Radiating Collapse Solutions

Exact gravitational solutions with radial pressure and heat flow are obtained by integrating the field equations. Junction conditions which match the collapse solutions to the exterior Vaidya metric show that, at the boundary, the pressure is proportional to the magnitude of the heat flow vector. This condition allows us to determine the time-dependent functions of the interior solutions.     

Inhomogeneous imperfect fluid spherical models without big-bang singularity

So far all known singularity-free cosmological models are cylindrically symmetric. Here we present a new family of spherically symmetric non-singular models filled with imperfect fluid and radial heat flow, and satisfying all the energy conditions. For larget anisotropy in pressure and heat flux tend to vanish leading to a perfect fluid. There is a free function of time in the model, which can be suitably chosen for non-singular behaviour and there exist multiplicity of such choices.     

Some solutions of Einstein's equations with viscous fluids

If we admit the bulk and shear viscosity coefficients to be homogeneous in all the stages of the cosmic evolution and the fact that these can be expressed in terms of the metric coefficients, we obtain some cosmological models that are exact solutions of Einstein's equations. The metric utilized is the one of Szekeres's class II and the curvature source is a viscous fluid without heat flux.     

Radiating star,shear-free gravitational collapse without horizon

We present a new model of dissipative energy fluid without appearance of horizon. The interior matter fluid is shear-free isotropic spherically symmetric and undergoing radial heat flow. The interior metric is matched with Vaidya exterior metric over the boundary. The model obeyed all the relevant physical and thermodynamic conditions. In this model, the collapse begins at infinite past with both infinite mass and radius and contracts to a point as time tends to zero without forming an event horizon.     

A Shearing Non-Adiabatic Solution of Einstein's Equations

An analytical solution of the Einstein's equations is found for a collapsing radiating body, consisting of an isotropic fluid with shear undergoing radial heat flow with outgoing radiation. The behavior of the density, pressure, heat flux, mass and luminosity are analyzed for a body of 6 M⊙. This revised version was published online in July 2006 with corrections to the Cover Date.     

The nonadiabatic general-relativistic stellar oscillations

We have derived the equations which govern the linear nonadiabatic general-relativistic radial oscillations. The perturbation produces a heat flux that is coupled with the geometry, through the Einstein field equations of a stellar configuration. The classical limit is recovered. The stability conditions are examined by means of a simplified one-zone model.     

Non-adiabatic gravitational collapse in higher dimensional space-time and its junctions conditions

Junction conditions are studied at the boundary of a higher dimensional spherical distribution containing an outgoing heat flow and radiation flux. Our analysis extends to higher dimension, an important observation of Santos that for a collapsing fluid with radial heat flow the isotropic pressure on the surface of discontinuity does not vanish. Some physically relevant parameters like luminosity, mass function for the bounded distribution and also the time required for horizon formation are also calculated and it is observed that the dimensionality of space-time does not qualitatively alter the analogous results of the standard space time.     

Dynamics of non-adiabatic charged cylindrical gravitational collapse

This paper is devoted to study the dynamics of gravitational collapse in the Misner and Sharp formalism. We take non-viscous heat conducting charged anisotropic fluid as a collapsing matter with cylindrical symmetry. The dynamical equations are derived and coupled with the transport equation for heat flux obtained from the Müller-Israel-Stewart causal thermodynamic theory. We discuss the role of anisotropy, electric charge and radial heat flux over the dynamics of the collapse with the help of coupled equation.     

Relativistic parametric embedding class I solutions of cold stars in Karmarkar space-time continuum

The aim of this paper is to explore a new parametric class of relativistic solutions to the Einstein field equations describing a spherically symmetric, static distribution of anisotropic fluid spheres to study the behavior of some of the cold stars in the setting of Karmarkar space-time continuum. We develop models of stellar objects for a range of parameter values of n and analyze their behavior through graphical representation. For each of these models, we have found that the metric potentials are well behaved inside the stellar interior and the physical parameters such as density, radial and tangential pressures, red-shift, radial speed, radial pressure density ratio and energy conditions display a continuous decrease from the center to surface of the stars whereas the mass, anisotropy, adiabatic indexes and compactification factor show a monotonous increase which imply that the proposed solution satisfy all the physical aspects of a realistic stellar objects. The stability of the solutions are verified by examining various stability aspects, viz., Zeldovich criteria, causality condition, Bondi condition, equilibrium condition (TOV-equation) and stable static criteria in connection to their cogency.     

