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We highlight here the fact that the distantly observed luminosity of a spherically symmetric compact star radiating thermal radiation isotropically is higher by a factor of $(1+z_{\rm b})^2$ compared to the corresponding flat space-time case, where $z_{\rm b}$ is the surface gravitational redshift of the compact star. In particular, we emphasize that if the thermal radiation is indeed emitted isotropically along the respective normal directions at each point, this factor of increment $(1+z_{\rm b})^2$ remains unchanged even if the compact object would lie within its {\em photon sphere}. Since a canonical neutron star has $z_{\rm b} \approx 0.1$, the actual X-ray luminosity from the neutron star surface could be $\sim 20 \%$ higher than what would be interpreted by ignoring the general relativistic effects described here. For a static compact object, supported by only isotropic pressure, compactness is limited by the Buchdahl limit $z_{\rm b} < 2.0$. However, for compact objects supported by anisotropic pressure, $z_{\rm b}$ could be even higher ($z_{\rm b} < 5.211$). In addition, in principle, there could be ultra-compact objects having $z_{\rm b} \gg 1$. Accordingly, the general relativistic effects described here might be quite important for studies of thermal radiation from some ultra-compact objects., Comment: 11 Pages, Published in Universe Journal

A Schwarzschild Black Hole (BH) is the gravitational field due to a neutral point mass, and it turns out that the gravitational mass of a neutral point mass: $M=0$ (Arnowitt, Deser, Misner, PRL 4, 375, 1960). The same result is also suggested by Janis, Newman, and Winicour (PRL 20, 878, 1968). In 1969, Bel gave an explicit proof that for a Schwarzschild BH, $M=0$ (Bel, JMP 10, 1051, 1969). The same result follows from the fact the timelike geodesic of a test particle would turn null if it would ever arrive at an event horizon (Mitra, FPL, 2000, 2002). Non-occurrrence of trapped surfaces in continued gravitational collapse too demands $M=0$ for black hole (Mitra, Pramana, 73, 615, 2009). Physically, for a point mass at $R=0$, one expects ${\it Ric} \sim M \delta (R=0)$ (Narlikar \& Padmanabhan, Found. Phys., 18, 659, 1988). But the black hole solution is obtained from ${\it Ric} =0$. Again this is the most direct proof that $M=0$ for a Schwarzschild black hole. Implication of this result is that the observed massive black hole candidates are non-singular quasi black holes or black hole mimickers which can possess strong magnetic fields as has been observed. The echoes from LIGO signals, if true, may be the direct evidence that the pertinent compact objects are BH mimickers and not true vacuum BHs., Comment: New references added, mentioned that echoes associated with LIGO signals may be direct evidence that the pertinent compact objects are black hole mimickers

The MACE (Major Atmospheric Cherenkov Experiment) is a 21 m diameter gamma-ray telescope which is presently being installed at Hanle in Ladakh, India (32^0 46^' 46^" N, 78^0 58^' 35^" E) at an altitude of 4270 m a.s.l. Once operational, it will become the highest altitude very high energy (VHE) gamma-ray telescope in the world based on Imaging Atmospheric Cherenkov Technique (IACT). In the present work, we discuss the sensitivity estimate of the MACE telescope by using a substantially large Monte Carlo simulation database at 5^0 zenith angle. The sensitivity of MACE telescope is estimated by carrying out the gamma-hadron segregation using the Random Forest method. It is estimated that the MACE telescope will have an analysis energy threshold of 38 GeV for image intensities above 50 photoelectrons. The integral sensitivity for point like sources with Crab Nebula-like spectrum above 38 GeV is ~2.7% of Crab Nebula flux at 5 sigma statistical significance level in 50 hrs of observation., Comment: Accepted for publication in Nuclear Instruments and Methods A, (2017)

A detailed case study of $\gamma$-hadron segregation for a ground based atmospheric Cherenkov telescope is presented. We have evaluated and compared various supervised machine learning methods such as the Random Forest method, Artificial Neural Network, Linear Discriminant method, Naive Bayes Classifiers,Support Vector Machines as well as the conventional dynamic supercut method by simulating triggering events with the Monte Carlo method and applied the results to a Cherenkov telescope. It is demonstrated that the Random Forest method is the most sensitive machine learning method for $\gamma$-hadron segregation., Comment: Accepted to RAA

This paper describes the validation of a new background discrimination method based on Random Forest technique by re-analysing the Markarian 421 (Mrk 421) observations performed by the TACTIC (TeV Atmospheric Cherenkov Telescope with Imaging Camera) gamma-ray telescope. The Random Forest technique is a flexible multivariate method which combines Bagging and Random Split Selection to construct a large collection of decision trees and then combines them to construct a common classifier. Markarian 421 in a high state was observed by TACTIC during December 07, 2005 - April 30, 2006 for 202 h. Previous analysis of this data led to a detection of flaring activity from the source at Energy $ >$ 1 TeV. Within this data set, a spell of 97 h revealed strong detection of a gamma-ray signal with daily flux of > 1 Crab unit on several days. Here we re-analyze this spell as well as the data from the entire observation period with the Random Forest method. Application of this method led to an improvement in the signal detection strength by $\sim 26\%$ along with a $\sim 18\%$ increase in detected $\gamma$ rays compared to the conventional Dynamic Supercuts method. The resultant differential spectrum obtained is represented by a power law with an exponential cut off $\Gamma = -2.51 \pm 0.10$ and $E_{0} = 4.71 \pm 2.20$ TeV. Such a spectrum is consistent with previously reported results and justifies the use of Random Forest method for analyzing data from atmospheric Cherenkov telescopes., Comment: Accepted NIMA

We have recently studied LS 5039, a gamma-ray binary, with Giant Meterwave Radio Telescope (GMRT) during its periastron and apastron passage. The results presented here show that the spectra are inverted at the low frequency and the flux densities do not differ significantly for two different orbital phases. Assuming that the free-free absorption of radio in stellar wind environment is responsible for the optically thick radio emission we calculated the free-free absorption optical depth and constrained the height of the radio emitting region from the orbital plane. The height is found to be around 1.6 AU for a spherical stellar wind geometry. This estimate may change if the stellar wind is focussed or the radio absorption is due to synchrotron self-absorption., Comment: Accepted for publication in MNRAS Letters

We emphasize that the pressure related work appearing in a general relativistic first law of thermodynamics should involve {\em proper volume element} rather than coordinate volume element. This point is highlighted by considering both local energy momentum conservation equation as well as particle number conservation equation. It is also emphasized that we are considering here a {\em non-singular} fluid governed by purely classical general relativity. Therefore, we are not considering here any semi-classical or quantum gravity which apparently suggests thermodynamical properties even for a (singular) black hole. Having made such a clarification, we formulate a global first law of thermodynamics for an adiabatically evolving spherical perfect fluid. It may be verified that such a global first law of thermodynamics, {\em for a non-singular fluid}, has not been formulated earlier., Comment: 4 pages; Published in Foundations of Physics (2011, online)

