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.

GRAVITATIONAL COLLAPSE OF SPHERICALLY SYMMETRIC ANISOTROPIC FLUID WITH HOMOTHETIC SELF-SIMILARITY

2003 ◽  
Vol 12 (07) ◽  
pp. 1315-1332 ◽  
Author(s):  
C. F. C. BRANDT ◽  
M. F. A. DA SILVA ◽  
JAIME F. VILLAS DA ROCHA ◽  
R. CHAN
Keyword(s):  
Physical Properties ◽  
Gravitational Collapse ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Tangential Pressure

We study spacetimes of spherically symmetric anisotropic fluid with homothetic self-similarity. We find a class of solutions to the Einstein field equations by assuming that the tangential pressure of the fluid is proportional to its radial one and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of these solutions are studied and found that some of them represent gravitational collapse of an anisotropic fluid.

scholarly journals Behaviour of the Kramer Radiating Star

1997 ◽  
Vol 50 (5) ◽  
pp. 959 ◽  
Author(s):  
S. D. Maharaj ◽  
M. Govender
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Nonlinear Differential Equation ◽  
Special Functions ◽  
Second Order ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Exterior Solution ◽  
Order Nonlinear Differential Equation ◽  
Radiating Star

We study the behaviour of the model for a radiating star proposed by Kramer. The evolution of the model is governed by a second order nonlinear differential equation. The general solution of this equation is expressed in terms of elementary and special functions. This completes the solution of the Einstein field equations for the interior of the star. The model matches smoothly to the Vaidya exterior solution and the condition p = qB is satisfied at the boundary. We briefly study the thermodynamics of the model and indicate the difficulty in specifying the temperature explicitly.

Non-adiabatic gravitational collapse in f(R,T) gravity with Karmarkar condition for anisotropic fluid

2020 ◽  
Vol 35 (13) ◽  
pp. 2050103 ◽  
Author(s):  
Riaz Ahmed ◽  
G. Abbas
Keyword(s):  
Gravitational Collapse ◽  
Coupling Parameter ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Interior Solution ◽  
Spatial Presence ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Radiating Star

In this paper, we have used the Karmarkar condition to the spherically symmetric non-static radiating star experiencing dissipative gravitational collapse with a heat flux in the framework of [Formula: see text] gravity, (where [Formula: see text] is Ricci scalar which replaces Lagrangian density and [Formula: see text] is the trace of energy–momentum tensor). To obtain the ultimate results of the gravitational field equations in [Formula: see text] scenario, we take a linear form of the function as [Formula: see text]. In this connection, the Karmarkar condition along with boundary condition generates a model of radiating star and enables us to completely indicate the spatial presence of gravitational potentials. Vadiya’s exterior solution across a time-like hypersurface is smoothly matched to the interior solution which allows to study the physical conduct of our model under consideration. Furthermore, we have analyzed the energy conditions of radiating star in [Formula: see text] gravity and analyzed the physical behavior of thermodynamics parameters which provide a detailed discussion of the model. For coupling parameter [Formula: see text], we successfully obtain the standard results of General Relativity.

scholarly journals GRAVITATIONAL COLLAPSE OF SELF-SIMILAR AND SHEAR-FREE FLUID WITH HEAT FLOW

2003 ◽  
Vol 12 (03) ◽  
pp. 347-368 ◽  
Author(s):  
R. CHAN ◽  
M. F. A. DA SILVA ◽  
JAIME F. VILLAS DA ROCHA
Keyword(s):  
Heat Flow ◽  
Gravitational Collapse ◽  
Energy Conditions ◽  
Free Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Spherical Shells ◽  
Naked Singularities ◽  
Self Similar

A class of solutions to Einstein field equations is studied, which represents gravitational collapse of thick spherical shells made of self-similar and shear-free fluid with heat flow. It is shown that such shells satisfy all the energy conditions, and the corresponding collapse always forms naked singularities.

RADIATING COLLAPSE WITH VANISHING WEYL STRESSES

2005 ◽  
Vol 14 (03n04) ◽  
pp. 667-676 ◽  
Author(s):  
S. D. MAHARAJ ◽  
M. GOVENDER
Keyword(s):  
Irreversible Thermodynamics ◽  
Temperature Profiles ◽  
Junction Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Extended Irreversible Thermodynamics ◽  
Recent Approach ◽  
Dust Solution ◽  
Limiting Case

In a recent approach in modeling a radiating relativistic star undergoing gravitational collapse the role of the Weyl stresses was emphasized. It is possible to generate a model which is physically reasonable by approximately solving the junction conditions at the boundary of the star. In this paper we demonstrate that it is possible to solve the Einstein field equations and the junction conditions exactly. This exact solution contains the Friedmann dust solution as a limiting case. We briefly consider the radiative transfer within the framework of extended irreversible thermodynamics and show that relaxational effects significantly alter the temperature profiles.

