Rimmanian Tensor which become singular at the Event Horizon and a Free Falling Observer Can Very Well Detect this singular surface contrary to the basic argument of BH paradigm: REF:
16. “A note on a local effect at the Schwarzschild sphere”
Karlhede, A.; Lindstrom, U.; Aman, J. E.: General Relativity and Gravitation, vol. 14, June 1982, p. 569-571 (1982)
17. “On the Local Detectability of the Passage Through the Schwarzschild Horizon”: Tammelo, Risto; Kask, Üllar, General Relativity and Gravitation, Volume 29, p.997-1009 (1997)
18. “Detecting Event Horizons and Stationary Surfaces”: Gass, Richard G. et al. (arXiv:gr-qc/9808055)
Eventually, these questions were uniquely settled by this blogger by showing that Black Holes Have a Unique Gravitational Mass M=0, and they represent only asymptotic final states of continued gravitational collapse which could be formed only after radiating away entire mass-energy and angular momentum of the collapsing body. REF:
19. Comments on “The Euclidean gravitational action as black hole entropy, singularities, and space-time voids” [J. Math. Phys. 49, 042501 (2008)]: A. Mitra, Journal of Mathematical Physics, Volume 50, pp. 042502 (2009); (arXiv:0904.4754)
20. “Why the astrophysical Black Hole Candidates may not be black holes at all”: A. Mitra 2004, (arXiv:astro-ph/0409049)
It has also been shown that continued collapse should naturally give rise to Eternally Collapsing Objects (ECOs):
An Eternally Collapsing Object (ECO) is a compact star that resembles a ball of fire; and it is so hot that its radiation helps it stay put despite its intense pull of gravity. Being extremely compact, ECOs mimic mathematical “Black Holes” in many ways, but there are observational reasons to believe that the so-called astrophysical “Black Holes” are really ECOs: The eruptions and jet formations from the black hole candidates are better understood if they are indeed hot balls of fire rather than a cold piece of vacuum with an imaginary surface from which “nothing, not even light can escape”.
ECOs however asymptotically shrink towards the mathematical Black Hole state of infinite compactness.
21.“ Radiation pressure supported stars in Einstein gravity: eternally collapsing objects”: A. Mitra, Monthly Notices of the Royal Astronomical Society, Volume 369, pp. 492-496 (2006)
22. “Sources of stellar energy, Einstein Eddington timescale of gravitational contraction and eternally collapsing objects”: A. Mitra, New Astronomy, Volume 12, p. 146-160 (2006)
23. “Likely formation of general relativistic radiation pressure supported stars or `eternally collapsing objects”’: A. Mitra & N.K. Glendenning, Monthly Notices of the Royal Astronomical Society: Letters, Volume 404, pp. L50-L54 (2010)
24. “Kruskal Coordinates and Mass of Schwarzschild Black Holes: No Finite Mass Black Hole at All”, A. Mitra, International Journal of Astronomy and Astrophysics, vol. 2, issue 04, pp. 236-248 (2012), 10.4236/ijaa.2012.24031
25. “The Mass of the Oppenheimer-Snyder Hole: Only Finite Mass Quasi-Black Holes”, A. Mitra & K.K. Singh, International Journal of Modern Physics D, Volume 22, id. 1350054 (2013)
26. “Does Pressure Accentuate General Relativistic Gravitational Collapse and Formation of Trapped Surfaces?”, A. Mitra, International Journal of Modern Physics D, Volume 22, id. 1350021 (2013)
What Could Explain The U-Turn of Thanu Padmanabhan?
Many greatest physicists including Eddington, Einstein and Dirac did not believe in Black Holes. However they could not offer any cogent reason which would resolve this paradox characterized by beautiful & exact GR solutions. The problem became even much more complex after it was found that indeed there are indeed valid Black Hole Candidates in X-Ray Binaries, Quasars and Many Galactic Centers. These massive compact objects certainly cannot be Neutron Stars or various other Alternatives like Star Clusters or Fictitious Super Massive Stars of Hoyle & Fowler.
