A Magnetospheric Eternally Collapsing Object
is a proposed alternative to a black hole
. In essence, this theory states that massive objects that suffer gravitational collapse
never actually form black holes since the build up of gravitationally trapped radiation pressure
slows the collapse to a very small rate when the object becomes sufficiently compact (see Eddington luminosity
). The main differences between MECO's and black holes lies in the fact that a MECO has a distantly observable intrinsic magnetic field, while emitting Eddington limited radiation from a highly redshifted surface which makes this "glow" from the MECO surface difficult to observe (black holes can't have magnetic fields and emit only weak Hawking radiation
). Recent evidence of intrinsic magnetic fields inside of what are thought to be super-massive black holes
in the centers of some quasars has brought attention to the possibility that they may actually contain MECOs.
History Of the ECO
The term Eternally Collapsing Object
(ECO) was first coined by astrophysicist Abhas Mitra
in 1998. He suggested the possibility that black hole candidates might actually be quasistatic ultra compact objects, called ECOs, that are asymptotically approaching a true black hole state with zero mass. He also suggested the possibility that under certain conditions ECOs may also possess intrinsic magnetic fields whose value could be modest (in extragalactic cases) or extremely high (in stellar mass ECOs). In contrast, the intrinsic magnetic field of black holes is zero. The current observation of magnetic field around the black hole candidates are commonly attributed to the accretion disk around the black hole. On the other hand, intrinsically magnetic ECOs might be identified as objects different from black holes by virtue of the existence of their intrinsic magnetic fields. Although Mitra did not further quantitatively develop the idea of intrinsically magnetized ECOs, he continued to make reference to the possibility of their existence in later papers preprints and papers,. Mitra also claimed that the beamed emission from the Gamma Ray Bursts
could be better understood if they are associated with birth of highly magnetized ECOs rather than non-magnetized black holes. The essential idea was that the non-singular ECOs are something like the Relativistic
version of Neutron Stars
Basic generic theory
The basic underlying concept of an "ECO" is a model independent generic result.
Strength of gravity
around a compact object or any object may be expressed by the observed surface gravitational redshift
. For the Sun, one has,
. For a neutron star
which is usually considered as one of the best examples of a relativistic compact object, one has
≈0.1–0.2. But the Event Horizon
of a Schwarzschild black hole
=∞. Thus compared to an event horizon, all other known objects practically have
≈0. Hence, during continued gravitational collapse, the collapsing object has to traverse an infinite distance in the
-space, starting from
=∞, in order to become a black hole.
It is known that, in strong gravity, i.e., for large
, many important general relativistic
effects must occur. For instance, it is known that, in strong gravity, photons
(not to talk of massive particles) move in curved paths. The corresponding angle of deviation from a rectilinear path is given by
≪1, and this result constituted the historical verification of GR by Eddington
Further, it is also known that realistic collapse of gravitational collapse must heat up the collapsing object and it must radiate out part of the energy gain due to release of gravitational energy during collapse. In the context of general relativity, this assertion has been made only in 2006.
Thus the quanta of "heat" i.e., photons and neutrinos generated within the collapsing object must move in increasingly curved trajectories as the continued collapse would proceed towards the
=∞ Black Hole stage. As a result they would increasingly fail to move out of the compact object due to its increasing self-gravity. In other words, the collapse generated radiation would tend to get trapped by self-gravity. This process of pure self-gravitational trapping during continued collapse has recently been elaborated..
It has been shown here that the energy density of the gravity trapped radiation would increase dramatically as
as the collapsing body would attain
≫1 during continued collapse. Since by definition, a black hole event horizon is marked by
=∞, the trapped radiation density would tend to increase unabated until collapse process would be halted. This halting would occur when the luminosity of the trapped radiation would attain the corresponding Eddington Luminosity
at an appropriately high value of
. It must be so because the very definition of an Eddington Luminosity implies
- The outward PUSH due to radiation = Inward PULL due to gravity …(1)
In other words, sooner or later, at a sufficiently high
, the catastrophic collapse must be halted by the outward trapped radiation pressure and the object must become a quasi-static Radiation Pressure Supported Star (RPSS).
