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In this talk, we address the issue of gravitational collapse in electromagnetic theory. For this purpose, we adopt two approaches one by assuming charged perfect fluid in the interior of a star and another by studying the dynamics of thin shell of matter on the surface of a charged star. The cylindrically symmetric charged perfect fluid collapse is explored by assuming that charged perfect fluid is moving along geodesics in the interior of cylinder. In this case, the analytic solution of the Einstein-Maxwell field equations represents gravitational collapse.  We formulate general dynamical equations using Israel thin shell formalism in charged background which helps to investigate gravitational collapse of scalar field and polytropic matter thin shell. In massless case, we find that scalar shell either expands to infinity or collapses to a point forming a curvature singularity.  Also, the massive scalar field shell can exhibit the bouncing behavior. It is found that expanding and collapsing polytropic matter as well as perfect fluid shell comes to rest, then re-expands to infinity or re-collapses to a point. The charged perfect fluid collapse with positive cosmological constant is investigated in Friedmann model. We find marginally bound solution in this case. Also, the formation of apparent horizons is discussed. The end state of charged perfect fluid gravitational collapse in both models has been found as a black hole.

We investigate the cylindrical gravitational collapse with an anisotropic non-dissipative fluid by considering the appropriate geometry of the interior and exterior spacetimes. We matched collapsing fluid to an exterior containing gravitational waves. It is shown that the radial pressure is vanishing on the hypersurface.

Thermal radiations from spherically symmetric black holes have been studied from the point of view of quantum tunneling. In this work we extend this approach to study radiation of fermions from charged and rotating black strings. Using WKB approximation and Hamilton-Jacobi method we work out the tunneling probabilities of incoming and outgoing fermions and find the correct Hawking temperature for these objects. We show that in appropriate limits the results reduce to those for the uncharged and non-rotating black strings.

The universe is becoming stranger by the day and now it is looking as if the dark energy may have been negative in the past. If “proved” this will be a very important twist in the tale and one that will require some new ideas if a consistent theoretical explanation are to be sought.  Causal Set theory, a quantum gravity candidate theory, already has a natural explanation for the magnitude of the dark energy without any fine tuning. The same model can explain a change in the sign of the dark energy as well. I will discuss the model and both these aspects in some detail.

Ricci flow is at the center of geometric analysis and has been used to prove the Poincare conjecture. It has also been found to have profound links to physics via the Renormalization group flow. The talk will explore the first non-trivial connection between Ricci flow equations and the Einstein equations. In particular it will show that solutions of the Einstein equations with scalar-matter sources correspond to Ricci solitons (self-similar solutions of the flow) in one higher dimension and will provide explicit examples with co dimension-two maximal symmetry. To generate more complete, non-singular examples of Ricci solitons, it will then revisit Ricci-flat solutions of two commuting hypersurface orthogonal Killing vector fields (which in Lorentzian signature are the axially symmetric static vacuum solutions) and present a new algebraic method of generating new one-parameter family of solutions from old ones.

Radiation belt science has several enigmatic issues among which are the yet unexplained electron acceleration in the million electron Volt (MeV) energy range.  An extensive data set of Relativistic Electron-Proton Tele-scope (REPT) on board the Radiation Belt Storm Probe (RBSP) is studied for the 28 June, 2013 electron acceleration event. Phase space density is first determined for 2.30 MeV particles from measured integral flux and then calculated for the appropriate energy that conserves the first adiabatic invariant. It is shown that the time dependent radial profile of phase space density supports the local acceleration mechanism.

The energy density of the universe is proportional to the Ricci scalar curvature in the dynamical Chern-Simon (CS) modified gravity. In this paper, we consider the Amended Friedman-Robertson-Walker (AFRW) universe and explore its scale factor and the Ricci Dark Energy. These turned out to be well-defined and definite. We compare the scale factors of FRW, Generalized Chaplygin gas (GCG) and AFRW models graphically. The combined graph of these models show that the behavior of both FRW and AFRW models is similar as these overlap each other for choosing particular values of the integration constants. Also, we draw a combined graph of the Ricci dark energy densities of FRW and AFRW models, in CS gravity, and the energy density of GCG. It shows that the densities of former two models are increasing with time while the energy density of GCG is decreasing.

The paper is devoted to explore the Killing vectors of Bertotti-Robinson metrics I and II by using two different sets of tetrad in the context of teleparallel theory of gravity. For this purpose, we consider diagonal and non-diagonal tetrad fields of the said metrics and solve the teleparallel version of the Killing equations. It is shown that the two sets of tetrad give different results. The comparison of the results with already available, in literature, in the context of General Relativity is given.

