Eternally Collapsing Object (ECO) Explained 2019

Eternally Collapsing Object (ECO)

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.


Suppose a massive spherical star started collapsing due to its own weight. Then by Newtonian physics, sooner or later,  in a FINITE time, the entire star material should collapse to a geometrical point forming a SINGULARITY  where the density of matter and strength of / are infinite. It  must be so because in Newtonian physical space-time has an absolute meaning and the (initial)  actual/locally measured  radius of the star, say R0,  is Fixed &                                                                Finite:

In contrast, in Einstein’s “General Relativity” (GR),  in the presence of gravity, the actual interior or PROPER radius (L)  is always larger than the externally perceived radius (R); 

i.e., L =  a*R > R, because of a>1.  Furthermore, the value of   “a”  will always increase if the strength of self-gravity will increase; i.e., if the star would get more compact.  In fact, in strong gravity, similar stretching  (dilation)  happens for time intervals too.  

In this sense, in GR,  space-time is like a rubber membrane which gets stretched with the increase of gravity:

Therefore, there is no a-prior certainty that a Newtonian type singularity must occur for GR collapse. Despite this, even after the introduction of GR, most general relativists believe in essentially the same Newtonian picture of gravitational collapse by which collapsing matter must converge in a point-like singularity in a finite ( proper/ physically measured) time.  This is, unfortunately, the case though not only  Einstein himself but also many great physicists like.


Sir Arthur Eddington, the best theoretical astrophysicist ever, Sir Paul Dirac (Nobel Laureate), one of the finest theoretical physicists ever,







Nathan Rosen and many others argued that this picture must be incorrect and the star must not collapse beyond what is known as its “Schwarzschild Radius”:

Here G is the gravitational constant and c is the speed of the light. For a star
like the Sun,~3 km and for star ten times more massive, Rs ~30 km.
        In particular,  Dirac’s comment made in Proc. Royal Soc. (London) A        270, 354 (1962),  was:

“The mathematics can go beyond the Schwarzschild Radius and get inside, but I would maintain that this inside region is not 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”.

Such objections, however, got ignored because of two misleading mathematical developments, and effectively mathematics beat physics:

1.  In 1939, two American physicists J.R. Oppenheimer & H. Snyder APPARENTLY showed that for general relativistic collapse of a DUST (a fictitious form of matter having no pressure at all!), not only does the DUST collapse to a singularity but a Black Hole (BH) is formed whose imaginary surface lies at Rs  and nothing can escape from within this surface, now called, an Event Horizon .


2.  Further, in 1965, while studying generic gravitational collapse, Sir Roger Penrose, a highly regarded mathematical physicist, ASSUMED that for continued gravitational collapse, sooner or later, a one way trap – door will form, and once the collapsing matter would enter this trap-door it will be doomed to hurtle inwards  no matter how much powerful rocket it would employ  to escape . He essentially ASSUMED that at the advanced stages of collapse,  any section of the star having mass M and radius R must plunge within its running Schwarzschild radius: 
  
                                     R(t) =2 G M(t)/c2  ----------------- (1)

Obviously, this idea was a sort of generalization of the concept of the formation of an “Event Horizon” and got known as a “TRAPPED SURFACE”. Once this ASSUMPTION was made, then under reasonable physical conditions, the collapsing matter must again end up in a singularity, as intended. Ideally, Penrose should have proved the inevitability of the formation of a trapped surface. 

 But instead, he just ASSUMED the crucial Eq.(1)  which he was expected to prove or at least attempt to prove! Nevertheless, post-1965, most of the mathematical relativists adopted the same ASSUMPTION. If a singularity will indeed form, the space-time membrane, after the initial dip, would suddenly be pinched off and the stellar matter would  hit the  BOTTOM of the pit:

It appears that only one humble mathematical physicist Kriele offered proof that at least for a homogeneous sphere, there cannot be any trapped surface.




http://seminariomatematico.dm.unito.it/rendiconti/cartaceo/50-1/147.pdf

 Unfortunately, Kriele could publish his result only in an obscure journal and maybe sensing trouble, he himself NEVER cited his important result!
Given this backdrop, in 1998,  completely unaware of Kriele’s work,  I showed that spherical GR collapse cannot form “trapped surfaces”  irrespective of whether the sphere is homogeneous or not.  I  published my proof in a peer-reviewed journal first in 2000 [4] and in a broader context later [5,6].    Note, if a trapped surface did not exist, then in principle, collapsing matter could form.

