Browsing by Author "Govender, Megandren."

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Dissipative gravitating systems.
(2011) Fleming, Darryl.; Govender, Megandren.; Maharaj, Sunil Dutt.
In this thesis we investigate the effect of shear on radiating stars undergoing gravitational collapse. The interior spacetime is described by the most general spherically symmetric line element in the absence of rotation. The energy momentum tensor for the stellar interior is taken to be an anisotropic fluid with heat flux. The thermodynamics of a relativistic fluid is reviewed for the Eckart and causal theories. Since the star is radiating energy to the exterior in the form of a radial heat flux, the atmosphere is described by Vaidya's outgoing solution. We provide the matching conditions required for the continuity of the momentum flux across the boundary, which determines the temporal evolution junction conditions for the metric functions. We provide a general method to obtain shearing solutions of the Einstein field equations describing a radiating, collapsing sphere. A particular exact solution satisfying the boundary condition and field equations is found. The validity of this specific model is investigated by employing a causal heat transport equation which yields the temperature profile within the stellar core. The energy conditions are studied and yield interesting features of this particular model which are absent in the shear-free case.
Dynamics of dissipative gravitational collapse.
(2008) Naidu, Nolene Ferrari.; Maharaj, Sunil Dutt.; Govender, Megandren.
In this study we generate the matching conditions for a spherically symmetric radiating star in the presence of shear. Two new exact solutions to the Einstein held equations are presented which model a relativistic radiating sphere. We examine the role of anisotropy in the thermal evolution of a radiating star undergoing continued dissipative gravitational collapse in the presence of shear. Our model was the first study to incorporate both shear and pressure anisotropy, and these results were published in 2006. The physical viability of a recently proposed model of a shear-free spherically symmetric star undergoing gravitational collapse without the formation of a horizon is investigated. These original results were published in 2007. The temperature profiles of both models are studied within the framework of extended irreversible thermodynamics.
New solutions for a radiating star.
(2018) Zitha, Vusi Monde.; Maharaj, Sunil Dutt.; Govender, Megandren.
On the physical viability of horizon-free collapse.
(2014) Ntshangase, Mlungisi Alex Doctor.; Govender, Megandren.; Govinder, Keshlan Sathasiva.
The so-called Cosmic Censorship Conjecture has drawn widespread attention amongst astrophysicists and particle physicists. In particular, the end-state of gravitational collapse of a bounded matter distribution is a source of much debate with the discovery of naked singularities resulting from the continued gravitational collapse of reasonable matter distributions. One of the first attempts at investigating the final outcome of gravitational collapse of a stellar object was undertaken by Oppenheimer and Snyder in 1939. Their model was highly idealised and focussed on a dust sphere contracting under its own gravity. With the discovery of the Vaidya solution, it became possible to model stars emitting energy to the exterior spacetime. In this dissipative model, the exterior spacetime is nonempty and the collapsing stellar body is enveloped by a zone of null radiation. The smooth matching of the interior spacetime to the Vaidya exterior was achieved by Santos in 1985. It was then possible to model radiating stars undergoing gravitational collapse. The energy momentum tensor for the interior stellar fluid was modelled on more realistic physics and was extended to include heat flux, neutrino transport, shear, pressure anisotropy, bulk viscosity and the electromagnetic field. It has been shown that the collapse of reasonable matter distributions always lead to the formation of a black hole in the absence of shear or in the case of homogeneous densities. In this study we investigate a radiating stellar model proposed by Banerjee et al (BCD model) in which the horizon is never encountered. The interior matter distribution is that of an imperfect fluid with heat flux and the exterior spacetime is described by the radiating Vaidya metric. Our approach is more general than the one proposed by Banerjee et al as they fix the gravitational potentials for the interior line element by making ad-hoc assumptions. A consequence of their model is that it undergoes horizon–free collapse. We start off with the fact that the horizon never forms throughout the collapse process. This restricts the gravitational behaviour of the model. We utilise the boundary condition to determine the temporal evolution of the model. As a result, we obtain new collapsing models in which the horizon never forms. In order to investigate the physical viability of our generalised BCD model we analyse the luminosity profile and the temperature profiles within the framework of extended irreversible thermodynamics. We highlight interesting physical features of our results.