By applying Birkhoff's theorem to the problem of the general relativistic collapse of a uniform density dust, we directly show that the density of the dust $\rho=0$ even when its proper number density $n$ would be assumed to be finite! The physical reason behind this exact result can be traced back to the observation of Arnowitt et al. that the gravitational mass of a neutral point particle is zero: $m=0$ (PRL, 4, 375, 1960). And since, a dust is a mere collection of {\em neutral point particles, unlike a continuous hydrodynamic fluid}, its density $\rho = m n=0$. It is nonetheless found that for $k=-1$, a homogeneous dust can collapse and expand special relativistically in the fashion of a Milne universe. Thus, in reality, general relativistic homogeneous dust collapse does not lead to the formation of any black hole in conformity of many previous studies (Logunov, Mestverishvili, Kiselev, Phys.Part.Nucl. 37, 317, 2006; Kisevev, Logunov & Mestvirishvili, Theor. Math. Phys., 164, 972, 2010; Mitra, J. Math. Phys. 50, 042502, 2009; Suggett, J. Phys. A, 12, 375 1979). Interestingly, this result is in agreement with the intuition of Oppenheimer & Snyder (Phys. Rev. 56, p.456, 1939) too: "Physically such a singularity would mean that the expressions used for the energy-momentum tensor does 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.", Comment: 7 pages, Published online as a Letter in Astrophysics & Space Science (2010)

As per general relativity (GR), there cannot be any superluminal propagation of energy. And thus, the sound speed in a continuous medium, $c_s=\sqrt{dp/d\rho}$, must be subluminal. However, if one would conceive of a {\em homogeneous} fluid, one would have $c_s=\infty$ unless pressure too would be homogeneous. Thus it is universally accepted that the maiden GR interior solution obtained by Schwarzschild, involving a homogeneous fluid having a boundary, is unphysical. However no one has ever shown how this exact solution is in reality devoid of physical reality. Also, this solution is universally used for approximate modelling of general relativistic stars and compact objects. But here first we show that in order that the Kretschmann scalar is continuous, one should have $\rho=0$ for strictly homogeneous static stars. Further, by invoking the fact that in GR, given one time label $t$ one can choose another time label $t_*=f(t)$ {\em without any loss of generality}, we obtain the same result that for a static homogeneous sphere $\rho=0$. Consequently, it is eventually found that the static homogeneous sphere having a boundary is just part of the vacuum where $c_s=0$ rather than $\infty$. Therefore all general relativistic stars must be inhomogeneous., Comment: 7 pages, Accepted for publication in Astrophysics & Space Science

Hoyle and Folwler showed that there could be Radiation Pressure Supported Stars (RPSS) even in Newtonian gravity. Much later, Mitra found that one could also conceive of their General Relativistic (GR) version, "Relativistic Radiation Pressure Supported Stars" (RRPSSs). While RPSSs have $z\ll 1$, RRPSSs have $z \gg 1$, where $z$ is the surface gravitational redshift. Here we elaborate on the formation of RRPSSs during continued gravitational collapse by recalling that a contracting massive star must start trapping radiation as it would enter its {\em photon sphere}. It is found that, irrespective of the details of the contraction process, the trapped radiation flux should attain the corresponding Eddington value at sufficiently large $z\gg 1$. This means that continued GR collapse may generate an intermediate RRPSS with $z\gg 1$ before a true BH state with $z=\infty$ is formed asymptotically. An exciting consequence of this is that the stellar mass black hole candidates, at present epoch, should be hot balls of quark gluon plasma, as has been discussed by Royzen in a recent article entitled "{\it QCD against black holes?}"., Comment: One typo corrected

One of the outstanding puzzles of theoretical physics is whether quantum information indeed gets lost in the case of Black Hole (BH) evaporation or accretion. Let us recall that Quantum Mechanics (QM) demands an upper limit on the acceleration of a test particle. On the other hand, it is pointed out here that, if a Schwarzschild BH would exist, the acceleration of the test particle would blow up at the event horizon in violation of QM. Thus the concept of an exact BH is in contradiction of QM and quantum gravity (QG). It is also reminded that the mass of a BH actually appears as an INTEGRATION CONSTANT of Einstein equations. And it has been shown that the value of this integration constant is actually zero. Thus even classically, there cannot be finite mass BHs though zero mass BH is allowed. It has been further shown that during continued gravitational collapse, radiation emanating from the contracting object gets trapped within it by the runaway gravitational field. As a consequence, the contracting body attains a quasi-static state where outward trapped radiation pressure gets balanced by inward gravitational pull and the ideal classical BH state is never formed in a finite proper time. In other words, continued gravitational collapse results in an "Eternally Collapsing Object" which is a ball of hot plasma and which is asymptotically approaching the true BH state with M=0 after radiating away its entire mass energy. And if we include QM, this contraction must halt at a radius suggested by highest QM acceleration. In any case no EH is ever formed and in reality, there is no quantum information paradox., Comment: 8 pages in Pramana Style, 6 in Revtex style

Following Einstein's definition of Lagrangian density and gravitational field energy density (Einstein, A., Ann. Phys. Lpz., 49, 806 (1916); Einstein, A., Phys. Z., 19, 115 (1918); Pauli, W., {\it Theory of Relativity}, B.I. Publications, Mumbai, 1963, Trans. by G. Field), Tolman derived a general formula for the total matter plus gravitational field energy ($P_0$) of an arbitrary system (Tolman, R.C., Phys. Rev., 35(8), 875 (1930); Tolman, R.C., {\it Relativity, Thermodynamics & Cosmology}, Clarendon Press, Oxford, 1962)); Xulu, S.S., arXiv:hep-th/0308070 (2003)). For a static isolated system, in quasi-Cartesian coordinates, this formula leads to the well known result $P_0 = \int \sqrt{-g} (T_0^0 - T_1^1 -T_2^2 -T_3^3) ~d^3 x$, where $g$ is the determinant of the metric tensor and $T^a_b$ is the energy momentum tensor of the {\em matter}. Though in the literature, this is known as "Tolman Mass", it must be realized that this is essentially "Einstein Mass" because the underlying pseudo-tensor here is due to Einstein. In fact, Landau -Lifshitz obtained the same expression for the "inertial mass" of a static isolated system without using any pseudo-tensor at all and which points to physical significance and correctness of Einstein Mass (Landau, L.D., and Lifshitz, E.M., {\it The Classical Theory of Fields}, Pergamon Press, Oxford, 2th ed., 1962)! For the first time we apply this general formula to find an expression for $P_0$ for the Friedmann- Robertson -Walker (FRW) metric by using the same quasi-Cartesian basis. As we analyze this new result, physically, a spatially flat model having no cosmological constant is suggested. Eventually, it is seen that conservation of $P_0$ is honoured only in the a static limit., Comment: By mistake a marginally different earlier version was loaded, now the journal version is uploaded

