arXiv subjects
Publications and source records attributed to Mofazzal Azam.
Employing Newton's stellar balance equation and using the flat rotation velocity of satellite galaxies, we have found the velocity of sound in the dark matter medium. What is interesting is that the velocity of satellite galaxies is very much larger than the velocity of sound in the dark matter medium. This indicates that there will be shock wave in the dark matter medium due to the supersonic movement of satellite galaxies.
Compact stars such as neutron stars and black holes are gravitationally bound many body systems. We investigate the importance of short and long range part of gravity for such systems. From our analysis, we conclude that the true essence of gravity lies with the long range nature of the interaction. At the end we show how these arguments in the manybody theory consistently leads to Dvali-Gomez picture of a black holes as a collective bound state of long wavelength gravitons.
We consider a spherically symmetric stellar configuration with a density profile $ρ(r)=\frac{c^2}{8πG r^2} $. This configuration satisfies the Schwarzchild black hole condition $\frac {2GM}{c^2 R}=~1$ for every $ r =R $. We refer it as "Planckonion". The interesting thing about the Plankonion is that it has an onion like structure. The central sphere with radius of the Plank-lenght $ L_p=\sqrt{(\frac {2\hbar G}{c^3})}$ has one unit of the Planck-mass $M_p=\sqrt {(\frac {c\hbar}{2G})}$. Subsequent spherical shells of radial width $L_p$ contain exactly one unit of $M_p$. We study this stellar configuration using Tolman-Oppenheimer-Volkoff equation and show that the equation is satisfied if pressure $P(r)=-ρ(r)$. On the geometrical side, the space component of the metric blows up at every point. The time component of the metric is zero inside the star but only in the sense of a distribution (generalized function). The Planckonions mimic some features of black holes but avoid appearance of central singularity because of the violation of null energy conditions.
Superfluid condensation of neutrinos of cosmological origin at a low enough temperature can provide simple and elegant solution to the problems of neutrino oscillations and the accelerated expansion of the universe. It would give rise to a late time cosmological constant of small magnitude and also generate tiny Majorana masses for the neutrinos as observed from their flavor oscillations. We show that carefully prepared beta decay experiments in the laboratory would carry signatures of such a condensation, and thus, it would be possible to either establish or rule out neutrino condensation of cosmological scale in laboratory experiments.
Quantum Eletrodynamics (QED) is considered as the most successful of all physical theories. It can predict numerical values of physical quantities to a spectacular degree of accuracy. However, from the very early days it has been known that, in QED, there are two important problems which are linked with the very foundation of the theory. In 1952, Dyson put forward strong argumnts to suggest that the perturbation seires in quantum electrodynamics can not be convergent. Just three years latter, in 1955, Landau argued that the effective running coupling constant in QED has a pole (Landau singularity) albeit at some very high energy scale. This paper addresses, in details, the question of stability of perturbative vacuum state of QED in the light of these two well known problems. Landau has been a cult-like figure for many of us who studied theoretical physics in the former Soviet Union. As an undergraduate student in the department of theoretical physics of People's Friendship University, Moscow, in 1970's, I grew up hearing colourful stories about the legendary persona of Lev Davidovich from my teachers some of whom had known him at personal level. It is a great honour for me to contribute this article to the Landau centenary volume of "Eletronics Journal of Theoretical Physics".
String theory, as well as the string inspired brane-world models such as the Randall-Sundrum (RS) one, suggest a modification of Newton's law of gravitation at small distance scales. Search for modifications of standard gravity is an active field of research in this context. It is well known that short range corrections to gravity would violate the Newton-Birkhoff theorem. Based on calculations of RS type non-Newtonian forces for finite size spherical bodies, we propose a torsion balance based experiment to search for the effects of violation of this celebrated theorem valid in Newtonian gravity as well as the general theory of relativity. We explain the main principle behind the experiment and provide detailed calculations suggesting optimum values of the parameters of the experiment. The projected sensitivity is sufficient to probe the Randall-Sundrum parameter up to 10 microns.
This paper has been withdrawn by the author because the arguments presented in the paper is incomplete.