And this is how ECOs are inevitably born in realistic continued gravitational collapse. In general, it has been shown that when the luminous compact object becomes extremely relativistic, it must become HOT and radiation dominated
like the very early Universe unlike the matter dominated
universe we know of.
- = Radiation Energy Density; = Rest Mass Energy Density
It is most interesting to note that the local mean temperature of such an extremely relativistic RPSS, i.e., an ECO is uniquely determined, by virtue of Eq.(2), by its mass alone:
- T = 600 MeV (M/Msolar)-1/2 …(3)
is the mass of the Sun
Enter The MECO
Quantitative observational and theoretical arguments supporting the existence of intrisically magnetized Eternally Collapsing Objects which contained strong intrinsic equipartition magnetic field in lieu of an event horizon were first given in a series of seminal papers published by two American astrophysicists Darryl Leiter and Stanley Robertson, the first of which was published in 2002. In this context, it was natural to add the term "Magnetospheric" to ECO to make it MECO, as was done by Darryl Leiter, Abhas Mitra and Stanley Robertson in 2001. However Mitra withdrew his name from a subsequent revised version of the Leiter and Robertson paper because he felt that the MECO picture was a special case of the more general ECO concept, which should have no crucial assumptions and thus be model independent. Nonetheless Leiter & Robertson were keen to make a specific model of MECO in order to be able to immediately apply it to astrophysical observations, and their paper bearing the same title was subsequently published.. Robertson and Leiter elaborated on this aspect by using the idea of disk-magnetospheric interaction. Further, by invoking the well known "magnetic propeller" mechanism, they offered a novel explanation for a hitherto unexplained universal correlation between observed radio and X-ray luminosities in black hole candidates.. In the final analysis the papers of Darryl Leiter and Stanley Robertson discussed above were the first to offer observational and theoretical evidence, based General Relativity and The Strong Principle of Equivalence, that MECOs could exist in the Universe and that black hole candidates actually contained MECOs instead of Black Holes.
Evidence of MECO Implied by the Strong Principle of Equivalence
In general relativity, preservation of the strong principle of equivalence (SPOE) requires that special relativity must hold locally for all time-like observers in all of spacetime. On this basis Darryl Leiter and Stanley Robertson argued that existence of MECO is implied by the idea that Nature requires that the SPOE must be dynamically preserved everywhere in spacetime for the timelike world lines of massive particles or fluids under the influence of both gravitational and non-gravitational forces. Preservation of the SPOE requires that the frame of reference of the co-moving observer in the massive collapsing fluid must always be connected to the frame of reference of a stationary observer by special relativistic transformations with a physical 3-speed that is less than the speed of light .
Since the left-hand side of the Einstein equation cannot by itself dynamically enforce the preservation of the SPOE, it follows that for collapsing objects there must exist SPOE-preserving non-gravitational processes in nature which must always be included in the energy–momentum tensor on the right-hand side of the Einstein equation. It was in this manner that the general relativistic MECO solutions to the Einstein-Maxwell equations were discovered, as was shown in the papers and developed in more detail in some subsequent papers . There it was shown that for a collapsing body, the structure and radiation transfer properties of the energy–momentum tensor on the right-hand side of the Einstein field equations, could describe a collapsing radiating object which contained equipartition magnetic fields that generated a highly red-shifted Eddington limited secular collapse process. This collapse process was shown to preserve the SPOE by dynamically preventing trapped surfaces, that lead to event horizons, from forming. In one of the research, it was shown that, by using the Einstein–Maxwell equations and quantum electrodynamics in the context of general relativistic plasma astrophysics, it was possible to virtually stop and maintain a slow (many Hubble times!), steady collapse of a compact physical plasma object outside of its Schwarzschild radius. The non-gravitational force was Compton photon pressure generated by synchrotron radiation from an intrinsic equipartition magnetic dipole field contained within the compact object. The rate of collapse is controlled by radiation at the local Eddington limit, but from a highly red shifted surface with an extremely small photon escape cone. In this paper, it was shown that the equatorial poloidal magnetic field, associated with a locally Eddington limited secular rate of collapse of the exterior surface, was strong enough to spontaneously create bound electron-positron pairs in the surface plasma of the MECO which contribute to the general relativistic surface drift currents, within the pair dominated plasma at the MECO surface. These electron-positron drift currents on the MECO surface generate the magnetic fields which create the MECO’s distantly observed intrinsic magnetic moment. Within the context of the MECO’s Eddington limited secular balance, the action of this QED pair production process was shown to be sufficient to stabilize the collapse rate of the MECO surface. For the collapsing, radiating pair dominated plasma associated with the MECO, the corresponding exterior solution to the Einstein equation is described by the time dependent Vaidya metric, where no coordinate transformation between MECO Vaidya metric and the black hole Kerr–Schild metric exists.