We show that the integration constant in the vacuum Schwarzschild solution has the unique value, alpha_0=0, accordingly Black Holes too have the same unique value of mass M0=0. Therefore the so-called Black Holes Candidates (BHC) cannot be true BHs. It is also shown that continued collapse of sufficiently massive bodies would generate radiation pressure and energy dominated quasistatic objects having surface gravitational redshifts z>>1. Under the assumption of baryon number conservation, such objects would take infinite time to collapse to the idealized BH state with M=0 and z=infty. The local temperature of such a stellar mass Eternally Collapsing Object (ECO) would be above Quark Gluon Phase transition. ECOs would undergo intermittent violent radiative eruptions and pollute the interstellar medium with freshly made hydrogen out of their QGP and also the light elements cooked in their envelope. It is shown that the extremely redshifted observed temperature of an ECO could be 2.75 K and superposition of ECO background radiation might generate the microwave back ground radiation. The predicted 2.75 K luminosity for the galactic centre ECO, i.e., Sgr A*, L~3x1036 erg/s, nicely matches with the corresponding estimate by Wilkinson Microwave Anisotropy Probe (WMAP)., Comment: 10 pages, pdf only

We start with a new version of Newtonian cosmology by incorporating the fact that the galaxies are losing mass due to emission of radiation. This yields accelerated recession for the galaxies. We point out that in the presence of accelerated expansion, the universe can be infinitely old and suggest that the observable universe is only a speckle of the true universe. We argue that the mean density of the universe must be zero and the cosmic fluid comprises infinite number of such speckles separated by infinite distances. The Microwave Background radiation is shown to be just the sum of redshifted thermal radiation of Eternally Collapsing Objects (ECO), the so-called Black Hole Candidates.The hot photosphere of the ECOs cooks light elements the same way they are supposed to be produced in hot early universe. This universe with nested infinities has zero baryon number as it contains equal number of matter and antimatter atoms. The predicted microwave luminosity of the galactic centre ECO (Sgr A) nicely matches with the corresponding WMAP estimate (abridged)., Comment: 10 pages

We point out that the {\em spacetime void} inferred by Castro[J. Math. Phys. 49, 042501, (2008)] results from his choice of a discontinuous radial gauge. Further since the integration constant $\alpha_0 = 2M_0$ ($G=c=1$) occurring in the vacuum Hilbert/Schwarzschild solution of a neutral "point mass" is zero [Arnowitt et al., in Gravitation: An Introduction to Current Research, ed. L. Witten, Wiley, Chap. 7, p.227; also Phys. Rev. Lett., 4, 375, (1960)]; A. Mitra, Adv. Sp. Res., 38, 2917 (2006)] Castro's gauge reduces to the well behaved and physical Hilbert gauge. Physically this means that true Hilbert/Schwarzschild black holes have unique gravitational mass M=0. Accordingly, the unphysical {\em spacetime viod} inferred by Castro is actually non-existent., Comment: Published in J. Math. Phys. General Relativity Section

We derive here the metric for Einstein's static universe (ESU) directly from Einstein equation, i.e., by considering both $G_{ik}$ and $T_{ik}$. We find that in order that the fluid pressure and acceleration are {\em uniform} and finite despite the presence of a coordinate singularity, the effective density $\rho_e = \rho + \Lambda/8 \pi =0$, where $\Lambda$ is the cosmological constant. Under weak energy condition, this would imply $\rho = \Lambda =0$ for ESU. This means that if one would need to invoke a source of ``repulsive gravity'' in some model, (i) the model must be non-static, (ii) the repulsive gravity must be due to a ``quintessence'' or a ``dark energy'' fluid with negative pressure and appear on the right hand side (RHS) of the Einstein equation through $T_{ij}$ rather than through a fundamental constant residing on the LHS of the same equation, and (iii) energy density of both normal matter and the ``dark energy fluid'' should be time dependent. In fact, the repulsive gravity would be due to a time independent $\Lambda$, it would be extremely difficult to understand why the associated energy density should be approximately $10^{120}$ times lower than the value predicted by quantum gravity. On the other hand, for a dark energy fluid whose energy density is time dependent, it would be much easier to understand such an extremely low present energy density: the original initial value of the energy density of the fluid could be equal to the quantum gravity value while the present low value is due to decay with time., Comment: Revised after referee comments

We discuss that in the extreme relativistic limit, i.e., when z >>1, where z is the surface gravitational redshift, there could be radiation pressure supported and dominated stars with arbitrary gravitational mass, high or low. Such Objects are called Eternally Collapsing Objects (ECOs). ECOs are practically as compact as Schwarzschil Black Holes (BH) and, observationally, are likely to be mistaken as BHs. Further since any object undergoing continued collapse must first become an ECO before becoming a true BH state charcterized by M=0, the observed BH Candidates are ECOs., Comment: Proceedings of IAU Symposium #238, held 21-25 August, 2006 in Prague, Czech Republic

We point out that although conventional stars are primarily fed by burning of nuclear fuel at their cores, in a strict sense, the process of release of stored gravitational energy, known as, Kelvin - Helmholtz (KH) process is either also operational albeit at an arbitrary slow rate, or lying in wait to take over at the disruption of the nuclear channel. In fact, the latter mode of energy release is the true feature of any self-gravity bound object including stars. We also highligh the almost forgotten fact that Eddington was the first physicist to introduce Special Relativity into the problem and correctly insist that, actually, total energy stored in a star is not the mere Newtonian energy but the total mass energy (E = M c^2). Accordingly, Eddington defined an ``Einstein Time Scale'' of Evolution where the maximum age of the Sun turned out to be t_E = 1.4. 10^{13} yr. We extend this concept by introducing General Relativity and show that the minimum value of depletion of total mass-energy is t_E =infty not only for Sun but for and sufficiently massive or dense object. We propose that this time scale be known in the name of ``Einstein - Eddington''. We also point out that, recently, it has been shown that as massive stars undergo continued collapse to become a Black Hole, first they become extremely relativistic Radiation Pressure Supported Stars. And the life time of such relativistic radiation pressure supported compact stars is indeed dictated by this Einstein -Eddington time scale whose concept is formally developed here. Since this observed time scale of this radiation pressure supported quasistatic state turns out to be infinite, such objects are called Magnetospheric Eternally Collapsing Objects (MECO)., Comment: New Astronomy (In press), Ref. on Brown Dwarf added in proof

It is known that, for a static fluid sphere, the GeneralRelativistic (GR) Effective Mass Energy Density (EMD) appears to be (rho + 3 p), where rho is the bare mass density, p is the isotropic pressure, from a purely localized view point. But since there is no truly local definition of ``gravitational field'', such a notion could actually be misleading. On the other hand, by using the Tolman mass formula, we point out that, from a global perspective, the Active Gravitational Mass Energy Density (AGMD) is sqrt{g_{00}} (rho + 3 p) and which is obviously smaller than (rho + 3p) because g_{00} < 1. Then we show that the AGMD eventually is (rho - 3p), i.e., exactly opposite to what is generally believed. We further identify the AGMD to be proportional to the Ricci Scalar. By using this fundamental and intersting property, we obtain the GR virial theorem in terms of appropriate ``proper energies''., Comment: The originally accepted journal version, subsequent modifications removed