The string inspired higher dimensional theories suggest modification of Newton's law at submillimeter length scales. Inter-particle distances in white dwarf and neutron stars are $10^{-10} cms$ and $10^{-13} cms$ respectively, and therefore, the effects of of short distance corrections to gravity deserve investigation. We show, by carrying out explicit analytical many-body calculations that, in the presence of corrections, the normal state of these compact stars become metastable. The actual quantum mechanical ground state of the stars turns out to be unstable. However, the tunneling probability to the unstable ground state is so small that the stars may remain trapped in the metastable state practically for ever.
It has been argued by Dyson that the perturbation series in coupling constant in QED can not be convergent. We find that similiar albeit slightly different arguments lead to the divergence of the series of $1/N_f$ expansion in QED.
Brane-World models suggest modification of Newton's law of gravity on the 3-brane at submillimeter scales. The brane-world induced corrections are in higher powers of inverse distance and appear as additional terms with the Newtonian potential. The average inter-particle distance in white dwarf and neutron stars are $10^{-10} cms$ and $10^{-13} cms$ respectively, and therefore, the effect of submillimeter corrections needs to be investigated. We show, by carrying out simple manybody calculations, that the mass and mass-radius relationship of the white dwarf and neutron stars are not effected by submillimeter corrections. However, our analysis shows that the correction terms in the effective theory give rise to force akin to surface tension in normal liquids.
The perturbative expansion series in coupling constant in QED is divergent. It is either an asymptotic series or an arrangement of a conditionally convergent series. The sum of these types of series depends on the way we arrange partial sums for successive approximations. The $1/N_f$ series expansion, where $N_f$ is the number of flavours, defines a rearrangement of this series, and therefore, its convergence would serve as a proof that the perturbative series is, in fact, conditionallyconvergent.Unfortunately, the $1/N_f$ series also diverges.We proof this usingarguments similar to those of Dyson. We expect that some of the ideas and techniques discussed in our paper will find some use in finding the true nature of the perturbative series in coupling constant as well as the $1/N_f$ expansion series.
In this paper, we argue that the Landau singularity of the coupling constant in QED reflects the instability of vacuum state, in other words the perturbative ground state in QED.We do not have a rigorous mathematical proof. We rather provide strong arguments derived from the theory of stability of matter developed by Lieb et al on the hand and the theory of weakly interacting fermion systems developed by Feldman et al on the other hand.
It is now, generally, believed that the presence of some form of dark matter is essential to explain the flat rotation curves of galaxies, and anomalous large velocities of galaxies in the clusters and superclusters. This dark matter turns out to be too elusive and, so far, there is no direct evidence for such matter although there is a large variety of candidates proposed by theoretical models. One would expect that the existence of vast amount of dark matter would lead to the formation of some dark galaxies or clusters which could be seen by gravitational lensing events.This could serve as a direct evidence for dark matter. However, so far, there is no conclusive lensing event pertaining to that. In spite of absence of any direct evidence, there is a consensus among physicists in favour of some form of non-baryonic dark matter. In this paper, we take a different viewpoint and would like to view dark matter as an emergent phenomenon - very much like many such phenomena known in condensed matter systems. We propose here a novel mechanism involving Voids, which can, in principle give rise to a difference between the gravitational and the inertial mass, and thereby, create effects similar to the dark matter.
We derive an exact equation for simple self non-intersecting Wilson loops in non-abelian gauge theories with gauge fields interacting with fermions in 2-dimensional Euclidean space.
The ultra-low density limit of Saha ionization formula suggests that, in this limit, matter would prefer to remain ionized.This has a very important implication for cosmic structures known as Voids.These are ultra-low density (much less than average density of matter in the Universe) regions in the galactic clusters and superclusters.The ionization formula implies that matter trapped in the Voids should be ionized.Therefore, we expect a very faint radiation glow from the Voids resulting from the motion of the charged particles.
We introduce a metric on the set of all subsets of natural numbers which converts it into a cantor set.On this set endowed with the metric, we introduce a very simple map which exhibits chaotic behaviour.This simple map is almost like a nursery rhyme of chaos.