Since the highly red shifted Eddington limited MECO Vaidya metric solutions preserve the SPOE, they do not have event horizons and the MECO exhibit distantly observed slowly rotating intrinsic magnetic dipole moments which can interact with their surrounding accretion disk environments. Hence, if supermassive MECO exist in the centers of AGN and Quasars, they should be able to observationally reveal themselves in a manner which distinguishes them
from that of central supermassive Black Holes.
Evolution of a MECO
The total mass energy of a MECO (or anything) is
and it is losing energy as per Eq.(4). Then it follows that, its observed time-scale at a given
- t(observed) = E/L ~ 4×108 (1+z) yr …(8)
This time scale has recently been termed as "Einstein-Eddington" time scale.
As the MECO evolves to approach
- t(observed) → …(9)
This explains the rationale behind the phrase "Eternally Collapsing Object". During this infinite journey towards the true black hole state, a MECO burns
its entire mass
into energy/radiation and hence the eventual black hole has M=0. In fact, this profound result has been obtained in a most straight forward manner by using the basic fact of Differential geometry
that the Proper 4-volume
associated with a black hole (or anything) is independent of the coordinates used to measure it. Recall that the Schwarzschild solution corresponds to the spacetime structure for a "Point Mass" or a "Massenpunkt". And it was shown long ago that even if there would be "Bare Mass" Mb
for a point particle, the "Clothed Mass" obtained after accounting for the negative self-gravitational interactions is zero for a "Neutral Point Particle".
Thus it is natural that the gravitational mass of a neutral Schwarzschild black hole, i.e., a neutral massenpunkt is just zero. Hence any object with finite mass, M
>0, cannot be a Schwarzschild black hole. In particular, the observed black hole candidates with masses much higher than the Chandrasekhar mass limit
, are least likely to be true black holes.
In reality, it would take not only infinite observed time but also infinite co-moving proper time to attain this ultimate state indicated by the vacuum Schwarzschild solution of a Massenpunkt
. To appreciate this, recall that the co-moving proper time of black hole formation in the Oppenheimer-Snyder Dust
- t ~ M-½ …(10)
so that, t
→ ∞ as M
→ 0. Thus the asymptotic (true) black hole state is never ever formed. And the MECOs with
≫1, in many ways, mimic this idealized asymptotic black hole state.
Since the MECOs are radiation-supported hot objects, the Chandrasekhar Mass Upper limit has no relevance for them. This limit is applicable only to cold objects supported either by cold quantum degeneracy pressure
or ordinary kinetic gas pressure.
Oppenheimer Snyder Collapse
In 1939, Oppenheimer and Snyder indeed exactly solved the general relativitity spherical collapse equations. And it is this exact solution which consolidated the idea of (finite mass) black holes apparently suggested by the static vacuum Schwarzschild solution in 1916. But it has generally been ignored that the Oppenheimer and Snyder "exact solution" was obtained at an enormous physics cost:
They were bound to completely ignore pressure, p=0, for the fluid. Consequently, there is no internal energy (e=0) and heat flux (q=0) for the Oppenheimer & Snyder idealized fluid termed as "Dust".
