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.

Dissipative collapse of a Karmarkar star

2020 ◽  
Vol 35 (20) ◽  
pp. 2050164 ◽  
Author(s):  
M. Govender ◽  
A. Maharaj ◽  
Ksh. Newton Singh ◽  
Neeraj Pant
Keyword(s):  
Stellar Structure ◽  
Spherically Symmetric ◽  
Isotropic Coordinates ◽  
Radial Heat ◽  
Radiating Star ◽  
Physical Tests ◽  
Dynamical Nature ◽  
Radial Heat Flux ◽  
Radiative Collapse ◽  
Static Core

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.

scholarly journals RADIATING SPHERICAL COLLAPSE WITH HEAT FLOW

2003 ◽  
Vol 12 (04) ◽  
pp. 667-676 ◽  
Author(s):  
M. GOVENDER ◽  
K. S. GOVINDER ◽  
S. D. MAHARAJ ◽  
R. SHARMA ◽  
S. MUKHERJEE ◽  
...  
Keyword(s):  
Heat Flux ◽  
Simple Model ◽  
Gravitational Collapse ◽  
Temporal Evolution ◽  
Junction Conditions ◽  
X Ray ◽  
Spherical Collapse ◽  
Radial Heat ◽  
Cold Star ◽  
Radial Heat Flux

We present here a simple model of radiative gravitational collapse with radial heat flux which describes qualitatively the stages close to the formation of a superdense cold star. Starting with a static general solution for a cold star, the model can generate solutions for the earlier evolutionary stages. The temporal evolution of the model is specified by solving the junction conditions appropriate for radiating gravitational collapse. The results will be useful in constructing models for the evolution of X-ray pulsars, like Her X-1.

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

2016 ◽  
Vol 26 (07) ◽  
pp. 1750065 ◽  
Author(s):  
M. Govender ◽  
R. S. Bogadi ◽  
S. D. Maharaj
Keyword(s):  
Heat Flux ◽  
Equation Of State ◽  
State Parameter ◽  
Hydrostatic Equilibrium ◽  
Temperature Profiles ◽  
Equation Of State Parameter ◽  
Radial Heat ◽  
Radiating Star ◽  
Radial Heat Flux ◽  
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.

NON-ADIABATIC GRAVITATIONAL COLLAPSE WITH ANISOTROPIC CORE

2007 ◽  
Vol 16 (09) ◽  
pp. 1479-1495 ◽  
Author(s):  
V. O. THOMAS ◽  
B. S. RATANPAL
Keyword(s):  
Heat Flux ◽  
Numerical Methods ◽  
Pressure Distribution ◽  
Gravitational Collapse ◽  
Space Time ◽  
Anisotropic Pressure ◽  
Spherical Distribution ◽  
Isotropic Pressure ◽  
Radial Heat ◽  
Radial Heat Flux

The non-adiabatic gravitational collapse of a spherical distribution of matter accompanied by radial heat flux has been studied on the background of a pseudo-spheroidal space–time. The spherical distribution is divided into two regions: a core consisting of anisotropic pressure distribution and an envelope consisting of isotropic pressure distribution. Various aspects of the collapse have been studied using both analytic and numerical methods.

RADIATING GRAVITATIONAL COLLAPSE WITH SHEAR VISCOSITY AND BULK VISCOSITY

2004 ◽  
Vol 13 (08) ◽  
pp. 1727-1752 ◽  
Author(s):  
P. C. NOGUEIRA ◽  
R. CHAN
Keyword(s):  
Heat Flow ◽  
Viscous Fluid ◽  
Gravitational Collapse ◽  
Bulk Viscosity ◽  
Shear Viscosity ◽  
Outgoing Radiation ◽  
Radial Heat Flow ◽  
Radial Heat ◽  
Radiating Star ◽  
Time Density

A model of a collapsing radiating star consisting of a fluid with shear viscosity and bulk viscosity undergoing radial heat flow with outgoing radiation is studied. This kind of fluid is the most general viscous fluid we can have. The pressure of the star, at the beginning of the collapse, is isotropic but, due to the presence of the shear viscosity and the bulk viscosity, the pressure becomes more and more anisotropic. The radial and temporal behaviors of the density, pressure, mass, luminosity, the effective adiabatic index and the Kretschmann scalar are analyzed. The collapsing time, density, mass, luminosity and Kretschmann scalar of the star do not depend on the viscosity of the fluid (nor the shear viscosity and neither the bulk viscosity).

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