By using virial theorem, Helmholtz and Kelvin showed that the contraction of a bound self-gravitating system must be accompanied by release of radiation energy irrespective of the details of the contraction process. This happens because the total Newtonian energy of the system E_N (and not just the Newtonian gravitational potential energy E_g^N) decreases for such contraction. In the era of General Relativity (GR) too, it is justifiably believed that gravitational contraction must release radiation energy. However no GR version of (Newtonian) Helmholtz- Kelvin (HK) process has ever been derived. Here, for the first time, we derive the GR version of the appropriate virial theorem and Helmholtz Kelvin mechanism by simply equating the well known expressions for the gravitational mass and the Inertial Mass of a spherically symmetric static fluid. Simultaneously, we show that the GR counterparts of global ``internal energy'', ``gravitational potential energy'' and ``binding energy'' are actually different from what have been used so far. Existence of this GR HK process asserts that, in Einstein gravity too, gravitational collapse must be accompanied by emission of radiation irrespective of the details of the collapse process. Consequently, all studies of strictly adibatic gravitational collapse are only of academic interest., Comment: Minor corrections, maiden derivation of proper GR virial theorem, shows there is no strict adiabatic collapse

Even when we consider Newtonian stars, i.e., stars with surface gravitational redshift, z<< 1, it is well known that, theoretically, it is possible to have stars, supported against self-gravity, almost entirely by radiation pressure. However, such Newtonian stars must necessarily be supermassive. We point out that this requirement for excessive large M, in Newtonian case, is a consequence of the occurrence of low z<< 1. On the other hand, if we remove such restrictions, and allow for possible occurrence highly general relativistic regime, z >> 1, we show that, it is possible to have radiation pressure supported stars at arbitrary value of M. Since radiation pressure supported stars necessarily radiate at the Eddington limit, in Einstein gravity, they are never in strict hydrodynamical equilibrium. Further, it is believed that sufficiently massive or dense objects undergo continued gravitational collapse to the Black Hole stage characterized by z =infty. Thus, late stages of Black Hole formation, by definition, will have, z >> 1, and hence would be examples of quasi-stable general relativistic RPSSs. This result is also supported by with our previous finding that that trapped surfaces are not formed in gravitational collapse and the value of the integration constant in the vacuum Schwarzschild solution is zero. Hence the supposed observed BHs are actually ECOs., Comment: Minor chages in proof. Discusses why the observed BHs are actually ECOs and Chandrasekhar limit is not applicable to them

By using elementary astrophysical concepts, we show that for any self-luminous astrophysical object, the ratio of radiation energy density inside the body (rho_r) and the baryonic energy density (rho_0) may be crudely approximated, in the Newtonian limit, as rho_r/rho_0 ~ GM/Rc^2, where G is constant of gravitation, c is the speed of light, M is gravitational mass, and R is the radius of the body. The key idea is that radiation quanta must move out in a diffusive manner rather than free stream inside the body of the star. When one would move to the extreme General Realtivistic case i.e., if the surface gravitational redshift, z >> 1, it is found that, rho_r/rho_0 ~ (1+z). Previous works on gravitational collapse, however, generally assumed rho_r/rho_0 << 1. On the other hand, actually, during continued general relativistic gravitational collapse to the Black Hole state (z --> infty), the collapsing matter may essentially become an extremely hot fireball a la the very early universe even though the observed luminosity of the body as seen by a faraway observer, L^\infty ~ (1+z)^{-1} --> 0 as z --> infty, and the collapse might appear as ``adiabatic''., Comment: Small changes at proof stage, shows zero radiation density for collapse implies zero restmass density, MNRAS Letters (in press)

In a recent preprint, gr-qc/0511123, Dadhich has given a brief yet beautiful exposition on some of the research works by Prof. A.K. Raychaudhuri. Here Dadhich highlights the fact that the apparently ``self-evident'' assumption of occurrence of ``trapped surfaces'' may not be realized atleast in some specific cosmological models though no general proof for non-occurrence of trapped surfaces exists in the cosmological context. However, Dadhich added, without sufficient justification, that trapped surfaces should occur for collapse of isolated bodies. We point out that actually trapped surfaces do not occur even for collapse of spherically symmetric isolated bodies. Further unlike the cosmological case, for isolated bodies, an exact proof for generic non-occurrence of trapped surfaces is available. Thus for isolated bodies, the above referred apparently ``self-evident'' assumption fails much more acutely than in cosmology. Many recent astrophysical observations tend to corroborate the fact trapped surfaces do not occur for isolated bodies. Two recent specific papers (PRD) are cited to show that when radiative non-diispative collapse can prevent formation of trapped surfaces., Comment: 3 new references added, 2 of them are specific examples where collapse generated radiation presuure prevents formation of Trapped Surfaces

It is shown here that the so-called spinning Black Hole Candidates (BHCs) cannot be Black Holes (BHs) at all and, on the other hand, must be spinning hot Eternally Collapsing Objects (ECOs). The question would then arise why the spinning BHCs do not reveal their spin pulsation unlike the spinning cold Neutron Stars (NSs). Even for magnetized NSs with ``hard surfaces'', there may be no observed spin pulsation if the dipole axis and spin direction are exactly same. However, spinning ECOs do not show spin pulsation because their surface gravitational red shift is extremely high, z >> 1 and could be in the range of 10^{7-8} for stellar mass range. In contrast NSs have z ~ 0.1 -0.3. The time profile of periodic signals generated on the surface of a spinning MECO get extremely distorted due to extreme general relativistic frame dragging effect as they traverse through extremely steep gravitational field. However, if any radiation would be formed in the ECO magnetosphere sufficiently away from the surface like in the pulsar ``outer slots''(which may happen for isolated spinning ECOs), it might be a pulsed one., Comment: 4 pages, paper presented in COSPAR colloquium on Spectra and Timing of Compact X-ray Binaries (2005), Proc. to be published by Elsevier Sc, final version, important new ref. added

It has been justifiably questioned that if the Black Hole Candidates (BHCs) have a ``hard surface'' why Type I X-ray bursts are not seen from them (Nayayan, R., Black Holes in Astrophysics, New J. Phys., 7, 199-218, 2005). It is pointed out that a ``physical surface'' need not always be ``hard'' and in could be ``gaseous'' in case the compact object is sufficiently hot (Mitra, A., The day of reckoning: the value of the integration constant in the vacuum Schwarzschild solution, physics/0504076, p1-p6; BHs or Eternally Collapsing Objects: A review of 90 years of misconceptions, in Focus on Black Hole Research, Nova Sc. Pub., NY, p1-p94, 2006). Even if a ``hard surface'' would be there, presence of strong strong intrinsic magnetic field could inhibit Type I X-ray burst from a compact object as is the case for Her X-1. Thus, non-occurrence of Type I bursts actually rules out those alternatives of BHs which are either non-magnetized or cold and, hence, is no evidence for existence of Event Horizons (EHs). On the other hand, from the first principle, we again show that the BHCs being uncharged and having finite masses cannot be BHs, because uncharged BHs have a unique mass M=0. Thus the previous results that the so-called BHCs are actually extremely hot, ultramagnetized, Magnetospheric Eternally Collapsing Objects (MECOs) (Robertson, S. & Leiter, D., Astrophys. J. 565, 447-451, 2002; MECO Model of galactic BH Candidates and active galactic nuclei, in: New Developments in BLack Hole Research, NOva Sc. Pub., NY, p1-p44, 2006) rather than anything else get reconfirmed by non-occurrence of Type I X-ray bursts in BHCs., Comment: Minor chages in proof, 5 pages, Advances in Sp. Res. (in press)