In contrast, for physical gravitational collapse, the radiation density and heat flux must increase dramatically much before any event horizon would form (cf. Eq.2):
Thus not only the Oppenheimer and Snyder Dust collapse, but all adiabatic collapse, in reality means no collapse because there cannot be any collapse without radiation. On the other hand, if one would insist for a collapse on the strength of only mathematics, the corresponding density of the fluid is
- ! .... (11)
For a pressureless "Dust", this result can also be obtained from simplest thermodynamical considerations too. The pressure of a fluid, including localized quantum degeneracy pressure, arises because of internal random motion of the fluid particles either on a macroscopic scale or on localized microscopic scale. And thus pressure can be absent, p=0, only when either
- There is no fluid : or,
- The fluid has no motion, i.e., it is at zero temperature.
In realistic cases, a fluid at T=0 (a perfectly degenerate case) would be already at a lowest thermodynamical state and cannot contract further. Thus if "collapse" would be still be feigned, one must have . In such a case, the mass of the fluid ball would be
- M= 0 ..(12)
Thus all the black holes mathematically generated in the Oppenheimer Snyder collapse or Adiabatic Collapse or any collapse that ignores the fact that ρr
>>1, corresponds to zero gravitational mass. To recall, the standard GR collapse and the black hole paradigm assumes that once the collapse would cross the neutron star stage with z
≈0.1, it would directly proceed to the infinitely far away
black hole stage in a flash (free fall time scale)!
Relevant radiative processes
One may also wonder what generates the luminosity of an ECO? Is it nuclear fuel or something else?
It is definitely not because of any nuclear fuel. Recall that cold Giant Molecular Cloud
with an initial temperature of T
≈ 10 K contract to make extremely hot pre-main sequence stars. This heating during the preceding gravitational collapse is certainly not due to burning of any nuclear fuel. The key to the understanding of this physical phenomenon is again virial theorem :
dictates that the fluid must become hotter during collapse. Although the MECO is quasi-static, in the strictest sense, it is always undergoing secular contraction. And it is this secular contraction which is generating fresh internal energy and radiation by the virtue of the E=Mc² formula.
But how does the fluid actually become hot?
The fluid becomes hot because of various radiative processes like Bremsstrahlung
, Compton Scattering
Process and other inherent Radiative processes
. All that is required here is that the fluid must be ionized. In addition, in order to have the synchrotron process, there must be an internal magnetic field and which is always the case. In fact, in the ultimate microphysical analysis, all energy generation by either nuclear or chemical means can be seen to be mediated by such basic radiative processes. At sufficiently high temperature and densities matter can directly burn mass
to form "energy" because of increased rate of such microphysical processes and by virtue of the E
² formula. In contrast, for a contracting cold molecular cloud, the energy release is mediated by interaction between various molecular energy levels which is a very inefficient process. Further since in strong gravitational field, charged particles moving in curved trajectories, they emit gravitational radiation due to Gravitational Bremsstrahlung
and Gravitational Synchrotron
Comparison with true black holes
A true black hole has an event horizon
=∞. In contrast, a MECO, the "intermediate state", has a finite but large
≫1 and as it becomes more and more compact during continued collapse, in principle, its
→∞. While a true black hole has a radius
, the Schwarzschild radius
, a MECO has practically the same radius because its
By definition, a MECO is radiating at its Eddington rate, which is the maximal luminosity. However, because of joint effect of gravitational redshift
(of emitted quanta) and gravitational time dilation
(slower ticking of clocks in stronger gravity), the observed luminosity of an ECO is
- L(observed) = 1.26×1038 (1+z)-1 (M/Msolar) erg/s …(4)
during one of these intermediate states. Then we will have
- L(observed) ~ 1031 erg/s …(5)
for a 10 Msolar
MECO. Note that the corresponding Eddington luminosity of a Neutron Star
would have been
- L (observed, Newtonian) ~ 1039 erg/s …(6)
which would be larger by a factor of (1+z) ~ 108
Thus unless the ECO would be very close by, it would be extremely difficult to detect this dim quiescent ECO luminosity. Therefore, observationally, it may be mistaken as a true black hole.