And definitely Padmanabhan, though a great scholar and prolific researcher, was in no position to face this challenge. In fact his two initial papers 1 & 2, though profound and EXACT, are rarely cited. On the other hand, his latter papers affirming his faith in the Black Hole Paradigm like a Neo-Convert got thousands of citations. Thanu is a bright researcher of course aspired to be not only a mainstream author but a sort of world leader, a Big Boss, in Gravitation Research. And this is possible only for a convert and not for someone who could be dubbed as a Crank or Heretic for being idiotic enough to challenge the holy scripture. A logical course of the initial phase of the Padamanabhan research could have been an attempt to show that the crucial assumption of “Trapped Surfaces” of Hawking & Penrose were incorrect. But such a research would immediately make him cross swords with Penrose, Hawking and all “leaders” one can conceive of. It would have also led him to challenge the idea of a “Black Hole Thermodynamics” and put on conflict course with Bekenstein, t’Hooft and who not?
Then let alone generous citation of his papers, they might not have been accepted in the first place, alteast in journals like PRD, PRL, CQG etc. May be despite his enormous talent, he would have been considered as a pariah with no entry to Blue Blood clubs. May be, no student would be ready to get associated with such iconoclastic research in order to protect their academic futures. May be, he would not have become “Distinguished Professor” and the would be Director of IUCAA. Such possibilities are actually endless…
Incidentally, the fact that, continued GR collapse does not allow “Trapped Surfaces” in order that matter like trajectories of the elements of a collapsing star do not become lightlike was proved by the present author:
27. “Quantum information paradox: Real or fictitious?”: A. Mitra, Pramana, vol. 73, pp. 615-622 (2009); (arXiv:0911.3518)
His books taught everywhere are silent on the conceptual difficulties of black holes, his discussions on Gravitational Collapse do not go beyond the idealized pressure-less collapse model of 1939 by Oppenheimer & Snyder about which my take is the following:
28. “The fallacy of Oppenheimer Snyder collapse: no general relativistic collapse at all, no black hole, no physical singularity”: A. Mitra, Astrophysics and Space Science, Volume 332, pp.43-48 (2011)
He is leading researcher in Gravity; but his real uniqueness lies elsewhere: He is the only researcher in the world who hides in own research, appears to be mortally afraid of citing his own papers 1 & 2 which challenge the BH paradigm.
This is so when these two papers are scientifically correct because (i) the blowing up of g(E) at the EH is an EXACT & CORRECT result, (ii) EHs are indeed physical singularities and correspond to the central singularity because M=0 for BHs. Can QG qualitatively change these conclusions? It should not because Quantum Green’s Function blows up at the Event Horizon, which again can be traced to metric singularity of the Schwarzschild metric there.
28. “Quantum Field Theory in Schwarzschild And Rindler Spaces”: D. Boulware, Phy. Rev. D11, 1404 (1975).
However, one may try to hide such singular behaviors by fudging the physics, by using the jargon of “near horizon” behavior, and by avoiding the EH. Even then most of the contributions of the relevant integrals naturally come from this “near horizon”. And then one can pretend that physics of the 3-D BH interior is encoded in the 2-D EH… then holography and justification of the most speculative hypothesis of BH Theromodynamics, Hawking Radiation can also follow. Of course, once on this glorious track, acceptance of the manuscript is guaranteed in any leading journal.
Incidentally, my prediction that the so-called BH candidates are ultramagnetized ECOs (MECOs) rather than true BHs have inspired several astrophysicists and here is a 2006 Center for Astrophysics, Harvard, press release to this effect:
One may partly appreciate this key to success of Padmanabhan research by recalling that post modern theoretical research, particularly, in the topics involving may not be about physical realities at all:
In their book A Different Approach to Cosmology, Fred Hoyle, Geoffrey Burbidge and Jayant Narlikar used the photo given below to illustrate the conformist approach to standard big-bang cosmology. ‘We have resisted the temptation to name some of the leading geese,’ they say. May be the same photo help explain the enormous success of the research career of Thanu Padmanabhan: