scholarly journals Radiating stars with composite matter distributions

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Sunil D. Maharaj ◽  
Byron P. Brassel
Keyword(s):  
Boundary Condition ◽  
Radiation Field ◽  
Spherical Geometry ◽  
Higher Dimensions ◽  
Junction Conditions ◽  
Matter Distribution ◽  
Radiating Stars ◽  
Radiating Star ◽  
Composite Distribution ◽  
Null String

AbstractIn this paper we study the junction conditions for a generalised matter distribution in a radiating star. The internal matter distribution is a composite distribution consisting of barotropic matter, null dust and a null string fluid in a shear-free spherical spacetime. The external matter distribution is a combination of a radiation field and a null string fluid. We find the boundary condition for the composite matter distribution at the stellar surface which reduces to the familiar Santos result with barotropic matter. Our result is extended to higher dimensions. We also find the boundary condition for the general spherical geometry in the presence of shear and anisotropy for a generalised matter distribution.

scholarly journals Radiating composite stars with electromagnetic fields

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
Sunil D. Maharaj ◽  
Byron P. Brassel
Keyword(s):  
Charge Distribution ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
External Observer ◽  
Composite Field ◽  
Special Cases ◽  
Radiating Star ◽  
Special Case ◽  
Internal Charge ◽  
Null String

AbstractWe derive the junction conditions for a general spherically symmetric radiating star with an electromagnetic field across a comoving surface. The interior consists of a charged composite field containing barotropic matter, a null dust and a null string fluid. The exterior atmosphere is described by the generalised Vaidya spacetime. We generate the boundary condition at the stellar surface showing that the pressure is determined by the interior heat flux, anisotropy, null density, charge distribution and the exterior null string density. A new physical feature that arises in our analysis is that the surface pressure depends on the internal charge distribution for generalised Vaidya spacetimes. It is only in the special case of charged Vaidya spacetimes that the matching interior charge distribution is equal to the exterior charge at the surface as measured by an external observer. Previous treatments, for neutral matter and charged matter, arise as special cases in our treatment of composite matter.

scholarly journals Some analytic models of plane symmetric radiating collapse

2017 ◽  
Vol 95 (1) ◽  
pp. 65-68 ◽  
Author(s):  
G. Abbas ◽  
Hassan Shah ◽  
Zahid Ahmad
Keyword(s):  
Thermal Behavior ◽  
Analytical Solutions ◽  
Adiabatic Index ◽  
Junction Conditions ◽  
Matter Distribution ◽  
Field Equations ◽  
Plane Symmetric ◽  
Symmetric Source ◽  
The Stability ◽  
Analytic Models

This paper deals with the analytical solutions of the field equations in the presence of radiating plane symmetric source. For this purpose we have solved the field equations as well as junction conditions by imposing the conformal flatness conditions. The effective adiabatic index (that determines the stability of the system) has been calculated for the present radiating source. It has been found that effective adiabatic index remains invariant throughout the matter distribution. To study the thermal behavior of the source, we have discussed the thermal profile of the source and found that in the absence of dissipation from the system the temperature of the system remains constant.

scholarly journals Charged radiating stars with Lie symmetries

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
G. Z. Abebe ◽  
S. D. Maharaj
Keyword(s):  
Electromagnetic Field ◽  
Differential Equations ◽  
Equations Of State ◽  
Lie Symmetries ◽  
Boundary Equation ◽  
Symmetries Of Differential Equations ◽  
Radiating Stars ◽  
Barotropic Equation ◽  
Radiating Star ◽  
General Relativistic

Abstract We consider the general model of an accelerating, expanding and shearing radiating star in the presence of charge. Using a new set of variables arising from the Lie symmetries of differential equations we transform the boundary equation into ordinary differential equations. We present several new exact models for a charged gravitating sphere. A particular family of solution may be interpreted as a generalised Euclidean star in the presence of the electromagnetic field. This family admits a linear barotropic equation of state. In the uncharged limit, we regain general relativistic stellar models where proper and areal radii are equal, and its generalisations. Our group theoretical approach selects the physically important cases of Euclidean stars and equations of state.

scholarly journals Embedding with Vaidya geometry

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
A. V. Nikolaev ◽  
S. D. Maharaj
Keyword(s):  
Equation Of State ◽  
Euclidean Space ◽  
Mass Function ◽  
Energy Conditions ◽  
Dimensional Euclidean Space ◽  
De Sitter ◽  
Radiating Star ◽  
Theory Of Gravity ◽  
Null String ◽  
Vaidya Metric

Abstract The Vaidya metric is important in describing the exterior spacetime of a radiating star and for describing astrophysical processes. In this paper we study embedding properties of the generalized Vaidya metric. We had obtained embedding conditions, for embedding into 5-dimensional Euclidean space, by two different methods and solved them in general. As a result we found the form of the mass function which generates a subclass of the generalized Vaidya metric. Our result is purely geometrical and may be applied to any theory of gravity. When we apply Einstein’s equations we find that the embedding generates an equation of state relating the null string density to the null string pressure. The energy conditions lead to particular metrics including the anti/de Sitter spacetimes.

scholarly journals A perturbative approach to the time-dependent Karmarkar condition

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Megandhren Govender ◽  
Wesley Govender ◽  
Kevin P Reddy ◽  
Sunil D Maharaj
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Gravitational Collapse ◽  
Time Dependent ◽  
Perturbative Approach ◽  
Radial Heat ◽  
Radiating Star ◽  
Static Regime ◽  
Radial Heat Flux ◽  
Static Core

