Pion condensation of quark matter in a static Einstein universe

In the framework of an extended Nambu–Jona-Lasinio model we study pion condensation in quark matter with an asymmetric isospin composition. We treat this against the gravitational field of a static Einstein universe at finite temperature and chemical potential. This particular choice of the gravitational field configuration enables us to investigate phase transitions of the system with exact consideration of the role of this field in the formation of quark and pion condensates. Also, we point out its influence on the phase portraits. We demonstrate the effect of oscillations of the thermodynamic quantities as functions of the curvature and also refer to a certain similarity between the behavior of these quantities as functions of curvature and finite temperature. Finally, the role of quantum fluctuations for spontaneous symmetry breaking in the case of a finite volume of the universe is briefly discussed.     

Confinement model for quarks

A confinement model of hadron with its constituent quarks bound in a strong gravitational field is presented. The gravitational field plays the role of a medium having, as if, space dependent permeabilities from a fixed centre. The massless Dirac equation modified by the gravitational field is solved. The solution for the wavefunction of the quarks obtained shows the characteristic features of confinement, i.e., (i) wavefunction with higher energy states lying closer to the centre, (ii) equispaced energy levels without continuum, (iii) the quark orbits lying within a distance ∼ 10⁻¹⁴ cm, the characteristic radius of a typical hadron.     

Gravitational Lensing in a Model of Nonlinear Electrodynamics: The Case for Electrically and Magnetically Charged Compact Objects

The astrophysical applicability of the electrically and magnetically charged black hole solutions obtained in a model of nonlinear electrodynamics proposed by Kruglov is investigated. Theoretical calculations of the bending angles and gravitational redshifts from the theory of general relativity are studied numerically by using the stellar data of charged compact objects and a hypothetical quark star model. Calculations have revealed that although the theoretical outcomes differ from the linear Maxwell case, the plotted bending angles coincide with the linear case and it becomes hard to identify the effect of nonlinearity. However, the calculation of the redshift has shown that while the increase in the electric field leads to a decrease in the gravitational redshift,the presence of the strong magnetic field contributes to the gravitational redshift in an increasing manner.     

Non-Spherical Gravitational Collapse of Strange Quark Matter

We study the non-spherical gravitational collapse of the strange quark null fluid. The interesting feature which emerges is that the non-spherical collapse of charged strange quark matter leads to a naked singularity whereas the gravitational collapse of neutral quark matter proceeds to form a black hole. We extend the earlier work of Harko and Cheng [Phys. Lett. A 266 （2000） 249] to the non-spherical case.     

Bounds on Higgs and top quark masses from vacuum stability(degeneracy) with gravitational contributions

Based on the two-loop RGE of standard model gauge, top-Yukawa as well as scalar quartic couplings with full one-loop gravitational contributions in harmonic gauge, we study the constraints on the Higgs and top quark mass from the requirement that the other degenerate vacua at the Planck-dominated region exists. Our numerical calculations show that nature will not develop the other degenerate vacua at the Planck-dominated region with current Higgs and top quark masses. On the other hand, requiring the existence of the other degenerate vacua at the Planck-dominated region will constrain the Higgs and top mass to lie at approximately 130 and 174 Ge V, respectively.     

Non-linear quark theory of spin 2 fields (gravitational mesons). II

An equation for spin 1/2⁺ and 3/2⁺ fermions interacting with a 27-plet of gravitational mesons is derived by the confluence method in the framework of non-linear quark theory of elementary particles. The case of spin 1/2⁺ baryons is examined in detail, and the equation for the baryon octet is derived in the form of an equation for a spinor field in curved space (the Fok-Ivanenko equation). An effective metric is defined by means of the 27-plet of gravitational mesons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 7–11, April, 1973.     

Quark and strange quark matter in f(R) gravity for Bianchi type I and V space-times

Behaviors of quark matter and strange quark matter which exist in the first seconds of the early Universe in f(R) gravity are studied for Bianchi I and V universes. In this respect, we obtain exact solutions of the modified Einstein field equations by using anisotropy feature of Bianchi I and V space-times. In particular, we investigate exact f(R) functions for Bianchi I as the contribution of strange quark and quark matter. Also, we have concluded that quark matter may contribute to the early acceleration of the universe since quark matter behaves like phantom-type dark energy. Furthermore, obtained f(R) solutions represents early eras of the Universe since f(R) solutions for quark matter coincide with f(R) equations for inflation. From this point, we can reach the conclusion that quarks may be source of the early dark energy of the universe or source of little inflation due to their repulsive force.     

A class of exact strange quark star model

Static spherically symmetric space-time is studied to describe dense compact star with quark matter within the framework of MIT Bag Model. The system of Einstein’s field equations for anisotropic matter is expressed as a new system of differential equations using transformations and it is solved for a particular general form of gravitational potential with parameters. For a particular parameter, as an example, it is shown that the model satisfies all major physical features expected in a realistic star. The generated model also smoothly matches with the Schwarzschild exterior metric at the boundary of the star. It is shown that the generated solutions are useful to model strange quark stars.     

Classical quark confinement from general relativity

By assuming covariance of physical laws under (discrete) dilatations, it seems possible to describe strong and gravitational interactions in a unified way. An Einstein-type equation with “cosmological” term is for instance suggested for strong field inside hadrons, which yields - among other things - a classical quark confinement in a very natural way. Further consequences are briefly discussed.     