(i) Quasi-static Objects (Chandrasekhar mass limit becomes irrelevant for very hot stars),

(ii) Rebound due to heat, radiation or pressure, or

(iii) Simply keep on contracting indefinitely!

As already mentioned, while the last option is absurd in Newtonian physics, it is not so in GR.  As gravity increases, the space-time membrane elongates/dips and forms a pit; a particle undergoing collapse has to slide down this membrane into the pit. And if indeed the strength of gravity would grow indefinitely  (a–> Infinity) during the continued collapse, then the
GRAVITATIONAL PIT TOO COULD BECOME ENDLESS & BOTTOMLESS
If so, continued gravitational collapse should indeed become ETERNAL without the formation of a true singularity.  Consequently, objects undergoing continued general relativistic collapse should end up as “Eternally Collapsing/Contracting Objects” rather than as Black Holes or “Naked Singularities” (Singularities not covered                                                      by any Event Horizon).

Later as  I interacted with several American astrophysicists like Darryl Leiter, Stanley Robertson [7] and Norman Glendenning, it became clear that as the contracting object would become hotter and hotter under gravitational compression, the Radiation Pressure would become so strong that it would almost counterbalance the inward pull of gravity. And it is in this way that ECOs conceived in 1998 could be realized in real life [8, 9, 10, 11, 12]. 
Thus ECOs are Extremely Hot and Relativistic Radiation Pressure Supported Stars

whose radius hovers just above the  INSTANTANEOUS “Schwarzschild Radius” as conceived by Einstein, Eddington, Dirac, Rosen and many other great physicists.


These quasi-static ECOs are however always radiating (unlike true black holes) and losing mass-energy by the E= Mc2 formula. Suppose as a given ECO radiates and it's mass decreases, it contracts by 1cm. But as it contracts, its gravity becomes a bit stronger and dips the rubber membrane of internal space maybe by 1.1 cm. Thus it becomes a hopeless unending chase for singularity.

Recall that the Acceleration Due to Gravity as measured by any static observer on the Event Horizon of a black hole is g=Infinity (limitless).

(And this is the reason,  why nothing can escape  from within the EH)
Similarly, gravitational red-shift of the EH, as seen by a distant observer too is infinite: z=Infinity (unbounded, limitless)

This means that, even if an extremely energetic gamma-ray photon would start its journey near the EH, its energy would reduce by a factor of (1+z) as it would reach the distant astronomer. And since z=∞, no energy would reach the astronomer, and he would see the EH as black.

In contrast, on the surface of an ECO, ” g’” and  “z” are extremely large, maybe thousands or even million times larger than the corresponding values for a Pulsar/Neutron Star which is supposed to be an extremely compact star (object). Accordingly, to a distant observer, an ECO appears almost as a “black hole” though it has a physical surface made of hot plasma (fire) unlike the fictitious mathematical surface of a black hole (Event Horizon).  As mentioned, it is the relentless heating due to extreme gravitational compression which makes the ECO essentially a “Ball of Fire”.

 - ABSOLUTE GROUND STATE OF COLLAPSE

In classical physics, an absolute ground  state is characterized by E=0 . So, if a star would really become “dead” and the “singularity” would be its “dead body”  or the absolute ground state, then the singularity too should have
           E=Mc2= 0; i.e.,  M=0::  Expected Mass of Singularity

Now recall that, the interior of an ASSUMED   (static) BH is swept clear of all matter/radiation because nothing can stay put inside its  ”trapped region”, and the “singularity” is the only source of matter/energy. Thus it is expected that a (neutral) BH may have unique mass M=0!  And indeed it was found that though the mathematical “black hole”  solution is a correct one, BHs nevertheless have unique gravitational mass
 M=0 [13, 14].

Note, in GR, an occurrence of M=0 need not mean the absence of matter! This is so because gravitational mass is the sum total of all sources of energy including the NEGATIVE self-gravitational energy. Thus, 
an occurrence of M=0 may imply that the (negative) self-gravitation has been so extreme that it has off-set the all other sources of energy like rest mass-energy of protons, neutrons constituting the star and all internal energies (heat, pressure etc).

And such proof confirms that the so-called BLACK HOLE CANDIDATES having huge masses cannot be true black holes.

In effect, the ECOs strive to become true mathematical black holes that have the unique mass M=0 [13]. However, an ECO never succeeds to attain this state. As an ECO continues to slide down the self-created pit, the pit gets deeper and deeper, i.e. the depth increases eternally :

Actually, near the singularity,” a” tends to blow up making interior radius L too blow up! Simultaneously, both “g” and “z” –> Infinity. Thus as if every sphere would internally be stretched to Infinity if self-gravitation would push them towards the gravitational singularity. Although such a scenario is weird, absurd from the point of view of Newtonian gravity,  it is plausible in GR;                                                                        as if all objects contain an                                                                             Infinity within themselves!