Relativistic modeling of Vela X-1 using the Karmarkar condition

2019 ◽  
Vol 34 (20) ◽  
pp. 1950157 ◽  
Author(s):  
Satyanarayana Gedela ◽  
Ravindra K. Bisht ◽  
Neeraj Pant
Keyword(s):  
Neutron Star ◽  
Physical Properties ◽  
Exact Solutions ◽  
Density Ratio ◽  
Stellar Model ◽  
Energy Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Parametric Class ◽  
Surface Redshift

The objective of this work is to explore a new parametric class of exact solutions of the Einstein field equations coupled with the Karmarkar condition. Assuming a new metric potential [Formula: see text] with parameter (n), we find a parametric class of solutions which is physically well-behaved and represents compact stellar model of the neutron star in Vela X-1. A detailed study specifically shows that the model actually corresponds to the neutron star in Vela X-1 in terms of the mass and radius. In this connection, we investigate several physical properties like the variation of pressure, density, pressure–density ratio, adiabatic sound speeds, adiabatic index, energy conditions, stability, anisotropic nature and surface redshift through graphical plots and mathematical calculations. All the features from these studies are in excellent conformity with the already available evidences in theory. Further, we study the variation of physical properties of the neutron star in Vela X-1 with the parameter (n).

scholarly journals THERMAL EVOLUTION OF A RADIATING ANISOTROPIC STAR WITH SHEAR

2006 ◽  
Vol 15 (07) ◽  
pp. 1053-1065 ◽  
Author(s):  
N. F. NAIDU ◽  
M. GOVENDER ◽  
K. S. GOVINDER
Keyword(s):  
Heat Flux ◽  
Relaxation Time ◽  
Heat Dissipation ◽  
Thermal Evolution ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Pressure Anisotropy ◽  
Radiating Star ◽  
Anisotropic Star

We study the effects of pressure anisotropy and heat dissipation in a spherically symmetric radiating star undergoing gravitational collapse. An exact solution of the Einstein field equations is presented in which the model has a Friedmann-like limit when the heat flux vanishes. The behavior of the temperature profile of the evolving star is investigated within the framework of causal thermodynamics. In particular, we show that there are significant differences between the relaxation time for the heat flux and the relaxation time for the shear stress.

ANISOTROPIC SELF-SIMILAR COSMOLOGICAL MODEL WITH DARK ENERGY

2006 ◽  
Vol 15 (07) ◽  
pp. 991-999 ◽  
Author(s):  
P. R. PEREIRA ◽  
M. F. A. DA SILVA ◽  
R. CHAN
Keyword(s):  
Dark Energy ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Accelerating Universe ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Normal Matter ◽  
Self Similar

We study space–times having spherically symmetric anisotropic fluid with self-similarity of zeroth kind. We find a class of solutions to the Einstein field equations by assuming a shear-free metric and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of the solutions are studied and we find that it can be considered as representing an accelerating universe. At the beginning all the energy conditions were fulfilled but beyond a certain time (a maximum geometrical radius) none of them is satisfied, characterizing a transition from normal matter (dark matter, baryon matter and radiation) to dark energy.

GRAVITATIONAL COLLAPSE OF THICK DOMAIN WALLS: AN ANALYTIC MODEL

1994 ◽  
Vol 09 (39) ◽  
pp. 3605-3609 ◽  
Author(s):  
ANZHONG WANG
Keyword(s):  
Domain Wall ◽  
Gravitational Collapse ◽  
Gravitational Radiation ◽  
Domain Walls ◽  
Analytic Model ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Pp Wave ◽  
Thick Domain Walls ◽  
Spacelike Infinity

An exact solution to the Einstein field equations is found, which represents the gravitational collapse of a thick domain wall. During the collapse, the wall emits gravitational radiation, which can be measured as a gravitational pp wave at the spacelike infinity. The time-reversed solution represents an expanding universe, in which a domain wall resides. It is shown explicitly that such a wall can be inflated away.

Analysis of compact stars in logarithmic-corrected R2 gravity

2019 ◽  
Vol 35 (02) ◽  
pp. 1950354 ◽  
Author(s):  
M. Farasat Shamir ◽  
Iffat Fayyaz
Keyword(s):  
Graphical Representation ◽  
Stellar Model ◽  
Compact Stars ◽  
Energy Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Logarithmic Corrections ◽  
Proposed Model ◽  
Physical Tests ◽  
Surface Redshift

We discuss the existence of compact stars in the context of [Formula: see text] gravity model, where additional logarithmic corrections are assumed. Here, [Formula: see text] is the Ricci scalar and [Formula: see text], [Formula: see text] are constant values. Further, the compact stars are considered to be anisotropic in nature, due to the spherical symmetry and high density. For this purpose, we derive the Einstein field equations by considering Krori–Barua spacetime. For our proposed model, the physical acceptability is verified by employing several physical tests like the energy conditions, Herrera cracking concept and stability condition. In addition to this, we also discuss some important properties such as mass–radius relation, surface redshift and the speed of sound are analyzed. Our results are compared with observational stellar mass data, namely, 4U 1820-30, Cen X-3, EXO 1785-248 and LMC X-4. The graphical representation of obtained solutions provide strong evidences for more realistic and viable stellar model.

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