Superluminal propagation of neutrinos is investigated. A tachyonic Dirac equation is developed, which shows that tachyons propagate in the Euclidean space. Lorentz invariance is achieved by the introduction of new gamma matrices as the consequence of superluminal Dirac equation. Charge density, current density and Hamiltonian appeared with a negative sign. These observations and solution of the superluminal Dirac equation leads towards the statement that “superluminal fermions are actually the anti-fermions”. Same technique guided the existence of superluminal bosons.

The Kinetic Theory of non-Maxwellian mode is developed with Orbital Angular Momentum (OAM) states for the un-magnetized plasmas. The Laguerre-Gaussian (LG) mode function is considered to model the modified non-Maxwellian dielectric function to study of Landau wave particle interaction.

In this work we studied the decay spectrum of bound muon in and beyond the standard model. In case of free muon decay in standard model, it is well known that due to the momentum conservation the maximum energy attained by the final state emitted electron is half of the muon mass. However, in the bound muon case the nucleus absorbs the three momentum of the emitted electron and hence it can have energy equal to the muon mass. This bound state nature changes the shape of the decay spectrum. Like-wise, we have also studied the binding effects in muon decay to electron and majoron. It is found that the future µ "e conversion experiments may be able to produce bounds on the µ "ej rates which are comparable with the ones from direct searches.

We study the Hard Wall AdS/QCD model, the simplest model of bottom up approach to AdS/QCD. We reveal the relation between the fields in the model and operators in QCD, fix parameters of model and calculate several quantities of interest. We underline the problems of the model and proposed the way to solve them.

Differential Equations play a significant role in mathematical modeling of physical problems in applied sciences from atoms to star. In this talk Linearization and its connection with Lie algebras will be discussed. Moreover their applications for Scalar ODEs will be discussed. Furthermore the extension of this approach for systems of ODEs will be discussed in details. Physical examples will be discussed to illustrate this approach.

In this paper, we construct spherically symmetric thin-shell wormholes in the scenario of Born-Infeld electrodynamics theory. We take the modified Chaplygin gas for the description of exotic matter around the wormhole throat. The stability of static wormholes with different values of charge and Born-Infeld parameter is investigated. We compare our results with those obtained for generalized Chaplygin gas and conclude that stable static wormhole solutions also exist even for large value of Born-Infeld parameter.

As an approach to explain the current accelerated expansion of the universe, there exists a way of modifying gravity at a long distance. In this presentation, among such gravity theories, we concentrate on extended teleparallel gravity called “F(T) gravity'', where T is the torsion scalar in teleparallelism. We discuss various cosmological aspects of F(T) gravity including the evolution of the equation of state for the universe, finite-time future singularities, thermodynamics, and a four-dimensional effective F(T) gravity theory coming from the higher-dimensional Kaluza-Klein (KK) and Randall-Sundrum (RS) theories.

In this talk, we will discuss the effects of some physical factors on the inhomogeneity of self-gravitating system filled with imperfect matter.

In the Einstein-Maxwell-complex vector field theory with negative cosmological constant, we build a holographic model of p-wave superconductor. We find that the charged vector condenses via a second order phase transition both in the black hole and AdS soliton background. Depending on two parameters, the mass and charge of the vector field, we find a rich phase structure: zeroth order, first order and second order phase transitions can happen in this model. We also find "retrograde condensation" in which the hairy black hole solution exists only for the temperatures above a critical value with the free energy much larger than the black hole without hair. We construct the phase diagram for this system in terms of the temperature and chemical potential. When an external magnetic field appears, it is found that the background magnetic field can induce the condensate of the vector field even in the case without chemical potential/charge density. In the case with non-vanishing charge density, the transition temperature rises with the applied magnetic field, and the condensate of the charged vector operator forms a vortex lattice structure in the spatial directions perpendicular to the magnetic field.

In this study, we derive the Noether gauge symmetries of a canonical Lagrangian for somegravity theories. To get the appropriate equations of motion in the considered theory of gravity, we set up an effective point-like Lagrangian in terms of its configuration space variables and their velocities. Using this effective Lagrangian, we calculate and classify Noether gauge symmetry generators. Furthermore, we give conservation laws admitted by Lagrangians for representing physical system.

We investigate the hydrostatic equilibrium of stellar structure by taking into account the modified Lane'-Emden equation coming out from f(R)-gravity. Such an equation is obtained in metric approach by considering the Newtonian limit of f(R)-gravity, which gives rise to a modified Poisson equation, and then introducing a relation between pressure and density with polytropic index n. The modified equation results an integro-differential equation, which, in the limit of General Relativity becomes the standard Lane'-Emden equation. We find the radial profiles of gravitational potential by solving for some values of n. The comparison of solutions with those coming from General Relativity shows that they are compatible and physically relevant. This analysis gives rise to unstable modes not present in the standard Jeans analysis (derived assuming Newtonian gravity as weak filed limit of f(R) =R). In this perspective, we discuss several self-gravitating astrophysical systems whose dynamics could be fully addressed in the frame work of f(R)-gravity.