One can appreciate Eq.(4) by noting that a true event horizon with
=∞ would correspond to
- L (observed, event horizon) = 0 …(7)
This is another expression of the concept that "nothing can escape the event horizon". Physically, the occurrence of an event horizon would correspond to an absolute trapping of light (
=∞). In contrast, the ECO is an intermediate state with
≫1 during the formation of this "absolute trapping".
The most important difference between a MECO and a true black hole is that the former is a dense ball of radiation supported plasma having a "physical surface" while the latter is the ultimate asymptotic singular state having no physical surface. Consequently, a MECO must possess strong intrinsic magnetic field like all other compact astrophysical plasmas while a non-spinning non-charged black hole has no intrinsic magnetic field.
Observational Evidence for The Existence of MECO In Radio Loud and Radio Quiet Quasars
Direct evidence to support the existence of MECO in quasars came in 2005 largely because of the efforts of the American astronomer Rudy Schild , .
"Schild monitored the quasar's brightness for 20 years, and led an international consortium of observers operating 14 telecopes to keep the object under steady around-the-clock watch at critical times.
The quasar Q0957+561 revealed its structure with very high resolution because of gravitational microlensing by the stars of an intervening galaxy along its line of sight. This structure has broad similarity with the one expected from a magnetized neutron star endowed with an accretion disc.
In their recently published paper in Astronomical Journal R. E. Schild, D. Leiter, and S. Robertson further elaborated on the fact that the object at the heart of the radio loud quasar Q0957+561 is not a supermassive black hole, as is currently believed to be the case for all quasars. Schild and his team at the Harvard-Smithsonian Center for Astrophysics found that the jets originated 8000 AU from the poles of the centre, in a region 1000 AU across. In addition they found that the accretion disc in this quasar appeared to be truncated at 2000 AU from the centre, and the inner edge surrounding the apparently empty inner region of the disc contained a very thin annular region that was found to be intensely radiating. There also appeared to be a broad conic wind outflow from the accretion disc which created a luminous Broad Line Emission Region Elvis structure (cf. Martin Elvis). On the basis of these observations they came to the conclusion that ''"This quasar appears to be dynamically dominated by an intrinsic magnetic field which is internally anchored to its central, rotating supermassive compact object".
In "radio loud" quasars, which make up about 10% of the total quasar populations,
some of that gas is forcefully ejected outward in two opposing jets at
nearly the speed of light. On the other hand the remaining 90% of the
quasars do not exhibit any jet structure and for that reason are "radio
quiet". In order to better understand the difference between the two
types of quasars, theorists struggle to understand the physics of the
accretion disk and jets, while observers struggle to peer into the
quasar's heart. However the manner in which the "central engine" is
able to turn on radio emitting jet structures in radio loud quasars,
while also being able to turn off the radio emitting jet structure
in radio quiet quasars, is difficult problem for both theorists and
observers because the central regions of quasars are so compact and the
quasars so far away from Earth.
Using newly developed optical telescope techniques involving gravitational
micro-lensing and reverberation analysis, Rudy Schild and his colleagues
have also studied the internal structure of the radio quiet quasar Q2237
(known as the Einstein Cross), as well as the radio loud quasar Q0957+561(known
as the Twin Quasar) both of which are located more than 9 billion light-years from
Earth. These two quasars, which are in distinctly different spectral states,
have been observed to have central compact objects containing masses on the
order of 3-4 billion Suns. For this reason most astrophysicists would consider
the central objects in these two quasars to be "black holes," but Schild, Leiter,
and Robertson's research has suggested otherwise. "We don't call the central
objects in these quasars black holes because our observations indicate that
these two quasars have central compact objects which contain internally anchored
magnetic fields that are able to penetrate through the surface of their
collapsed central objects and interact with the quasars accretion disk
and its environment," they commented.