Note, in principle, one should solve Einstein’s equations analytically to see whether singularities are indeed formed or not. Unfortunately, even the infinitely simplified Newtonian collapse equations cannot be solved analytically (or numerically, without many simplified assumptions) because one does not know the exact equation of state of matter and radiation transportation properties at extremely high density and temperature. Thus, so far no-body has analytically solved Einstein’s equations for truly realistic cases (without making various assumptions) to show that singularities are formed! And the only way one can solve collapse equations analytically and without making convenient simplifications is by setting pressure=0! Of course, one must not hope that such an extremely unrealistic assumption would ever lead to a true physical picture.

In hindsight, Penrose overlooked that

(a)     Gravitational collapse must be radiative,  and the value of  M and Rs must keep on decreasing [15], and there is no fixed goal post which collapsing matter can target
(b)   Also, unlike what he ASSUMED, pressure always decreases effective gravity and continues to oppose collapse in general relativity as it does so in Newtonian gravity [16].

Effectively,  at least for a spherical case,  Penrose assumed the gravitational free-fall of the star by ignoring resistive effects like pressure gradient and radiation/ heat flow, etc.

In fact, what Roger Penrose,  John Wheeler, and many GR experts forgot was the intuitive comments by none other than Oppenheimer & Snyder THEMSELVES before they embarked on the idealistic, unrealistic computation about gravitational collapse:

“Physically such a singularity would mean that the expressions used for the energy-momentum tensor do not take into account some essential physical fact which would really smooth the singularity out. Further, a star in its early stages of development would not possess a singular density or pressure, it is impossible for a singularity to develop in a finite time.”

And maybe research works cited here have indeed substantiated the above comment made in 1939 by the persons who are (incorrectly) credited with proving the inevitability of formations of “Black Holes’’ and “Singularities’’ in GR!.

Incidentally, in 2011,  it was shown that even the apparent formation of “Trapped Surface” and “Black Hole” in Oppenheimer & Snyder Collapse was only a mathematical illusion and physically it does not correspond to any gravitational collapse at all as because when pressure is strictly zero, density too is zero, and there is no matter, no gravity [17]!

RADIATION PRESSURE SUPPORTED STARS (RPSS)

Most of the stars we know of, resist their gravity by means of gas pressure, i.e., the pressure due to electrons, ions and atoms. But, in the 1960s,   Sir Fred Hoyle, who many believe should have got the Nobel not once but twice,  and Nobel Laureate William Fowler  first pointed out that stars can be supported by radiation pressure alone if they would be sufficiently hot:

There is NO UPPER MASS LIMIT FOR RPSSs
They went on to suggest that QUASARS contain such hot RPSSs rather than true BHs. Similarly, ECOs too are hot RPSSs. But there are an important difference

The RPSSs conceived by Hoyle & Fowler were strictly static Newtonian stars (z <<1 1="" an="" and="" ascribed="" central="" efficiency="" energy="" generation="" having="" nbsp="" power="" source="" span="" their="" thermonuclear="" to="" was="">a la Sun; and the possibility of power generation by slow gravitational contraction was ignored.  Thus the RPSSs of Hoyle & Fowler were perceived to run out of nuclear fuel.
As the star contracts and becomes more compact, its negative gravitational potential energy becomes even more negative. Then, in order to conserve total energy, the star creates additional positive energy. Part of this positive energy makes the star even hotter, and the rest of it is radiated away, a process explained independently by Lord Kelvin &  Hermann von Helmholtz approx. 150 years ago:

The net  energy which can be tapped in this way is 100%:
E0=M0 c2 
the initial mass-energy of the star.  In this case, there is no need for invoking any specific fuel! Furthermore, ECOs are dynamic solutions and they are extremely relativistic with z>>1.

As the exterior radius of the contracting star R(t) shrinks, Rs = 2GM(t)/c2      too shrinks (very slowly)  because of loss of mass by radiation.  So as if there is a perennial chase R(t) –>Rs = 2GM(t) /c2 , and by the time R(t) would catch up with  Rs,  both would attain nil values as the final ground state must correspond to    E=Mc2 =0.  Yet, it is likely that
 L(t)= a(t) R(t)–>;∞, because of a(t) –>;∞  
infinitely fast!

0 comments

My Blog List

Welcome to Whole Universe Theory!