Prof. Jayant Narlikar is a highly respected and noted cosmologist. He was closely associated with one of the greatest astrophysicists, namely, Prof. Sir Fred Hoyle who many believe should have got the Nobel Prize in physics. Prof. Narlikar is the founder Director of Inter University Centre for Astronomy & Astrophysics, a world renowned institute. And Prof. Narlikar is best known for Quasi Steady State cosmology. Similarly Prof. Thanu Padmabhan of IUCAA is a world renowned scholar in the area of gravitation & cosmology. And here I shall highlight the paper

**“The Schwarzschild Solution:Some Conceptual Difficulties’**‘ by J.V. Narlikar & T. Padmanabhan published in *Foundations of Physics, Vol. 18, pp.659-668 (1988)*

http://adsabs.harvard.edu/abs/1988FoPh…18..659N

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ABSTRACT:

“*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*.”

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This paper was submitted on April 27, 1987, and got published in June 1988. And this delay indicates that, despite the academic stature of Prof. Narlikar, the referee may not have promptly accepted this manuscript. In those days, the editor of Foundations of Phys. was Prof. Alwyn van Merwe who was a very fair and liberal editor quite unlike any editor of any mainstream journal of these days. Thanks to the wisdom of Prof. Merwe that he allowed publication of this very interesting and important paper.

Having made this introduction, I shall just paste excerpts from this paper which would convince anybody that Narlikar & Padmanabhan (NP) thought, and correctly argued that, finite mass black hole solution is unphysical and black hole formation should preferably be avoided in continued gravitational collapse:

“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.”

As is well known, the Schwarzschild black hole solution begins with a **Point Particle** at r=0. And, by studying this solution in the *finite point mass limit, *in pp. 663, NP comment:

“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

comoving time.”

The latter comment by them that gravitational collapse must lead to a point singularity in a finite comoving time is actually based on the *dust solutions which ignore all pressure, radiation, heat flow etc. *

The SECTION 3 of their paper is titled as

**“ARE BLACK HOLES RELEVANT TO PHYSICS?”**

And then it elaborates,

“Black holes are generally believed to have formed by gravitational collapse of massive bodies. In a strict sense what is a black hole (BH)? It is an object surrounded by an event horizon. By contrast we may call an object a quasi-black hole (QBH) if it is highly collapsed and very dim but still outside its event horizon. It is well known that as an object collapses toward its event horizon the intensity of its radiation as received by an external Schwarzschild observer (with trajectory r=const) rapidly falls.

Thus a QBH will be invisible for all practical purposes although still outside the event horizon. Most astrophysical scenarios using black holes are concerned with QBH’s only. However, the laws of black hole physics apply to BHs, as does the notion of an evaporating BH. Our question is: *are the BH phenomena really relevant to physics*?

It is agreed that for a scientific hypothesis to be taken seriously,* it must be testable*–if not in practice (owing to limitations of technology available) at least in principle. So far as a BH is concerned, it is supposed to come into existence only when its outer surface enters the event horizon…..

For the detection of any object by whatever means, it must come within the observer’s past light cone. This does not ever happen for a BH. So none of the laws describing the behavior of BHs (as opposed to the QBHs) are in principle detectable or testable by the class of observers who stay outside their event horizons. Since most observers (including those on the Earth) are of this type, to them the** BH’s are not relevant as physical objects**.”

They correctly emphasize that the 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. In SECTION 4, they concluded:

“In other words, no observers in the Schwarzschild metric (whether they stay outside or inside the Event Horizon choose to fall inside) will ever be able to observe either the formation or the physical effects of a singularity at r = 0. We leave it to the reader to decide whether a singularity that can never be observed and that can never affect any physical process **“exists” in any sense of the word**.”

“To interpret the Schwarzschild solution as the metric produced by the point particle, one has to satisfy two conditions: (i) Einstein’s equations, with a point mass as the source, located at the origin, have to be satisfied by the metric and (ii) the source particle should follow a timelike trajectory. In Section 2 we pointed out that condition (i) is **violated** in the Schwarzschild metric. It is now clear that condition (ii) is **also violated in any collapse that leads to a point source**.”