We estimate that the vacuum electric field associated with a spinning Magnetospheric Eternally Collapsing Object MECO (www.phys.uni-sofia.bg/~astro/abbrev.html) could be higher by a factor of ~ 10^4 than the corresponding pulsar value because of extreme relativistic Frame Dragging Effect. Thus isolated spinning MECOs could be source of UHE cosmic ray acceleration and VHE gamma-ray production. However because of the steeply varying gravitational field close to the surface of the MECO, any signal generated there would be both extremely redshifted and distorted. As a result, there may not be any significant pulsed X-ray or Radio emission from close to the surface, and consequently, the $\gamma$-ray source may appear as ``Unidentified'' and the particle accelerator may appear as ``Dark''., Comment: To be presented in 29th Int. Cosmic Ray Conf., Pune, 4 pages

It is known that spinning pulsars could be source of VHE-UHE cosmic particle acceleration. It is also conjectured that (fictitious) spinning Black Holes (BH) could be sites of cosmic particle acceleration. However, it has been shown by Mitra and Leiter and Robertson that General Relativity (GR) actually does not allow the existence or formation of finite mass BHs. It was predicted that the BH Candiadates (BHCs) have strong intrinsic magnetic fields (like pulsars) instead of Event Horizons. And this prediction has tentatively been verified in a series of papers by Robertson & Leiter. Thus all observed BH Candidates are actually not BHs, and, they are expected to be MECOs. Stellar mass MECOs are GR analogs of conventionally known isolated pulsars. While pulsars are/have (i) COLD, i.e., not supported by radiation pressure, MECOs are HOT, i.e., supported primarily by trapped radiation pressure, (ii) upper mass limit of 3-4 Msolar MECOs, being HOT, have no Upper Mass Limit, (iii) surface gravitational red shift, z ~ 0.1 -0.2, MECOs have z >> 1 so that photons can remain almost permanently trapped inside them, (iv) magnetic field B <10^{13} G, for MECOs the local value of B >> 10^{13} G. It may be recalled that isolated (non- accreting) uncharged BHs are cold and dead objects without any physical activity. On the other hand, isolated spinning MECOs are like extreme GR pulsars., Comment: To be presented in 29th ICRC, 4 pages, Oral, Typos removed

We point out that the contentions of Chapline (astro-ph/0503200)[1] that (i) General Relativity (GR) is in conflict with Quantum Mechanics (QM) and (ii) GR fails even on macroscopic length scales are incorrect and based on (i) misunderstanding of GR and (ii) completely misconceived ``thought experiments''. Even without introduction of any QM, GR actually does not allow formation of any Event Horizon and is competent to figure out the actual nature of the supposed Black Hole candidates. The resultant picture is not in conflict with QM at all., Comment: comments on astro-ph/0503200, 10 pages, last 3 more typos removed

The stongest theoretical support for Schwarzschild Black Holes (SBHs) is the existence of vacuum Schwarzschild/Hilbert solution. The integration constant alpha_0 in this solution is interpreted as the mass of the BH. But by equating the 4-volumes (an INVARIANT) associated with the Schwarzschild and the Eddington-Finkelstein metrics, we directly obtain here the stunning result that SBHs have the unique mass, M_0 = 0! Thus the Event Horizon of a SBH (R_g = 2M_0 =0) gets merged with the central singularity at R=0 and, after 90 years, the mysterious EH indeed gets erased from the non-singular R >0 region of a completely empty (R_0=0) spherical POINT MASS spacetime in accordance with the intuition of the founders of GR. Consequently the entropy of SBHs have the unique value of zero, which instantly removes the quantum mechanical``information paradox'' and the apparent conflict between GR and QM, the two pillars of modern physics. This direct result firmly establishes the exciting fact, as far as isolated bodies are concerned, GR is a singularity free theory even at the classical level! The Black Hole Candidates with mass M >0 are thus NOT BHs and instead could be HOT compact objects whose possibility has so far been overlooked in favour of COLD Neutron Stars or BHs. With alpha_0 =0, the BH paradigm collapses instantly because it was built with the ASSUMPTION alpha_0 >0. This result is dedicated to the occurrence of 100 years of Relativity., Comment: 8 pages, Most direct result

In a recent paper[1], it has been shown that, there cannot be any rotating (Kerr) Black Hole (BH) with finite mass in order that the generic properties associated with the symmetries of stationary axisymmetric Einstein equations are obeyed, i.e, in order to have m\ge 0, we must have $a=0$. In other words, all observed chargeless BHs with finite masses must be non-rotating Schwarzschild BHs. Here, by comparing the invariant 4 volume associated with original Kerr metric [2] with the Boyer-Lindquist version of the same [3], we further find that, stationary axisymmetric {\em vacuum} Einstein solutions actually correspond to m=0 in addition to a=0! This means that if the Kerr solution is a unique one, the Schwarzschild BHs too correspond to only m=0 and therefore the observed BH candidates (BHs) with m >0 are not BHs at all. This is in agreement some detailed analysis of recent observations[4-7] which suggest the the BHCs have strong intrinsic magnetic moment rather than any Event Horizon. If one would derive the Boyer-Lindquist metric in a straightforward manner by using the Backlund transformation, it would follow that a= m sin phi, where phi is the azimuth angle. This relationship directly confirms the result that for a supposed rotating BH, actually, both a=m=0., Comment: 8 pages

We present here a very simple, short and new proof which shows that no trapped surface is ever formed in spherical gravitational collapse of isolated bodies. Although this derivation is of purely mathematical nature and without any assumption, it is shown, in the Appendix, that, physically, trapped surfaces do not form in order that the 3 speed of the fluid as measured by an observer at a fixed circumference coordinate $R$ (a scalar), is less than the speed of light $c$. The consequence of this result is that, mathematically, even if there would be Schwarzschild Black Holes, they would have unique gravitational mass M=0. Recall that Schwazschild BHs may be considered as a special case of rotating Kerr BHs with rotation parameter a=0. If one would derive the Boyer-Lindquist metric [1] in a straight forward manner by using the Backlund transformation[2], one would obtain a= M sin phi where phi is the azimuth angle. This relation demands that BHs have unique mass M=0 (along with a=0) which in turn confirms that there cannot be any trapped surface in realistic gravitational collapse where the fluid has real pressure and density. Since there is no trapped surface and no horizon there is no Information Paradox in the first place., Comment: Typos removed, minor changes, 10 pages

