A perturbative approach to the time-dependent Karmarkar condition

In this work we employ a perturbative approach to study the gravitational collapse of a shear-free radiating star. The collapse proceeds from an initial static core satisfying the time-independent Karmarkar condition and degenerates into a quasi-static regime with the generation of energy in the form of a radial heat flux. The time-dependent Karmarkar condition is solved together with the boundary condition to yield the full gravitational behaviour of the star. Our model is subjected to rigorous regularity, causality and stability tests.

The influence of some design parameters on the heat transfer in thermal fuel flowmeter

The article analyzes the influence, relationship and value of design parameters of the heat flow meter on its radial and axial heat fluxes in the tube (tube diameter, heater diameter and their ratio, thermal conductivity of the tube material, etc.). It is shown that at the stage of choosing the design parameters of the flowmeter it is necessary to take into account the influence of its radial heat flux on the axial one. The influence of radial heat flux in the flowmeter tube on the error of fuel loss measurement is substantiated. Analytical dependences which allow to define an axial heat stream are resulted, their analysis concerning influence of flowmeter tube constructive parameters on heat transfer is carried out. Measures are planned and recommendations are developed for the choice of design flowmeter parameters, development or use, provided that the influence of radial heat flow on the axial is reduced, which will reduce the total error of fuel consumption measurement. Regarding the choice of design parameters of heat meters while reducing the error of measuring fuel consumption, it is shown that the maximum possible decrease in the diameter of the heater and increase the diameter of the flow tube reduce the impact of radial heat flow on the axial and thus reduce the total fuel consumption error. Numerical ratios of tube diameter to flowmeter heater diameter for different thermal conductivities of tube materials are given under the condition of minimal influence on fuel consumption measurement error. For tube materials with a thermal conductivity 0.16… 0.25 W / (m ∙ K) (ebonite, fluoroplastic F-5, etc.) the tube diameters ratio and the heater should be within 1.51… 1.62, and for materials with more high thermal conductivity (thermal conductivity greater than 14.9 W / (m ∙ K)), this ratio should be equal to 1.99.

Dissipative collapse of a Karmarkar star

In this paper, we employ the Karmarkar condition to model a spherically symmetric radiating star undergoing dissipative gravitational collapse within the framework of classical general relativity. The collapse ensues from an initial static core satisfying the Karmarkar condition in isotropic coordinates and proceeds nonadiabatically by emitting energy in the form of a radial heat flux to the exterior Vaidya spacetime. We show that the dynamical nature of the collapse is sensitive to the initial static configuration that inherently links the embedding to the final remnant. Our model considered several physical tests on how an initially static stellar structure onset to a radiative collapse.

Collapse and expansion of plane symmetric charged anisotropic source

In this paper, we have investigated the final evolutionary stages of charged non-static plane symmetric anisotropic source. To this end, we have solved the Einstein–Maxwell field equations with the charged plane symmetric source. We have found that vanishing of radial heat flux in the gravitating source provides the parametric form of the metric functions. The new form of the metric functions can generate a class of physically acceptable solutions depending on the choice parameter. These solutions may be classified as expanding or collapsing solutions with the particular values of generating parameter. The gravitational collapse in this case ends with the formation of single apparent horizon while there exists two such horizons in the case of charged spherical anisotropic source.

The influence of an equation-of-state during radiative collapse

We study the role played by an equation-of-state during gravitational collapse of a radiating star. Starting from an initially static matter configuration obeying a linear equation-of-state, the star loses hydrostatic equilibrium and undergoes dissipative collapse in the form of a radial heat flux. We show that the equation-of-state parameter plays an important role in determining the temperature profiles of the collapsing body.

THE ROLE OF SHEAR IN DISSIPATIVE GRAVITATIONAL COLLAPSE

In this paper, we investigate the physics of a radiating star undergoing dissipative collapse in the form of a radial heat flux. Our treatment clearly demonstrates how the presence of shear affects the collapse process; we are in a position to contrast the physical features of the collapsing sphere in the presence of shear with the shear-free case. By employing a causal heat transport equation of the Maxwell–Cattaneo form we show that the shear leads to an enhancement of the core temperature thus emphasizing that relaxational effects cannot be ignored when the star leaves hydrostatic equilibrium.

NONADIABATIC SPHERICAL COLLAPSE WITH A TWO-FLUID ATMOSPHERE

In this paper, we present an exact model of a spherically symmetric star undergoing dissipative collapse in the form of a radial heat flux. The interior of the star is matched smoothly to the generalized Vaidya line element representing a two-fluid atmosphere comprising null radiation and a string fluid. The influence of the string density on the thermal behavior of the model is investigated by employing a causal heat transport equation of Maxwell–Cattaneo form.