The researchers chose Q0957 and Q2237 because of their association with
natural cosmic lenses. The gravity of nearby galaxies bends space,
forming multiple images of the distant quasars and magnifying their
light. Stars and planets within nearby galaxies can also affect the
quasars light, causing small fluctuations in brightness (in a process
called "micro-lensing") when they drift into the line of sight between
Earth and the quasars.
Using this micro-lensing-reverberation technique on the radio loud
quasar Q0957 Schild monitored the quasar's brightness for a period of
20 years, and led an international consortium of observers operating 14
telescopes to keep the object under steady around-the-clock watch at
critical times. "With micro-lensing, we were able to discern more
detail about the so-called 'black hole' in this quasar which is two-
thirds of the way to the edge of the visible universe than we can from
the black hole at the center of the Milky Way," said Schild. Through
careful analysis, the team teased out details about the inner structure
of this quasar For example, their calculations pinpointed the location
where the jets form. "How when and where do these jets form? Even after
60 years of radio observations, we had no answer. Now the evidence is
in, and we know," said Schild.
Schild, Leiter, and Robertson found that the jets in the radio loud quasar
Q0957 appear to emerge from two regions 1,000 AU in
size (about 25 times larger than the Pluto-Sun distance) located 8,000 AU directly above the poles of the central compact object. (An astronomical unit/AU is defined as the average distance from the Earth to the Sun, or 93 million miles). However, that location
would be expected only if the jets were powered by reconnecting
magnetic field lines that were anchored to the rotating super massive
compact object within the quasar. By interacting with a surrounding
accretion disk, such spinning magnetic field lines spool up, winding
tighter and tighter until they explosively unite, reconnect and
break, releasing huge amounts of energy that power the jets. "This
quasar appears to be dynamically dominated by an intrinsic magnetic
field which is internally anchored to its central, rotating super
massive compact object," they stated.
The accretion flow in the equatorial plane is halted by the magnetic pressure of the central compact object and the inner radius of the disk is determined by the Alfven Radius. The accretion plasma flow then gets guided by the central dipole magnetic field towards the poles of the central magnetized compact object. During this process, the joint effect of spin and magnetic field may fling part of the accretion flow in an outward relativistic jet. Probably the fastest known astrophysical jet has a bulk Lorentz Factor of > 10, and it is associated with a X-ray binary Cir X-1 which contains a magnetized neutron star rather than a black hole candidate. This shows that presence of strong central magnetic field may be necessary to launch strong jets. There may be a wind outflow from the accretion disk itself. The magnetic push due to the central dipole field may also lend the wind an oppositely moving twin cusp-like structure. This "cusp like" picture may be compared with the "hour glass" picture of magnetic field structure recently observed in a collapsing magnetized Molecular cloud.
Thus, the observations of the accretion disc of this quasar made with the aid of a gravitational lens seem to indicate that Q0957+561 has a magnetic field, which a black hole cannot have. The researchers deduced the existence of a magnetic field from the fact that the accretion disk has a gap of 4000 AU around the central object. A small part of the disk just outside of the gap seems to be glowing, which is interpreted as being a sign that the material is heated by a strong magnetic field. Such a glow is also expected because most of the accretion power is released at the inner edge of the disk, truncated by the magnetic pressure of the central compact object. In contrast, for black hole accretion, even though, the inner edge of the disk formally lies at 3 Rs, where Rs is the Schwarzschild Radius, the flow is actually never truncated and, on the other hand, proceeds first to the event horizon and then, all the way up to the central singularity. The flow might get quasispherical in between and a glow is expected from region lying between the event horizon and the inner edge of the disk.
