arXiv subjects

Abhas Mitra

Publications and source records attributed to Abhas Mitra.

At least 55 records · Page 3Linked to original sources

arXiv2000

Non-occurrence of trapped surfaces and Black Holes in spherical gravitational collapse: An abridged version

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.

astro-ph↗

arXiv2000

General Relativistic Collapse of Neutron Stars to Strange Stars: A Mechanism for Gamma Ray Bursts

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 $ν-\barν$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.

astro-ph↗

arXiv2000

Cosmic Acceleration: A Natural Remedy For Horizon and Flatness Problems

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.

physics.gen-ph↗

arXiv2000

Comments on the paper ``Polarimetric Constraints on the Optical Afterglow Emission from GRB 990123'' by Hjorth et al. (Science, 26 1999)

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 <= π/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.

astro-ph↗

arXiv1999

Towards the Final State of Spherical Gravitational Collapse and Likely Source of Gamma Ray Bursts

We invoke the global properties of the actual GTR field equations for spherical collapse to directly show that the condition for formation of trapped surfaces, 2GM/R >1 is not allowed by GTR. And therefore all singularity theorems based on the assumption of formation of trapped surfaces are invalidated! Our conclusion is in perfect agreement with Einstein's intuitive idea that a Sch. like surface can not occur in reality. Further as singularity is approached R ->0, in order that 2GM/R <= 1, we must have M ->0! Harrison, et al. had also pointed out that collapse should come to a decisive end with M=0. This is possible in GTR if the fluid radiates its entire original mass-energy during the relentless graviatational contraction process, Q->M c^2! Since the actual efficiency for gamma ray production by the relevant blast wave may hardly exceed 10-20% and there could be a stronger (undetected) nu-anti-nu burst precding GRBs, the actual energy released for GRB 990123, even accounting for probable weak beaming, or for GRB 971214 (unbeamed) could be ~10^{54-55} erg. And such energy release may not be properly accountable without realizing that trapped surfaces are indeed not formed. All authors concerned with this subject, and particularly those, who would like to differ with our derivation are requested to send their criticism either directly or express the same openly for a healthy scientific discussion.

astro-ph↗

arXiv1999

Kruskal Dynamics For Radial Geodesics. I

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.

gr-qc↗

arXiv1999

Comment on ``Velocity at the Schwarzschild Horizon Revisited'' by I. Tereno

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.

astro-ph↗

arXiv1999

Final Comments on ``Another view on the velocity at the Schwarzschild horizon'' by Tereno

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.

astro-ph↗

arXiv1999

Why General Theory of Relativity Allows the Existence of Only Extremal Black Holes

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.

hep-th↗

arXiv1999

Kruskal Coordinates and Mass of Schwarzschild Black Holes

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''.

astro-ph↗

arXiv1999

The Mass of the Oppenheimer-Snyder Black Hole

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.

astro-ph↗

arXiv1999

A Model for Most Luminous and Long Duration Cosmic Gamma Ray Bursts

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.

astro-ph↗

arXiv1999

Non-occurrence of Trapped Surfaces and Black Holes in Spherical Gravitational Collapse

We point out that although the pioneering work of Oppenheimer and Snyder (OS), technically, indicated the formation of an event horizon for a collapsing homogeneous dust ball of mass $M_b$ and radius $R_b$, the Eqs. (32) and (36) of their paper actually demand that no trapped surface is formed $ 2GM_b/ R_b c^2 \le 1$, and $M_b \equiv 0$! Anybody may verify it. Further, by analyzing the general inhomogeneous dust solutions of Tolman in a proper physical perspective, we show that, all dust solutions are characterized by $M_b=0$. Next, for a collapsing fluid endowed with radiation pressure, we discover that the collapse equations obey the same Global Constraint $2GM /R c^2 \le 1$ and which specifically shows that, contrary to the traditional intuitive Newtonian idea, which equates the gravitational mass ($M_b$) with the fixed baryonic mass ($M_0$), the trapped surfaces are not allowed in general theory of relativity (GTR). For continued collapse, the final gravitational mss $M_f \to 0$ as $R\to 0$. Thus we confirm Einstein's and Rosen's idea that Event Horizons and Schwarzschild Singularities are unphysical and can not occur in Nature. This, in turn, implies that, if there would be any continued collapse, the initial gravitational mass energy of the fluid must be radiated away $Q\to M_i c^2$. This also implies that, gravitational collapse of massive stars should give rise to Ultra Compact Objects and emission of energy much more than what is obtained in Supernova Events

gr-qc↗

arXiv1998

On the Nature of the Compact Objects in the AGNs

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).