The gravitational bending of light by celestial bodies is a "most curious" effect, yielding rare transient events. Given that it probes mass, it provides us with an unparalleled opportunity to study populations of faint or dark objects over a mass range spanning nine decades from black holes, neutron stars, and white dwarfs over brown dwarfs and planets, down to satellites. With emerging technology and new instruments, we are just on the verge of fully exploiting this tremendous potential for pushing the frontier of astronomical exploration at several fronts.

On astrophysical scales, quantum plasmas are found naturally in dense end-stage stars, for instance white dwarfs and neutron stars. Similarly quantum plasma effects are notable in high energy density matter and next generation laser-dense target interaction experiments. Rapidly increasing attention has been noted in the past decade in quantum plasmas due to their potential applications in various important physical systems.

Pair plasma (broadly known as Electron-positron (EP) plasma) is a class of plasmas with equal mass and absolute charge which is believed to having existed abundantly in early universe. Such plasmas are ubiquitous in many astrophysical environments, e.g., in the bipolar outflows (jets) in active galactic nuclei in the interior of accretion disks surrounding black holes, in the magnetospheres of pulsars and neutron stars, polar regions of neutron stars, at the center of Milky Way galaxy, and so on. Such plasmas of astrophysical origin particularly in neutron stars are highly degenerate and ultra-dense.

The aim of the present work is to study the low frequency (lower than the electron cyclotron frequency for electron mode and ion cyclotron frequency for ion mode) electrostatic and electro- magnetic modes in a dense and highly degenerate EP as well as warm EPI plasmas. We emphasize the dispersive and degeneracy effects, ion weak thermal effects as well as the properties of such modes when magnetic field is enormously high as the case of neutron stars.

The scattering phenomenon of scalar and electromagnetic waves by a spherically symmetric nonrotating Schwarzschild black is considered and presented. We discussed the scattering of electromagnetic wave incident upon a Schwarzschild black hole. By applying the partial wave analysis techniques for the electromagnetic scattering cross section interesting numerical results are obtained that are in good agreement with analytical approximations. In present talk the scattering of electromagnetic waves is compared with the scattering of scalar waves.

This lecture gives a review of the study of symmetry in Einstein's General Theory of Relativity mainly from the global, geometrical viewpoint. Although concentrating mostly on metric (Killing) symmetry, the techniques described are applicable also to homothetic, conformal, projective and affine symmetry together with the symmetries of the curvature tensor and Weyl's conformal and projective tensors and these are briefly described. A discussion will also be given of Killing orbit theory including the possible dimensions and types of such orbits and of the associated isotropies. As examples, these results will be applied to cosmology and plane waves in general relativity. A few brief remarks are given on local symmetry.

We review a recently proposed framework for studying axially symmetric dissipative fluids. Some general results are discussed at the most general level. Next, the shear-free case is considered. It follows in this case that all geodesic and shear-free fluids are irrotational, and as consequence of this, they are also purely electric. Such a result holds for a general fluid (non necessarily perfect). Now, if following Bel we define a state of intrinsic gravitational radiation (at any given point), to be one in which the super-Poynting vector does not vanish for any unit timelike vector, then since the vanishing of the magnetic part of the Weyl tensor implies the vanishing of the super-Poynting vector, it is clear that when looking for gravitationally radiating sources (at least under the geodesic condition) we should consider shearing fluids. Therefore as a further step to the understanding of gravitationally radiating sources, we shall next discuss the simplest fluid distribution compatible with a non-vanishing super-Poynting vector, namely: perfect fluid under the geodesic condition. Two cases are clearly differentiated: with and without vorticity. In the latter case, explicit expressions for the scalars defining the magnetic part of the Weyl tensor are found, but no gravitational radiation is expected. The purely magnetic subcase is analyzed in some detail. The case with non-vanishing vorticity is expected to produce gravitational radiation, and is also considered in detail, some specific models are found.

In this paper we investigate Noether symmetries of Bianchi type V spacetimes. Our study is mainly divided into three main parts. (a) First we carry out complete classification of Bianchi type V spacetimes using Lie algebra of Noether symmetries. (b) Then we employ Noether's theorem to obtain conservation laws in each case and discuss their analytical properties. (c) Lastly we give a brief comparison of their Noether symmetry algebras, conformal Killing vectors, homotheties, Weyl and Ricci collineation.