Since standard black hole models were found to be unable to explain the
observed internal structure seen in the quasar Q0957, Schild and his
colleagues, Darryl Leiter (Marwood Astrophysics Research Center and
currenty a visitor at the National Radio Astronomy Observatory in Charlottesville
Virginia) and Stanley Robertson (Southwestern Oklahoma State University), were led to
propose a revolutionary new general relativistic theory for the quasar
Q0957 in which the structure of the dominant magnetic field is intrinsic to the quasar's central, super massive compact object, rather
than only being part of the accretion disk as thought by most researchers. "Our finding challenges the accepted view of black holes," said Leiter. "We've even proposed a new name for them Magnetospheric Eternally Collapsing Objects, or MECO," a magnetic generalization of the
name coined in 1998 by Indian astrophysicist Abhas Mitra.
This research suggests that, in addition to its mass and spin, the
central compact object in Q0957 may have physical properties more like
a highly red shifted, spinning magnetic dipole than like a black hole.
According to this theory, a MECO does not have an event horizon, so any matter that is able to get by the magnetic propeller is gradually slowed down and stopped at the MECO's highly red shifted surface, with just a weak signal connecting the radiation from that matter to a distant observer. For this reason this signal has not been detected from Q0957 since it is very hard to observe.
Hence in [AstrJ, 135, pg 947 (2008)]Schild, Leiter, and Robertson were led to the conclusion that a simple and unified answer to the long-standing question: "Why are some quasars radio loud?" emerges naturally if the central objects of quasars are MECO, with radio-loud andradio-quiet states similar to the case of galactic black hole candidates.
The observed radiation from the MECO surface or interior would be extremely redshifted by a factor of (1 + z
) >>1. The observed magnetic field would be smaller approximately by the same factor. The corresponding redshift factor could also be (1 + zs
), where zs
is the redshift of the MECO "photosphere". At present we do not have any basic theory to predict the value of either z
for a MECO with a given mass M
. But despite such uncertainties, it is expected that the quiescent and extremely faint MECO thermal radiation could peak in the infrared, millimeter, microwave or radio band.
A very pertinent question here would be how can MECOs have z>> 1 when the Buchdahl inequality states that for a spherical object z
is bounded: z
<2. Recall that the Buchdadl inequality corresponds to absolutely cold objects, having no radiation, and whose external spacetime is determined by strictly static vacuum Schwarzschild Metric. In contrast, in a strict sense, an ECO/MECO is always contracting and radiating. The spacetime exterior to an ECO is thus given by the famous radiative and dynamic Vaidya Metric
rather than by non-radiating and static Schwarzschild metric. In such a case, the occurrence of z>>1 is allowed.
The existence of ECOs/MECOs is certainly not widely accepted at present.
But this is not necessarily because of any theoretical inconsistency or of any lack of observational evidence for ECOs. On the other hand, it could be so simply because the concept of a static black hole looks simpler and exact; and, also, four generations of astrophysicists and physicists have got used to working within the black hole paradigm. To appreciate this statement, note that a true observational signature of a black hole would be the detection of its event horizon. But neither has any event horizon ever been detected nor is it possible in principle. Also one faces innumerable puzzles and contradictions in the black hole paradigm due to presence of an infinite redshift event horizon. Yet, at present, most of the astrophysicists use the black hole paradigm because (i) of the existence of the unique and exact vacuum Schwarzschild solution, (ii) the existence of the unique and exact Oppenheimer - Snyder collapse solution. But we saw that such exact solutions actually correspond to a unique mass of the eventual black hole: M
=0. And a MECO is just the intermediate finite mass
state preceding this unique and ultimate zero mass
black hole state. Hence the concept of a MECO is really not in conflict with the mathematical idea
of a black hole. Far from it, it is an integral part of true black hole formation process because both the concepts involve the same physical ingredient of bending of light in strong gravity
Formation of a black hole event horizon may be seen as an extreme result of trapping of radiation by gravitation (z=
). But before this ultimate gravitational trapping state would occur, there must be initially minor and then gradually severe stages of light trapping. Thus there is no denying that the collapse generated quanta would tend to move within the fluid in almost closed circular orbits until they collide with electrons, pairs, protons etc. Even after collisions, the quanta would tend to move in almost closed orbits because of extreme self-gravity (z>> 1).