Relativistic collapsing radiating stars

A new class of exact solutions of Einstein’s equations is proposed for a collapsing radiating spherically symmetric shear-free isotropic fluid undergoing radial heat flow. In remote past the solutions are static perfect fluid which then gradually starts evolving into radiating collapse. The interior solutions are matched with Vaidya exterior metric over the boundary.     

Shear-free and cavity models with plane symmetry

This paper aims to explore anisotropic planar analytical models for dissipative as well as non-dissipative matter distributions. We relate the Weyl tensor and physical variables of matter distribution. Darmois junction conditions are formulated on internal and external hypersurfaces. It is found that our dissipative models show the presence of cavity with non-zero expansion. Finally, we investigate two types of solutions with zero shear as well as heat flux by a specific choice of the mass function and by restricting pressure.     

Plasma disks around compact objects

Considering the azimuthal velocity fields for different radial dependence we obtain the pressure profiles for the thin disk using the general formalism obtained earlier and further look at the profiles of the luminosity flux function using the approach as given recently by Hanawa (1988). It appears that the profile of this function is not very sensitive to change in ther-dependence of the velocity fields.     

On purely magnetic diagonal Bianchi type VI h cosmologies

A class of purely magnetic diagonal Bianchi type VI _h Cosmologies is investigated. If the energy-momentum tensor is specialized to that of a perfect fluid with (non-zero) heat-flux, with respect to the co-moving fluid 4-velocity, then the only solution is of Bianchi type V and un-physical. Further, it is shown that if certain metric functions are functionally related then the spacetime is conformally flat. Unfortunately, all these results (somewhat indirectly) invalidate a claim by Kumar and Srivastava of finding a non-conformally flat purely magnetic diagonal Bianchi type V cosmology. Finally, we consider non-zero anisotropic pressure in place of non-zero heat flux. It is shown that these spacetimes are necessarily Bianchi type VI ₀. We highlight the fact that there is a known solution that generalizes the purely magnetic perfect fluid Wylleman-Van den Bergh spacetime. Physical properties of this solution are discussed.     

Padé approximant calculations for dispersive,isotropic scattering,homogeneous media

Exact relations for radiation heat flux at the boundaries of a slab with diffusely reflecting boundary conditions and internal source are obtained in terms of the reflection and transmission coefficients of a source free slab with isotropic boundary conditions. The integral equation defining the radiation heat flux contains explicitly the internal source. So, the particular solution for radiative transfer equation is not required. Available exact values for albedos give exact values of radiation heat flux. Padé approximant technique is used to obtain numerical values for homogenous media.     

On radiating stellar collapse with shear

Relativistic models of radiating stellar collapse with shear require careful checking of all the equations and quantities involved. We illustrate this by showing that, in a recently proposed model, the metric ansatz is in fact too restrictive to allow any radial evolution to occur, and only tangential evolution is possible. Furthermore, the assumption of pressure isotropy is shown to reduce the model to the static case without radiation or shear.     

Size and compositional constraints of Ganymede's metallic core for driving an active dynamo

Ganymede has an intrinsic magnetic field which is generally considered to originate from a self-excited dynamo in the metallic core. Driving of the dynamo depends critically on the satellite's thermal state and internal structure. However, the inferred structure based on gravity data alone has a large uncertainty, and this makes the possibility of dynamo activity unclear; variations in core size and composition significantly change the heat capacity and alter the cooling history of the core. The main objectives of this study is to explore the structural conditions for a currently active dynamo in Ganymede using numerical simulations of the thermal history, and to evaluate under which conditions Ganymede can maintain the dynamo activity at present. We have investigated the satellite's thermal history using various core sizes and compositions satisfying the mean density and moment of inertia of Ganymede, and evaluate the temperature and heat flux at the core-mantle boundary (CMB). Based on the following two conditions, we evaluate the possibility of dynamo activity, thereby reducing the uncertainty of the previously inferred interior structure. The first condition is that the temperature at the CMB must exceed the melting point of a metallic core, and the second is that the heat flux through the CMB must exceed the adiabatic temperature gradient. The mantle temperature starts to increase because of the decay of long-lived radiogenic elements in the rocky mantle. After a few Gyr, radiogenic elements are exhausted and temperature starts to decrease. As the rocky mantle cools, the heat flux at the CMB steadily increases. If the temperature and heat flux at the CMB satisfy these conditions simultaneously, we consider the case as capable of driving a dynamo. Finally, we identify the Dynamo Regime, which is the specific range of internal structures capable of driving the dynamo, based on the results of simulations with various structures. If Ganymede's self-sustained magnetic field were maintained by thermal convection, the satellite's metallic core would be relatively large and, in comparison to other terrestrial-type planetary cores, strongly enriched in sulfur. The dynamo activity and the generation of the magnetic field of Ganymede should start from a much later stage, possibly close to the present.     