astro-ph↗

arXiv1998

Maximum Accretion Efficiency in General Theory of Relativity

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 $ε= z_x/(1+z_x)$. 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%.

astro-ph↗

arXiv1998

On the true energy budget of GRB970508 and 981214

We emphasize a that since GRB970508 released an energy of Q_g~10^{51} Ωergs in soft gamma rays alone, the actual energy of the e^+e^- p FB driving the blast wave could be considerably higher than this value, Q_{FB} >Q_g. For reasonably large values of Ω, as is probably suggested by the radio observations, the value of Q_{FB} ~ 5.10^{51}~t_m^3~n_1 erg, for GRB970508; here t_m is the epoch in months when the associated radio-blastwave degrades to become mildly relativistic. We discuss that it is unlikely that this energy, Q_{FB}~sim 10^{53}erg was liberated by the central engine by a direct electromagnetic mode. On the other hand, as conceived by several previous authors and as is suggested by supernova theories, their FB driving the blast wave is likely to be preceded by a much stronger neutrino burst: ν+ anti ν- e^+ +e^-. Although, the efficiency for pair production by this latter route is usually found to be as low as ~.001, we point out that for very high values of neutrino energy release Q_ν>Q_{FB}, it is possible that, its value increses substantially. By considering that, the value of $Q_{FB}$ for such GRBs is indeed ~sim 10^{53} erg, we envisage that the energy of the actual neutrino burst/wind could be as high as ~ 10^{54-55} erg. This energy might be had from general relativistic collapse of a massive stellar core having INITIAL gravitational mass, say, M_i~ few~M_sun to a stage having a potential well much deeper than what is present on a canonican neutron star surface. Accordingly, we predict that the new generation large nu elescopes may detect neutrino burst of energy ~10^{54-55} ergs, with neutrino energies touching ~ 1 GeV, in coincidence with GRBs.

astro-ph↗

arXiv1998

Comments on the paper ``Bare Quark Surfacees of Strange Stars and Electron-Positron Pair Emission''

In a recent paper (Ushov, PRL, 80, 230, 1998), it has been claimed that the bare surface of a strange star can emit electron-positron pairs of luminosity \~10^{51} ergs/s for about 10s. If true, obviously, this mechanism may explain the origin of cosmic Gamma Ray Bursts. However, we point out that such a mechanism is does not work because (i) if pair production really occurs the supposed pre-existing supercritical electric field will be quenched and this discharge process may at best release ~10^{24} ergs of electromagnetic energy, and (ii) there is no way by which the trapped core thermal energy of few 10^{52} ergs can be transmitted electromagnetically on a time scale of ~10s or even on a much larger time scale. The only way the hot core can cool on a time scale of ~10 s or much shorter is by the well known process of emission of nu-antinu pairs.

astro-ph↗

arXiv1998

Constraining the Magnetic Field in Gamma Ray Burst Blast Waves

We point out that the already existing literature on relativistic collisionless MHD shocks show that the parameter sigma= upstream proper magnetic energy density/upstream rest mass energy density, plays an important role in determining the structure and accelerating properties of such shocks. By adopting a value of sigma= 0.002 which corresponds to the relativistic shock associated with the Crab nebula, and by using appropriate relativistic shock jump conditions, we obtain here a generous upper-limit on the value of (proper) the magnetic field, B ~ 1.5 10^{-3} eta n^{1/2} G, for gamma ray burst (GRB) blast wave. Here, eta= E/Mc^2, where E is the energy and M is the mass of the baryons entrained in the original fireball (FB), and n is the proper number density of the ambient medium. Further, we point out that, in realistic cases, the actual value B could be as low as 5 10^{-6} eta n^{1/2} G. for realistic cases.

astro-ph↗