In fact, by using a perturbation technique, three relativists found that collapse of Newtonian Supermassive Stars would produce an ECO rather than a black hole.
From this view point a MECO theory never denies the fundamental importance of the exact vacuum Schwarzschild solution. But it relies on the fact that the value of the INTEGRATION CONSTANT a= 2M happens to be zero for a MASSENPUNKT (and not for an object with finite radius) as is also indicated by the classic ADM paper (cf. Ref. 18, 19). Thus a MECO is really not an "alternative" to black holes; far from it, it is the natural and necessary quasistatic state preceding a true black hole state. Without the MECO phase, i.e., without any radiation trapping, there would not be any black hole at all. It is a different matter that the eventual black hole state would have M=0 because the MECO would radiate away its entire mass energy during this infinite journey.
A MECO has properties of mass and spin, like a black hole
, but unlike a black hole, it has other physical properties that make it more like a highly redshifted spinning magnetic dipole
. Black holes do not have magnetic moments, so a MECO is expected to have a structure that can generate a magnetic field. MECOs do not have event horizons
. Instead, approaching a MECO, the rotating magnetic field would accelerate infalling material away, and any which do not get flipped away is gradually slowed down and stopped at or near the highly redshifted surface. This phenomenon allows only a very weak interaction between those within the grasp of the MECO and the outside universe.
One may also wonder how a star with an initial finite "radius"
can continue to contract indefinitely
howsoever slow the rate of contraction may be. In General Relativity
, the actual radius of the star measured locally is larger than
. Imagine a horizontal rubber membrance fixed across a flexible circular ring. The externally perceived "radius" of the star is akin to the radius of the peripheral ring,
while the internal radius of the star is the radius of the membrane
measured along its surface.
When there is no weight
on the membrane, it is "flat" and
. But now, suppose, a marble is placed on the membrane. Then the membrane will sag and its radius measured along its surface will be larger than the radius of the ring:
. At the same time, the ring will shrink a bit. The increasing grip of gravity during continued collapse may be simulated here by imagining that the weight
of the marble keeps on increasing indefinitely. If so, while on one hand,
, on the other hand, the ring would tend to shrink to a point,
. And since the membrane always sags with a finite speed (less than the speed of light) the process would continue eternally. Thus while externally perceived space may shrink towards a point, the gravity may stretch the internal space indefinitely. If the membrane represents the local space of a plasma, it will always have some intrinsic magnetic field. During the contraction, the value of this field, in a naive theory, would increase as
. Thus the star or anything else undergoing continued collapse may eventually become a MECO.
It is worth mentioning also, that MECO's are not a widely-accepted scientific concept.
- "Magnetospheric Eternally Collapsing Objects (MECOs): Likely New Class of Source of Cosmic Ray Particle Acceleration", A. Mitra, Proc. 29th Int. Cos. Ray Conf., Vol 3. pp.125-128 (2005),
- "The Magnetospheric Eternally Collapsing Object (MECO) Model of Galactic Black Hole Candidates and Active Galactic Nuclei", S.L. Robertson and D.J. Leiter, in "New Developments in Black Hole Research", ed. P.V. Kreitler (Nova Sc., NY, 2006), pp. 1-43, [ISBN 1-59454-641-X],
- "Sources of Stellar Energy, Einstein - Eddington Time Scale of Gravitational Contraction and Eternally Collapsing Objects", A. Mitra, New Astronomy, Vol. 12(2), pp.146-160 (2006)
- "Eternally Collapsing Objects or Black Holes: A Review of 90 Years of Misconceptions", A. Mitra, Invited Review Article in "Focus on Black Hole Research", ed. P.V. Kreitler (Nova Sc. NY, 2006), p. 1-94, [ISBN 1-59454-460-3]
- "Radiation Pressure Supported Stars in Einstein Gravity: Eternally Collapsing Objects", A. Mitra, Mon. Not. Roy. Astron. Soc., Vol. 369, pp. 492-496 (2006)