Spherically symmetric anisotropic and inhomogeneous cosmological models

Spherically symmetric cosmological models filled with dust (pressure-free fluid) content are analyzed. It has been pointed out that these models are anisotropic (of non-vanishing shear) and inhomogeneous (∂p/ρr ≠ 0), the characteristics related directly to the presence of the free gravitational field. It is demonstrated that when the free gravitational field vanishes these models degenerate to the corresponding Friedmann-Robertson-Walker (FRW) models. It is further shown that the energy density of the free gravitational field can be introduced into observational cosmology as a new parameter since it enters into the expansion and deceleration equations, as well as conservation law for total energy, implying that the present Hubble velocity can be reached in a shorter time from the big bang. Finally, the effect of shear on the redshift is also discussed. This paper is dedicated to my teacher Professor V V Narlikar on the occasion of his 81st birthday.     

Dynamics of a gravitational field. I

A dynamic theory of a gravitational field is constructed by analogy with electromagnetic field theory in a two-dimensional space. The main point of this paper is the determination in Einstein spaces of the analogs of inertial and quasiinertial frames of reference in twodimensional space. The possibility is discussed of interpreting the velocity field of the basis of such frames of reference as potentials of the gravitational field. This then permits a dynamic theory of the gravitational field (field equations, energy characteristics) to be constructed in Maxwellian form.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 97–103, May, 1973.In conclusion, I take this opportunity of expressing thanks to Professor V. I. Rodichev for constant attention to the work.     

Influences of the bag constant on properties of hybrid stars

Influences of the bag constant on the properties of hybrid stars are investigated by using relativistic mean field theory and the MIT bag model to describe the hadron phase and quark phase in the interior of neutron stars, respectively. Our results indicate that the onset of hadron-quark phase transition is put off and the appearance of hyperon species is increased with the increase in bag constant. As a result, the hybrid star equation of state for a mixed phase range stiffens whereas that of the quark phase range softens, and the gravitational mass as well as the corresponding radius of hybrid stars are increased obviously. The gravitational mass of a hybrid star is increased from 1.42 Mo (M<,⊙> is solar mass) to 1.63M<,⊙> and the corresponding radius is changed from 9.1 km to 12.2 km when the bag constant (B<'1/4>) is increased from 170 MeV to 200 MeV. It is interesting to find that hybrid star equations of state become non-smooth when the TM2 parameter sets in the framework of relativistic mean field theory used to describe the hadronic matter, and consequently, the third family of compact stars appear in the mass-radius relations of hybrid stars in the narrow scope of the bag constant from 175 MeV to 180 MeV. These show that the choice of the bag constant in the MIT bag model has significant influence on the properties of hybrid stars.     

Critical character of gravitational-wave modulation of electric and magnetic fields in isotropic media

The exactly integrable model of the evolution of electric and magnetic fields in an isotropic dielectric medium under the action of gravitational radiation is analyzed. It is shown that as a result of the action of the gravitational radiation field, the dynamic characteristics of an electromagnetic field as a function of the dielectric constant lose continuity in a neighborhood of the value n=1.V. I. Ul'yanov Lenin Kazan' State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 28–33, September, 1993.     

How black holes form in high energy collisions

Abstract We elucidate how black holes form in trans-Planckian collisions. In the rest frame of one of the incident particles, the gravitational field of the other, which is rapidly moving, looks like a gravitational shock wave. The shock wave focuses the target particle down to a much smaller impact parameter. In turn, the gravitational field of the target particle captures the projectile when the resultant impact parameter is smaller than its own Schwarzschild radius, forming a black hole. One can deduce this by referring to the original argument of escape velocities exceeding the speed of light, which Michell and Laplace used to discover the existence of black holes. Second Award in the 2007 Essay Competition of the Gravity Research Foundation.     

Problems of classical and quantum-gravitational collapse V. (Quantum cosmology. scalar field. continuation)

The study of the system of homogeneous gravitational and scalar fields is continued in the framework o f the formalism of canonical quantization. Solution of de Witt's equation by perturbation theory leads to the prediction of production of scalar matter by a nonstationary quantized gravitational field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 115–118, August, 1977.We are very grateful to V. G. Krechet for stimulating discussions and also to V. R. Khalilov and D. V. Gal'tsov for valuable comments and discussion of the work.     

Asymptotes of the effective potential in an external gravitational field

Renormalization group equations are derived which permit study of the behavior of the quantum theory effective potential of a field in curved space-time. Within the framework of asymptotically free models the asymptotes of the potential are studied for the limit of a strong gravitational field, the limit of large scalar fields, and the composite limit. The conditions for stability of quantum field theory in an external gravitational field are investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 26–32, October, 1985.The authors are indebted to I. V. Tyutin for evaluating the study.     

Analytical properties of the polarization operator and dispersion relations for of a photon in an external non-abelian field

Thresholds of photoproduction of SU(2) color quarks in an external field are determined. Analyticity of the polarization operator in a chromomagnetic field is studied. The dispersion relation for the trace of the polarization operator of a photon with an internal quark loop is derived. M. E. Rasulzade Baku State University; M. V. Lomonosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 11–16, June, 2000.     

Covariant models of energy-information processes induced by the gravitational wave field in open hydro-gasdynamic systems

A covariant approach to the investigation of kinetic subsystems subjected to the action of the hydrodynamic component evolutionizing in the gravitational wave field is formulated. The list of model forces which are a covariant generalization of the well-known classical forces as well as the forces of purely gravitational origin is compiled.V. I. Ul'yanov-Lenin State University, Kazan'. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 79–84, June, 1992.     

Gravitational-wave background as an initiator of longitudinal structure formation in a confined relativistic gas

Exactly integrable models of a confined relativistic gas in the field of a high-intensity gravitational wave are investigated. It is shown that the development of irreversible phenomena and structure formation under the action of modulation of boundary conditions form the principal element of the effect of gravitational waves on physical systems.V. I. Ul'yanov-Lenin University, Kazan'. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 73–78, June, 1992.