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Last year, I received an invitation from Elsevier for writing an article on my research for their Electronic Science Portal http://www.scitopics.com/. It is then that, I put up an article “Eternally Collapsing Object” in SciTopics. However, few days back, I received another email from Elsevier that they are going to wind up or rather lock up SciTopics, and the contributors would not be able to edit their articles after Oct. 31, 2011.

Then at the eleventh hour, I thought I would do some minor final updating for this article; but in hurry, I pressed the “delete” button, and it got lost for ever. I found that it had received more than 1100 hits in the past 18 months and got disappointed in not being able to retrieve it. Nonetheless, now I find that, the article is still available in google cache, though shorn off its link to SciTopics. -Here, I reproduce the body of this article from google cache:

—————ETERNALLY COLLAPSING OBJECT——————————–

An “Eternally Collapsing Object” (ECO) is a hot ball of ultra-compact self-gravitating plasma. It is so compact that even photons and neutrinos tend to move in closed circular orbits within it and find it extremely difficult to escape out of its gravitational clutch. The preceding compactification process renders it so hot that the associated radiation pressure (almost) counters the pull of self-gravity to help it remain in a quasi-static state. In a very strict sense, however, the object is always radiating and contracting at an infinitesimal rate and is striving to asymptotically attain the true Black Hole (BH) state. This is the reason behind the epithet “eternally collapsing”.

This degree of ultra-compactness of an ECO is expressed by the fact that its surface gravitational red-shift z »1. In contrast, the Sun has z ~ 2×10 ^-6, a typical White Dwarf has z~2x 10 ^-5 -10 ^-4 and a Neutron Star has z~ 0.15. On the other hand, a Schwarzschild/Hilbert Black Hole (BH) has z=∞ The radius of an ECO is practically equal to that of a supposed Black Hole of same mass: i.e., R=R _s=2GM/c ², the Schwarzschild/Hilbert radius.

In view of the fact that an ECO has z»1, to a far away observer, it resembles a BH in many respects and accordingly it is a proposed alternative to the concept of a `Black Hole’. Despite such apparent similarities with a BH, there are important differences between an ECO and a finite mass Black Hole:

1. All matter in a static Black Hole is believed to be concentrated in a point like central singularity where both density ρ=∞ and the tidal gravitational field or the Kretshmann scalar K=∞. Otherwise, the region of the BH extending up to the Event Horizon (R=R _s) is empty and without any matter or radiation. In contrast, as mentioned in the beginning, an ECO is filled with plasma and radiation. Further though both ρ and K could be very high for an ECO, they are finite and there is no physical singularity.

2. Also unlike a Black Hole, an ECO has a physical surface at R≈R _s. But unlike a Neutron Star, the ECO surface is soft rather than hard. Consequently matter falling onto an ECO just merges with the pre-existing plasma without generating much accretion luminosity or Type I X-ray bursts.

3. A neutral Black Hole has no intrinsic magnetic moment. In contrast, an ECO being an ultra-comprssed astrophysical plasma, must have strong intrinsic magnetic field. Accordingly, a spinning ECO behaves like an extremely relativistic pulsar though steep spacetime curvature around the ECO obliterates the intrinsic pulsations. A spinning ECO is likely to have a magnetosphere and is thus often mentioned as “Magnetospheric ECO” or “MECO”.

The term “ECO” was first coined by the Indian astrophysicist Abhas Mitra in 1998 though the idea of ECO got developed later. In particular, American astrophysicists Stanley Robertson, Darryl Leiter, Rudy Schild and Norman K. Glendenning too contributed to the developments of the idea of an ECO.

An ECO may also be considered as an extremely relativistic version of a Radiation Pressure Supported Star (RPSS) first conceived by Hoyle and Fowler in 1963. In 2006, Mitra showed that if one would allow the RPSSs to be extremely relativistic, i.e., z>>1, then radiation pressure supported stars are possible for arbitrary mass, high or low.

In 2010, Mitra and Glendenning showed that , during continued collapse, as a massive collapsing star would enter its photon sphere (z> √3 -1) in its attempt to form a true Black Hole with z=∞, it would start trapping its own radiation in a dramatic fashion as ~(1+z) ² . As a result, a stage will be arrived at an appropriate high z»1, where trapped radiation flux would attain its Eddington Value and the collapse would degenerate into an eternal quasistatic contraction.

This above mentioned concept of an ECO is based only on standard General Relativitstic ingredients such as radiation trapping & Vaidya metric and the astrophysical concept of an “Eddington Luminosity”. Since no new assumption/hypothesis is invoked at all, the concept of an ECO is no new theory, either mainstream or fringe!

However, this concept of an ECO got strengthened by the following later theoretical developments:

First, radiative gravitational collapse avoids trapped surface formation (Mitra 2009a), i.e., the ECO surface radius R(t)≥R _s(t) even though both R (t) and R _s(t) are shrinking ever. As a result an ECO always hovers just above its Schwarzschild/Hilbert radius and never plunges within the same.

Further there is an independent exact mathematical proof that the true Black Holes have necessarily zero gravitational mass (Mitra 2009b). This means that the so-called Black Hole candidates (or anything else with a finite mass) cannot be true Black Holes. Thus the concept of an ECO with z»1 and which is eternally contracting and radiating to attain a true Black Hole state having z=∞ and M=0 actually provides the missing link between the formation of a photon-sphere and a true Event Horizon. Note, the fact that M=0 for a true BH means that K~M ^-4 =∞ at the EH. And this resolves the century old mystery: why acceleration blows up at the EH and nothing can escape out of the EH.

In addition, it has also been shown recently that the Active Gravitational Mass Density of a quasistatic sphere decreases rather than increases with its pressure p; ρ _g = ρ-3p/c ² (Mitra2010). Therefore as an ECO would tend to become a perfect ball of radiation with p=(1/3)ρ c ²and z=∞, its ρ _g= ρ -3p/c ².→0, so that its gravitational mass M→0 in perfect accordance with the result that a true Black Hole has z=∞ and M=0.

Hence, contrary to the likely misinterpretation, the concept of an ECO is actually in perfect conformity with the exact solution for a Schwarzschild/Hilbert Black Hole.

The mean local temperature of an ECO is T≈600 MeV (M/M _solar) ^-1/2. This means that stellar mass ECOs are so hot that the neutrons and protons with it are in the molten Quark Gluon Plasma (QGP) state.

In fact Schild, Leiter and Robertson have already provided strong evidence that the central compact object s of the well studied quasars Q0957+561 and Q2237+0305 have strong intrinsic magnetic moment implying lthem to be ECOs rather than true Black Holes.

Preliminary numerical computations of Cuesta, Salim and Santos have indicated that the collapse of a Newtonian supermassive star is likely to form an ECO rather than a true Black Hole.

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