It is believed that the basic component of the central engine of quasars, micro-quasars, and energetic Gamma Ray Bursts are the rotating or the Kerr Black Holes (BH)[1]. But by using a generic property[2-4] of the metric components of a stationary axisymmertic rotating metric in its standard form}, namely, g_phi \phi = sin^2 theta g_theta theta, where phi is the azimuth angle and theta is the polar angle measured from the axis of symmetry, we have found the unexpected and surprising result that (i) in order to have a mass of a Kerr BH m ge 0, it is necessary that its rotation parameter a=0 and if one insists for an a ge 0, one must have m le 0! Thus if the suspected Black Hole candidates with m >0 are really rotating they cannot be BHs at all which is in agreement with some detailed analysis of recent observations[5-8]. However, if it is assumed that such objects are strictly non-rotating, they could be non-rotating Schwarzschild BHs (a=0) with m ge 0 if we ignore the physical difficulties associated with the existence of such objects. This result calls for new theoretical efforts to understand a vast range of astrophysical phenomenon. If one derives the Kerr Metric in a straightforward manner by using the Backlund transformation, it is seen that a=m sin phi. This relationship confirms that a=m=0 for Kerr BHs., Comment: Thoroughly revised, new eqs. new ref., new supporting proof, many points clarified, physical interpretation included

In a recent paper (FPL 13(6), 543, 2000, astro-ph/9910408), from several independent considerations we showed that GTR does not allow formation of trapped surfaces and finite mass BHs. We rediscuss here several subtle issues involved in this work. So far only the scientific critique to this work was due to Tereno (astro-ph/9905144, astro-ph/9905298) and which was answered in Mitra (astro-ph/9905175, astro-ph/9905175, astro-ph/9905329). Now Tereno (gr-qc/0111073) has also admitted that the local 3-speed of a free particle as conventionally defined by all previous authors and as measured in any coordinate system, is indeed c at the EH. Further since the acceleration SCALAR BLOWS UP at the EH, our result that there cannot be any EH at a finite R is reconfirmed. We explicitly show here that the final state of spherical collapse of very massive stars corresponds to a zero mass BH with 2M/R ->0. But at any finite epoch there would be a Eternally Collapsing Objects (ECO) of finite mass. However, if quantum back reaction in the strong gravity regime would cause a phase transition p ~ rho, there could be static ultracompact objects (UCO) of ~ 10 M (solar). Further, if the phase transition goes proceeds to p= -rho, there could be UCOs of arbitrary high mass (Mazur & Mottola, astro-ph/0109035). Both ECOs and UCOs are expected to possess strong internal magnetic field whereas the the same for a BH is zero. Robertson & Leiter (ApJ 565, 447, 2002, astro-ph/0102381) have shown that the BH candiadates may indeed possess such strong intrinsic mag field. Thus the BHCs are likely to ECOs/UCOs rather than BHs. We also discuss that there is no real evidence for detection of EH., Comment: Accepted for publication in Found Phys Lett, few typos removed

There are many observational evidences for the existence of massive compact condensations in the range $10^6 -10^{10} M_\odot$ at the core of various galaxies. At present such condensations are commonly interpreted as Black Holes (BHs). However, we point out that while such Black Hole Candidates (BHCs) must be similar to BHs in many respects they, actually, can not be BHs because existence of Black Holes would violate the basic tenet of the General Theory of Relativity (GTR) that the worldline of a material particle must be timelike at any regular region of spacetime. On the other hand general relativistic collapse of very massive bodies should lead to Eternally Collapsing Configurations (ECOs) or Ultra Compact Objects (UCOs). While ECOs/UCOs may practically be as compact as corresponding BHs, they will have a physical surface. Also while BHs do not have any intrinsic magnetic field ECOs may have strong intrinsic magnetic field. We point out that despite many claims actually there is no real evidence for the ``Event Horizon'' (EH) of supposed BHs and on the other hand, there are tentative evidence for the existence of strong magnetic field in several BHCs (or ECOs). The presence of such intrinsic magnetic field may render the task of explaining high energy radiation phenomenon in many Active Galactic Nuclei easier., Comment: Invited Talk Delivered in international symposium ``Gamma-ray Astrophysics through Multi-wavelength Experiments: GAME-2001'', Mt. Abu, India, March 8-10, 2001

There are many observational evidences for the detection of compact objects with masses significantly larger (in galactic cases) or much larger (in extragalactic cases) than the upper limits of masses of em cold Neutron Stars. Such compact objects are commonly interpreted as Black Holes (BHs). However, we point out that while such Black Hole Candidates (BHCs) must be similar to BHs in many respects they, actually, can not be BHs because existence of Black Holes would violate the basic tenet of the General Theory of Relativity that the worldline of a material particle must be TIMELIKE at any regular region of spacetime. We arrive at this unique conclusion by approaching the problem from various directions. We feel that such ``operational'' Black Holes could be able to explain hard X-ray tail found in the galactic BHCs because Lorentz factor of the plasma accreting on such objects should be considerably higher than the corresponding NS case., Comment: Invited Talk given in a Workshop on Black Holes, Calcutta, Organized by Centre for Space Physics, 11 pages, amitra@apsara.barc.ernet.in

It is known that Neutron Stars may be converted into more compact Strange Stars (SS) on capture/formation of a ``seed'' of strange matter. It is also known that the binding energy of the nascent hot SS is likely to be radiated as $\nu -\bar\nu$s so that an electromagnetic pair fireball (FB) may be created by neutrino annihilation. And already this process has been considered as a probable source of Gamma Ray Bursts (GRB) by several authors, the most notable of which is due to Cheng & Dai (PRL, 77, 1210, 1996). They mentioned that this process may generate a FB luminosity (outside the neutrinosphere) of 10**(49) erg. But we point out here that a SS is a relativistic object with surface gravitation z=0.5. Accordingly, we present here a Relativistic Model of this process, and show that, for a massive SS with M=2 solar mass, one may explain a GRB energy of ~ 10**(53) erg., which is 4 orders higher than previous non-relativistic estimate. Further since the baryonic mass of the thin crust of a strange star is negligible, this FB will generate an extremely relativistic blast wave. Thus this process may be one of the viable routes for the genesis of hitherto unexplained cosmic Gamma Ray Bursts. While some of the GRBs might be beamed, many of them do not show any long term spectral break in their afterglows and are likely to be quasi-spherical. A particular example is GRB 971214 for which estimated GRB energy is 3. 10**(53) erg. Our model may be useful for understanding the genesis of such powerful and unexplained bursts., Comment: 4 pages, uses mn.sty, revised version submitted to MNRAS Letter