Clearly, therefore, realistic gravitational collapse should not lead to the formation of a point singularity. However, being **misled** by the Oppenheimer Snyder dust collapse picture, NP, at the same time thought, normal gravitational collapse should lead to a point singularity/black hole. It may be relevant here to mention that, in 2011, I categorically showed that the example of “Dust Collapse” is misleading, it is an illusion. In reality a dust has zero density (i.e., it does not exist physically), and dust collapse does not lead to any singularity/black hole

“**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)

http://adsabs.harvard.edu/abs/2011Ap%26SS.332…43M

However NP were not aware of this, and their intellectual dilemma was more acute: To put the physical as well as mathematical inconsistency in the BH paradigm, defenders argue that, inside the Event Horizon,* distance becomes time & time becomes distance. By analyzing such proposals, NP concluded:*

“We therefore find that considering observers inside the event horizon makes the problems of interpretation even more difficult, and we wonder **whether nature allows gravitational collapse to continue inside the event horizon at all**.”

In the concluding section, NP demanded

“Those who believe that black holes (and not just the quasi-black holes) have physical relevance should produce a thought experiment to demonstrate to an

external observer that a black hole (and not a QBH) has formed in a given region.”

“We have no solution to offer for this difficulty nor do we believe that one exists within the conventional classical framework. These problems can be avoided by

introducing negative energy or stresses to reverse the gravitational collapse before the event horizon is formed.”

**But how can matter with positive pressure suddenly develop negative pressure or negative energy? **

And clearly, here, they forgot the famous quote by **Sir Arthur Stanley Eddington:**

“The star has to go on radiating and radiating and contracting and contracting until, I suppose, it gets down to a few km radius,** when gravity becomes strong enough to hold in the radiation**, and the star can at last find peace. … I think there should be a law of Nature to prevent a star from behaving in this absurd way!”

And in 2006-10, I along with Norman Glendenning showed that Eddington’s intuition was was correct: As the contracting object would plunge within its **photon sphere**, *gravity becomes strong enough to hold in the radiation, and *sooner or later, the outward radiation pressure would arrest the catastrophic collapse of the star:

1. “A generic relation between baryonic and radiative energy densities of stars”

A. Mitra, Monthly Notices of the Royal Astronomical Society: Letters, Volume 367, Issue 1, pp. L66-L68 (2006); http://adsabs.harvard.edu/abs/2006MNRAS.367L..66M

2. “Radiation pressure supported stars in Einstein gravity: Eternally Collapsing Objects”

A. Mitra, Monthly Notices of the Royal Astronomical Society, Volume 369, Issue 1, pp. 492-496 (2006); http://adsabs.harvard.edu/abs/2006MNRAS.369..492M

3. “Likely formation of general relativistic radiation pressure supported stars or `eternally collapsing objects”’

A. Mitra, Monthly Notices of the Royal Astronomical Society: Letters, Volume 404, Issue 1, pp. L50-L54 (2010); http://adsabs.harvard.edu/abs/2010MNRAS.404L..50M

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And this was not enough. The popular idea that continued collapse must give rise to singularity is based on the “Singularity Theorems” of Hawking, Penrose & others. This theorem **presumes** that during continued collapse, a surface of no-return, “Trapped Surfaces” should form. In turn, this **presumption** is based on the idea of pressureless “Dust Collapse”. And in full generality, I showed that this *presumption is not realized:*

“Quantum Information Paradox: Real or Fictitious?’ A. Mitra, Pramana, 73:615, (2009) http://www.ias.ac.in/pramana/v73/p615/fulltext.pdf

And this proof demands that any point singularity that may be assumed to be formed (in a mathematical sense) must have zero gravitational mass: M=0.

This means that while an extended object like the Earth, Sun, or galaxy must indeed have finite gravitational mass, *their mass must shrink to zero if they would be assumed to shrink to a point.*

And this consequence was also **independently **proved by me in the same year:

“Comments on “The Euclidean gravitational action as black hole entropy, singularities, and space-time voids”

A. Mitra, Journal of Mathematical Physics, Volume 50, Issue 4, pp. 042502-042502-3 (2009). http://adsabs.harvard.edu/abs/2009JMP….50d2502M

Thus the physical and mathematical conundrum experienced by Einstein, Dirac, Eddington, Hoyle, Rosen as well as by Narlikar and Padmanabhan (any many more) got completely resolved by work.

Finally Narlikar & Padmabhan were correct: General Relativity does not allow true Black Holes; on the other hand, it may permit only “Quasi Black Holes” whose practical form could be the `Eternally Collapsing Objects”.