AbstractIn 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.

scholarly journals NON-SPHERICAL COLLAPSE OF A RADIATING STAR

2003 ◽  
Vol 12 (02) ◽  
pp. 317-323 ◽  
Author(s):  
S. G. GHOSH ◽  
D. W. DESHKAR
Keyword(s):  
Junction Conditions ◽  
Local Conservation ◽  
Plane Symmetric ◽  
Spherical Collapse ◽  
Radial Heat Flow ◽  
Conservation Of Momentum ◽  
Radial Heat ◽  
Vaidya Solution ◽  
Radiating Star ◽  
Physical Quantities

We study the junction conditions for non-spherical (plane symmetric) collapsing radiating star consisting of a shearing fluid undergoing radial heat flow with outgoing radiation. Radiation of the system is described by plane symmetric Vaidya solution. Physical quantities relating to the local conservation of momentum and surface red-shift are also obtained.

scholarly journals Inhomogeneous and Radiating Composite Fluids

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1400
Author(s):  
Byron P. Brassel ◽  
Sunil D. Maharaj ◽  
Rituparno Goswami
Keyword(s):  
Energy Conditions ◽  
Type I ◽  
System Of Equations ◽  
Type Ii ◽  
Matter Distribution ◽  
Relativistic Fluids ◽  
Barotropic Fluid ◽  
Gravitating Systems ◽  
Type Ii Fluid ◽  
Null String

We consider the energy conditions for a dissipative matter distribution. The conditions can be expressed as a system of equations for the matter variables. The energy conditions are then generalised for a composite matter distribution; a combination of viscous barotropic fluid, null dust and a null string fluid is also found in a spherically symmetric spacetime. This new system of equations comprises the energy conditions that are satisfied by a Type I fluid. The energy conditions for a Type II fluid are also presented, which are reducible to the Type I fluid only for a particular function. This treatment will assist in studying the complexity of composite relativistic fluids in particular self-gravitating systems.

scholarly journals Charged anisotropic spherical collapse with heat flow

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Kali Charan ◽  
Om Prakash Yadav ◽  
B. C. Tewari
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Gravitational Collapse ◽  
Energy Conditions ◽  
Junction Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Radiating Star ◽  
Large Round ◽  
High Degree

AbstractIn this article, we study the shear-free gravitational collapse of a charged radiating star. The Einstein field equations of gravitational collapse for the charged stars are known to give rise to a high degree of non-linearity in the ordinary differential equation coming from junction conditions. The attempts to solve it analytically proved to be unfortunate. Numerical methods have been suggested in the past. However, the high degree of non-linearity tends to introduce fluctuations and large round off errors in the numerical calculation. A new ansatz is proposed in the present work to reduce the degree of non-linearity. An ordinary differential equation is derived by satisfying junction conditions, and its numerical solution is demonstrated. Physical quantities associated with the collapse process are plotted to observe the effect of charge on these quantities. It is concluded that the charge can delay the collapse of a star and can even prevent it depending upon the amount of charge. It is also verified that the solution satisfies all the energy conditions.

A GENERALIZED VACUOLE MODEL IN HIGHER DIMENSIONS

2003 ◽  
Vol 12 (06) ◽  
pp. 1035-1045
Author(s):  
A. BANERJEE ◽  
S. CHATTERJEE
Keyword(s):  
Exact Solution ◽  
Frequency Shift ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Boundary Surface ◽  
Blue Shift ◽  
Higher Dimensions ◽  
Junction Conditions ◽  
Higher Dimensional ◽  
Arbitrary Dimensions

We extend to higher dimensions a recent work of Bonnor, which generalizes the Einstein–Straus model utilizing the inhomogeneous Tolman–Bondi universe in place of the homogeneous Friedmann one. Following Israel's junction conditions, the criteria of matching between the higher dimensional Schwarzschild-like interior and the Tolman–Bondi-like exterior is obtained. We also give a new exact solution for a five-dimensional TB type of metric and use it to study the dynamical behavior of the vacuole boundary. Furthermore the transformation relations which transform the inhomogeneous TB metric to the homogeneous Friedmann model are explicitly given for any arbitrary dimensions. The frequency shift of radiation coming from the boundary surface is calculated and it is found that, depending on initial conditions both redshift and blue-shift are possible for an expanding vacuole. This is at variance with Bonnor's result where only redshift is possible under similar situation. It is also observed that higher dimensional models are less stable against perturbation than the usual 4D ones.

scholarly journals A Study of the Irradiation of Secondaries of Algol Binaries

1989 ◽  
Vol 107 ◽  
pp. 343-343
Author(s):  
A. Gimenez ◽  
A. Claret
Keyword(s):  
Boundary Condition ◽  
Radiation Field ◽  
Model Atmosphere ◽  
External Radiation ◽  
Numerical Oscillations ◽  
Effects Of Irradiation On ◽  
Upper Boundary

In order to investigate the effects of irradiation on the spectra of the cooler components of Algol binaries, a modified version of the Upsalla Model Atmosphere code (U.M.A.) has been used. The upper boundary condition was changed to take into account the external radiation field and an automatic procedure to prevent numerical oscillations was introduced. In order to simulate the external flux from the hot component we have used the Kurucz grid interpolated for the wavelenghts adopted in U.M.A. code. Since secondary stars of Algoltype binaries normally have deep convective layers, we impose the condition that the entropy of these zones must be the same in the irradiated and in the non-irradiated models.

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