Effect of Induced Toroidal Rotation on Poloidal Rotation and Ion Heat Conductivity of Tokamak Edge Plasmas

The transport processes in edge (collisional) plasmas of tokamaks with smooth profiles of macroscopic plasma parameters and induced poloidal and toroidal plasma flows, are considered. The toroidal and poloidal velocities of particles, the radial electric field and the ion heat flux are derived. It is shown that forces, induced by radio frequency waves, plasma turbulence or neutral beam injection, can be used to control the poloidal and toroidal plasma velocities, as well as ion heat conductivity, in a wide range of these values.     

Convective flows around sunspot-like objects

Results are given for calculations of convective flows around objects in the outer layers of the Sun that have similar characteristics to small sunspots. These objects are allowed to radiatively (diffusively) exchange heat with their surroundings, but convective motions and exchange are absent. This assumption is based on the simple presumption that a sunspot magnetic field maintains pressure equilibrium with the surrounding medium and prevents convective exchange with that medium.The flow structure around the object, and the question of the overall balance or redistribution of the emerging heat flux as suggested by earlier empirical models, are studied and discussed.After a period of adjustment, shortly after the sunspot-like object is placed into the domain, the layer readjusts itself so that most of the heat flux actually reappears at the surface, although some fraction of the flux is carried horizontally far from the object. There is no indication of long term storage of the heat flux that would normally appear in the place where the object resides. Finally, when the object is removed, the surrounding medium responds very quickly and soon returns to the undisturbed state before the object was in place.The present numerical treatment includes restrictions that may influence aspects of the heat redistribution, convective flows and time scales. In particular, the shape of the object and its size (somewhat smaller than a sunspot) are important, as is the number of spatial dimensions and the treatment of some boundary conditions. Since all of these issues require further investigation, some discussion is presented regarding the applicability of our results to real sunspots.     

Pressure shocks in relativistic viscous heat-conducting fluids

It is shown that thek=0 FRW metric which admits a dust solution in the Brans-Dicke (BD) theory, also admits and imperfect fluid distribution along with an electromagnetic field. The solutions are functions of time and radial coordinates and they satisfy all necessary energy and thermodynamic conditions.     

On the appearance of magnetic flux in the solar photosphere

Ideas and models for the appearance of photospheric magnetic structure are confronted with observational data. Some findings are: The magnetic flux emerging in an active region consists of a bundle of flux tubes which were already concentrated before penetrating into the photosphere. A model of a rising bunch of flux tubes joining into a few strands at larger depths describes the coalescence of spots near the leading and following edges of the active region while more flux may surface near the center of the region. There is no observational evidence for appreciable helical twists in the flux bundles.Throughout the region's lifetime the magnetic elements move coherently, the whole magnetic structure rotates faster than the quiet photosphere. In active regions the convective flow at scales larger than the granulation is arrested by the magnetic structure. The long-lived supergranular cells around spots and in the enhanced network in turn determine the decay properties of spots and facular clusters. The modulation of the convective flow by the magnetic structure explains the slow dispersal of faculae.The hierarchy of magnetic elements (sunspots-pores-knots-facular clusters-facular points) may be explained by a set of magnetostatic flux tube models in the top of the convection zone. The underlying assumptions are that the heat flow along the magnetic field is reduced and that there is no heat exchange across the field except by radiation.A tentative model is proposed to account for the amplification, ascent and emergence of intense flux bundles. The assumptions are: (i) the field is concentrated in toroidal bundles by differential rotation, (ii) in the deep convection zone flux bundles are contained by the external turbulent pressure, and (iii) for field strengths up to the equipartition value efficient lateral heat exchange is possible. After a loop has surfaced radiative cooling and subsequent convective downflow reduce the temperature in the top of the flux tubes which then contract to field strengths well above the local equipartition value. There the heat flow is channelled along the field, which creates the conditions for the magnetostatic flux tube models without requiring a blocking of the heat flow somewhere within the tubes.The paper contains a brief review on the evolution of the magnetic field from the emergence in active regions up to the enigmatic disappearance, and a list of topics for further observational investigation.