The standard big bang cosmology has been greatly successful in explaining many observational aspects of the real universe. However, two particular diffficulties faced by it are the so-called ``horizon'' and ``flatness'' problems. By assuming that the recently found cosmic acceleration to be a genuine and ever present effect, we show that, the resultant modified Friedman model is free from both the above referred problems, and there is no need to invoke the additional ``inflationary'' initial phase as a seperate ingredient. The important cosmological milestones of the standard big babg cosmology (which predicts cosmic deceleration) like GUT symmetry breaking epoch or radiation matter decoupling epoch may remain more or less unchanged in the modified cosmology in terms of redshift values. However, in terms of cosmic time $t$, all such epochs occur earlier as the universe becomes older in this case., Comment: To be presented in the Cosmology Symp. associted with 24th IAU General Assembly at Manchester from Aug 7-18, 2000

GRB 990123 is the most luminous event detected so far, and in an important paper, Hjorth et al. (1999) reported an upper limit on the degree of linear polarization of the optical afterglow for this burst (P <2.3%). One of the interprtations for this small value of P was that the emission was probably due a relativistic jet with ordered magnetic field, and the viewing angle in the lab frame theta' <= Gamma^{-1}, where Gamma is the bulk Lorentz factor of the jet at the time of the optical emission. We point out that this conclusion resulted from a confusion between the angles measured in the lab frame and in the plasma rest frame. For ordered magnetic field, one would actually obtain a large value of P because the above mentioned angle would correspond to a very large angle, theta <= \pi/2, in the plasma rest frame. And this is probably the case with the blazars. On the other hand, it is indeed possible to have P ~ 0 if the magnetic field of GRB 990123 was completely chaotic and the viewing angle was considerably smaller than the semi-angle of the jet., Comment: A ref. by Dai & Lu added. Concluded that although nothing definitive can be said at this stage, it is more likely that GRB 990123 was quasi-spherical rather than ultra narrow jet type. An abridged version of it will be published in Astronomy and Astrophysics

We have shown in that for arbitrary EOS and radiation transport properties, (even) the idealized spherical gravitational collapse DOES NOT lead to the formation of trapped surfaces: 2GM(r,t)/R <=1. Hence all singularity theorems of Hawking, Penrose and Geroch, built on the assumption of formation of trapped surfaces, get invalidated! And this inequality, demands that M->0 if indeed R->0. We have shown that the final state corresponds to a zero mass BH state and, this state would occur only after infinite proper time indicating that GR is indeed the only naturally singularity free theory for isolated bodies (as was cherished by Einstein). This M->0 state would materialize after the body radiates its entire initial mass-energy. Thus there is no event horizon at any finite R or M, and, therefore all the great theoretical confusions like whether there could be (i) White Holes, (ii) whether t (R) becomes spacelike (timelike) inside the EH (iii) Loss of information in gravitational collapse, and (iv) validity of cosmic censorship conjecture get resolved. At any finite proper time, the collapsed object would be either static (z<2) or may appear static (R almost frozen) though, in extreme cases, internally, in terms of proper radial length, it might be collapsing at a speed ~c! We call the latter as Eternally Collapsing Objects., Comment: To be published in the Dec., 2000 issue of Foundation of Physics Letters. Several small changes, more discussion on the nature of Eternally Collapsing Objects (supposed BHs). The problem addressed from 4 directions, (i) Speed of the collapsing fluid must be less than c, (ii) In Sch. coordinates, the metric becomes null on the Event Horizon (EH), (iii) Even in Kruskal coordinates the metric becomes null on the EH, (iv) When crucial errors of Oppenheimer and Snyder paper are removed, they show that trapped surfaces are not allowed

The total spacetime manifold for a Schwarzschild black hole (BH) is described by the Kruskal coordinates u=u(r,t) and v=v(r,t), where r and t are the conventional Schwarzschild radial and time coordinates respectively. The relationship between r and t for a test particle moving on a radial or non-radial geodesic is well known. Similarly, the expression for the vacuum Schwarzschild derivative for a geodesic, in terms of the constants of motion, is well known. However, the same is not true for the Kruskal coordinates. Here, we, first, explicitly obtain the value of the Kruskal coordinates on the Event Horizon as a function of the constant of motion (E=energy per unit rest mass) for a test particle on a radial geodesic by directly using the r-t relationship as obtained by Chandrasekhar and also by Misner, Thorne and Wheeler. It is found that u_H and v_H are finite for E <1. And then, we derive here the expression for the Kruskal derivative for a radial geodesic in terms of the constants of motion. In particular, it is seen that the value of |du/dv| (= 1) is regular on the Event Horizon of the Black Hole. The regular nature of the Kruskal derivative is in sharp contrast with the Schwarzschild derivative, |dt/dr| =infty, at the Event Horizon., Comment: 8 pages, REVTEX

We have recently shown that at the Event Horizon of a Schwarzschild BH, the Kruskal derivative assumes a form du/dv = +,- f(r,t)/f(r,t) = +, - 1. Corespondingly, du^2 = dv^2, and the geodesic of a material particle becomes NULL at the EH. Physically this means that the free fall speed measured by the Kruskal observer V=1 at the EH. However, Tereno has difficulty in accepting this limiting value of du/dv=1. We point out that Eq.(4) of his paper shows (1-2M/r) dt/dr =-1, at r=2M, and, indeed, the mod of V=1. However, rather than accepting this, Tereno has obtained and incorrect expression for t=t(r) and has tried to find V graphically. We point out that, instead, if he uses the correct t=t(r) relation by using Eq. (12.2.24) of Shapiro and Teukolsky, he would indeed find V=1. It is simple to understand, physically, why one must have V=1 at the EH. If the free fall speed measured by the static Sch. Observer is Vs and the relative velocity of the other observer is Vso with respect to the Sch. observer, then the velocity of free fall of the test particle, V, can be found by using the Special Relativistic velocity addition formula (locally). Since Vs =1 at r=2M, one would always find, V=1 too. We shall not respond to any further preprint on this line., Comment: Final attempt to convince Tereno. We add here an even simpler derivation for the Kruskal derivative which does not require working out of any limit

Supersymmetric String theories find occurrences of extremal Black Holes with gravitational mass M=Q where Q is the charge (G=c=1). Thus, for the chargeless cases, they predict M=0. We show that General Theory of Relativity, too, demands a unique BH mass M=0. And we do this by considering the problem from various angles, both mathematically and physically. Our analysis may be understandable even to the readers not having sufficient background in GTR. Physically, this M=0 result means that, continued gravitational collapse indeed continues for infinite proper time as the system hopelessly tries to radiate its entire original mass energy to attain the lowest energy state M=0. Since no event horizon is formed, the problem of loss of information associated with creation of finite mass BHs or their evaporation ceases to exist., Comment: 5 pages, Revtex