In this paper we study the dynamics of scalar field thin shell in a string cloud background. We formulate equation of motion using Israel junction conditions. The corresponding effective potentials and scalar fields are evaluated numerically for massless and massive cases.

It is an empirical fact based on solar physics of sunspots, that our sun and generally stars are spinning gravitational sources for bodies in orbit in any such solar system. Thus, a planetary  theory for the gravitational field of a star or a satellite dynamics around a (spinning) planet-including the problem of artificial satellites- should in principle, take into account the possible effect of axial symmetry. But to the best of our knowledge, existing formalisms of gravitation physics do not address the problem of spin referred to above. This paper proposes the following strategy to handle this kind of computational physics. Our calculations suggest that this kind of spin should give rise to a slight residual perturbation on constant areal velocity, computed by the standard model of orbital theory. In particular, the second law of planetary motion might require revision. Also, it turns out that the classical result of Kepler is recoverable from our result as a special case.

Role of quantum corrections has been studied during the inflationary era, employed to the Non-Super Symmetric Hybrid models. These correction terms are the result of Yukawa interaction between inflaton field and right handed neutrinos. In contrast to tree level hybrid inflationary (TLHI) model, red tilted spectral index ns is obtained for radiatively corrected hybrid inflationary (RCHI) model, consistent with PLANCK data for sub-Planckian inflaton field. The predicted tensor-to-scalar ratio by RCHI model for sub-Planckian inflaton field lies well below the precision of PLANCK mission to observe primordial gravitational waves.

We discuss the dynamics of a charged particle around slowly rotating Kerr black hole.

We studied some significant characteristics of Hawking’s radiation spectrum as a tunneling phenomenon of charged particles. Hawking radiation effects are investigated by considering charged fermions tunneling through black hole horizon by applying semi-classical approximation to the general covariant Dirac equation. From this process, we evaluate the tunneling probabilities of outgoing charged particles and their corresponding Hawking temperatures.

The work is based on the non-flat geometry which contains the framework of interacting generalized ghost pilgrim dark energy with cold dark matter. Some well-known cosmological parameters (evolution parameter and squared speed of sound) and planes ($\omega_{\Lambda}$-$\omega'_{\Lambda}$ and state finder) are constructed in this scenario. The results of obtained cosmological parameters and planes are compared with present-day observational data.

I will present the proposed satellite eLISA/NGO as an ESA space-based mission to detect gravitational waves from space. I will give an overview of the main scientific goals. In particular, this mission will be able to study in great detail black hole mergers and this way test general relativity in the case of strong gravity to high accuracy. Moreover, it will give a census of black hole masses and spins and distinguish between competing scenarios for the formation and growth of massive black holes through hierarchical merger and accretion.

Stars are formed following the gravitational collapse of cold molecular clouds found in the Universe. As the cloud or portions of it collapses, approximately half of the gravitational energy gained is used to increase the internal temperature of the cloud and the remaining energy is irradiated as electromagnetic radiation in space.

Zero Age Main Sequence (ZAMS) is the time when a star first joins the main sequence on the Hertzsprung-Russell diagram (HR diagram) by burning hydrogen in its core through fusion reactions. After this time, the star enters into a phase of stellar evolution that is quite stable, and steadily processes Hydrogen into higher elements. As a result, the main sequence is a broadband that is displaced slightly from this zero-age strip.

Stars are comparatively easier to analyse than some other astronomical objects because they have simple shapes and structure i.e. spherically symmetric. The stellar model contains four basic first-order differential equations; two represent the variability of the matter and pressure with radius; and other two represent how temperature and luminosity vary with radius.

In our paper, the Statstar code has been used to model ZAMS star of mass. The star is in hydrostatic equilibrium i.e. its size is fixed and the atmosphere, rotation and magnetic field of the star are exempted in this model. We have solved some basic stellar structure equations by assuming star into spherically symmetric mass shells with specified boundary conditions and calculated associated properties of the star such as temperature, pressure, density and opacity in each zone.

Study shows that the temperature and the pressure of the star are higher at the core while the luminosity and opacity of the star is higher at the surface.

Hawking radiation of uncharged and charged scalars/Fermions from accelerating and rotating black holes is studied. We calculate the tunneling probabilities of these particles from the rotation and acceleration horizons of these black holes. Using the tunneling method we recover the correct Hawking temperature as well.

In this paper, we study the qualitative behaviour of a competitive system of second-order rational difference equations. More precisely, we investigate the boundedness character, existence and uniqueness of positive equilibrium point, local asymptotic stability and global stability of the unique positive equilibrium point, and rate of convergence of positive solutions of the system. Some numerical examples are given to verify our theoretical results.