In a recent preprint (astro-ph/9905144) Tereno has tried to find the physical 3-velocity (V) at the Event Horizon of a Kruskal Black Hole. This has been done in the backdrop of the recent work by Mitra (astro-ph/9904162) where it was shown that the radial geodesic of material particle, unphysically, becomes null at the Event Horizon. Although Tereno stops short of finding the precise value of V at r=2M, he concludes that V <1. It is pointed out with reference to Eq.(13) of Tereno's work that since his delta = (r -2M)/r tends to 0 as r tends to 2M, V indeed tends to 1. It appears that Tereno's conclusion is driven by his inability to conceive proper limiting value of fractions. Similarly, his idea that, the velocity addition formula of Sp. Theory of Relativity breaks down when both the velocities approach unity is due his same inability. In particular, our central result that Schwarschild BHs must have M=0 has been obtained independently from three different considerations (gr-qc/9810038, astro-ph/9904162, 163). And we also offer here the essential physical reason why the speed of free fall at the Event Horizon must be equal to the speed of light in coordinate system. Yet we are thankful to Tereno for making the first attempt to scientifically criticize our relevant work., Comment: 3 pages Revtex, Some typos removed and the manuscript reorganized

Schwarzschild coordinates (r,t) fail to describe the region within the event horizon (EH), (r <= 2 M), of a Black Hole (BH) because the metric coefficients exhibit singularity at r=2 M, and the radial geodesic of a particle appears to be null (ds^2 =0) when actually it must be timelike (ds^2 >0), if, indeed, r_g =2 M >0. Thus, both the exterior and the interior regions of BHs are described by singularity free Kruskal-Szekeres coordinates. However, we show that, in this case too, ds^2= 0 for r=2M. And this result can be physically reconciled only if the EH coincides with the central singularity or if the mass of Schwarzschild black holes M= 0. This conclusion agrees with the result of our following paper (astro-ph/9904163) which points out that the Oppenheimer-Snyder paper showing formation of a BH, too, corresponds to a BH of mass M=0. It means that Schwarzschild singularity and the central singularity are synonymous, and there is no spacetime beneath the EH. Hence the concept of ``White Holes'' and ``Other Universes'' suggested by the Kruskal diagram naturally ceases to exist. We insist that our derivation is straightforward and there is no scope for any ambiguity, any reader may be able to verify it. The proper time for formation of a zero mass BH may be seen to be infinite. Therefore at any finite epoch there would not be any BH. On the other hand, there would be such eternally collapsing configurations with arbitrary high but finite surface red-shifts. If accretion onto such collapsing configurations is advection dominated, there would be little radiation output. Observationally, such collapsing configurations may be identified as ``Black Holes''., Comment: 5 pages using Revtex, evaluates Kruskal derivative and shows that metric become null at Event Horizon, implying zero mass BH

The only instance when the General Relativistic (GTR) collapse equations have been solved (almost) exactly to explicitly find the metric coefficients is the case of a homogeneous spherical dust (Oppenheimer and Snyder in 1939 in Phy. Rev. 56, 455). The equation (37) of their paper showed the formation of an event horizon for a collapsing homogeneous dust ball of mass M in that the circumference radius the outermost surface, r_b = r_0= 2M in a proper time proportional to r_0^{-1/2} in the limit of large Schrarzschild time t= infinity. But Eq.(37) was approximated from the Eq. (36) whose essential character is t = log (y+1/y-1), where, at the boundary of the star y=r_b/ r_0 = r_b /2 M. And since the argument of a logarithmic function can not be negative, one must have y >= 1 or 2M/r_b <= 1. This shows that, atleast, in this case (i) trapped surfaces are not formed, (ii) if the collapse indeed proceeds upto r=0, we must have M=0, and (iii) proper time taken for collapse =infinity. Thus, the gravitational mass of OS black holes are unique and equal to zero. In the preceding paper (astro-ph/9904162), we assumed the existence of a finite mass BH and studied its properties in terms of Kruskal-Szekeres coordinates. And we showed that the radial geodesic of a material particle which must be timelike at r=2M, if M >0, actually becomes null. And this independently showed that BHs have unique mass, M=0., Comment: 6 pages using Revtex; graphically analyzes the Oppenheimer-Snyder paper to show that the resulting BH has zero mass

If the cores of Galaxies and AGNs comprise Supermassive Stars (SMSs) (Hoyle and Fowler 1963), nuclear energy generation may not be ignited for masses $M > 6\times 10^4 M_\odot$, and highly supermassive stars are likely to generate their luminosity, $L_{KH}$ slow gravitational contraction. We show that for such massive Newtonian SMSs, both the value of $L_{KH}$ and the the accretion luminosity, $L_{acc}$, could be much less than the appropriate Eddington value. Such highly SMSs will have a surface density as low as $10^{-14}$ g/cm$^3$ and they will not behave like a compact object with a ``hard surface'. For all such reasons, it is indeed possible to have $L_{SMS} \ll L_{ed}$. And this effect may be incorrectly interpreted as the evidence for the existence of central Super Massive Black Holes with Event Horizons. In fact, in a very detailed work, and from various angles, we have recently shown that, the General Theory of Relativity does not permit the occurrenes of ``trapped surfaces'' and Black Holes (Mitra 1998a, gr-qc/9810038)., Comment: Preliminary draft of paper to be presented in the 19th Texas Symp, 4 pages, additional e-address: mitra_abhas@hotmail.com

We exploit the fact that General Theory of Relativity (GTR) predicts the existence of compact objects having surface gravitational redshift z_s < =z_c=0.615 when the Equation of State (EOS) has the stringest general constraint that the speed of sound c_s < = 0.57 c. This z_c can be occur if a Neutron Star (NS) has a mass of ~2 M (solar) and radius ~8 Km, as is allowed by most of the existing EOSs. Thus massive spherical stars can indeed collapse to such (more compact) NSs. We have shown that the efficiency for production of electron-positron pairs out of the annihilation of resulting neutrino-antineutrino burst rises dramatically with the value of z_c and can saturate to ~40%. This may explain a gamma ray burst of energy as high as ~5. 10**53 erg. By using the already existing detailed (Newtonian) calculations, it follows that the neutrino heating driven mass loss should be negligible, and the bulk Lorentz factor of the initial fireball could be ~1000. Most of the existing supernova calculations also show that it is extremely difficult to simulate the direct neutrino driven mass loss, and, the shock is not launched if the gravitational field becomes stronger. Since the gravitation potential well of the more compact NS is indded very deep, we do not expect additional baryonic mass ejection. So, without invoking any exotic physics (like strange stars) or overstretching any theory, we may explain most of the luminous GRBs in this simple model., Comment: Extensively revised folowing referee comments. Emphasized that an UCO is nothing but a NS with somewhat more mass and smaller radius as allowed by existing EOSs and GTR. Pointed out that baryonic pollution could be negligible, It may explain all luminous GRBs recorded so far (5. 10**53 erg) which are suggested to be spherical by late afterglow observations, except probably GRB990123

We derive here the expression for the accretion luminosity, $L(\infty)$, as seen by a distant inertial observer $S_\infty$, for the case of spherical accretion onto a static compact object having a surface gravitational red-shift $z_x$. It is found that the ``efficiency'' for conversion of mass energy into accretion energy is given by $\epsilon = z_x/(1+z_x)$. And since the maximum value of $z_x$ permitted by General Theory of Relativity (GTR) is 2, the maximum theoretical value of the accretion efficiency is 66.66%., Comment: 4 pages using revtex, submitted to Annals of Physics