Radiating solutions with heat flow in general relativity.
(1994) Govender, Megandren.; Hughes, Arthur R. W.; Maharaj, Sunil Dutt.
In this thesis we model spherically symmetric radiating stars dissipating energy in the form of a radial heat flux. We assume that the spacetime for the interior matter distribution is shear-free. The junction conditions necessary for the matching of the exterior Vaidya solution to an interior radiating line element are obtained. In particular we show that the pressure at the boundary of the star is nonvanishing when the star is radiating (Santos 1985). The junction conditions, with a nonvanishing cosmological constant, were obtained. This generalises the results of Santos (1985) and we believe that this is an original result. The Kramer (1992) model is reviewed in detail and extended. The evolution of this model depends on a function of time which has to satisfy a nonlinear second order differential equation. We solve this differential equation in general and thereby completely describe the temporal behaviour of the Kramer model. Graphical representations of the thermodynamical and gravitational variables are generated with the aid of the software package MATHEMATICA Version 2.0 (Wolfram 1991). We also analyse two other techniques to generate exact solutions to the Einstein field equations for modelling radiating stars. In the first case the particle trajectories are assumed to be geodesics. We indicate how the model of Kolassis et al (1988) may be extended by providing an ansatz to solve a second order differential equation. In the second case we review the models of de Oliveira et al (1985, 1986, 1988) where the gravitational potentials are separable functions of the spatial and temporal coordinates.
Relativistic astrophysical models of perfect and radiating fluids.
(2019) Mewalal, Narenee.; Hansraj, Sudan.; Govender, Megandren.
Abstract available in PDF file.
Relativistic thermodynamics of radiating stars.
(2016) Bogadi, Robert Sacha.; Govender, Megandren.; Maharaj, Sunil Dutt.
In this research, on the topic of relativistic thermodynamics of radiating stars, the following three case studies are investigated: Gravitational collapse in spacially isotropic coordinates { The nature of a dissipative collapse process of a spherically symmetric star which has been perturbed into a dynamical state from an initial static con guration is studied. The collapse process involves dissipation of energy in the form of a radial heat flux. The perturbation in the density and pressure profi les are such that the star is always close to hydrostatic equilibrium. The temperature profi les are studied using a causal heat transport equation. Radiating collapse in the presence of anisotropic stresses { The effect of anisotropic stresses are investigated for a collapsing fluid sphere dissipating energy in the form of a radial flux. The collapse process starts from an initial static sphere described by the Bowers and Liang solution, and then proceeds until the time of formation of the horizon. We fi nd that the surface redshift increases as the stellar fluid moves away from isotropy. The evolution of the temperature pro les is analysed by employing a causal heat transport equation of the Maxwell-Cattaneo form. Both the Eckart and causal temperatures are enhanced by anisotropy at each interior point of the stellar con guration. The influence of an equation of state during radiative collapse { A linear equation of state is imposed on a static con guration which undergoes radiative gravitational collapse. Various values of the equation of state parameter allow descriptions of di erent matter content from classical stars to dust and also dark energy stars. The physical parameters are shown to behave in a meaningful and realistic manner.
Thermal evolution of radiation spheres undergoing dissipative gravitational collapse.
(2014) Reddy, Kevin Poobalan.; Govender, Megandren.; Maharaj, Sunil Dutt.
In this study we investigate the physics of a relativistic 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. We first consider a particular exact solution found by Thirukkanesh et al [1] which is expanding, accelerating and shearing. By employing a causal heat transport equation of the Maxwell-Cattaneo form we show that the shear leads to an enhancement of the core stellar temperature thus emphasizing that relaxational effects cannot be ignored when the star leaves hydrostatic equilibrium. We also employ a perturbative scheme to study the evolution of a spherically symmetric stellar body undergoing gravitational collapse. The Bowers and Liang [2] static model is perturbed, and its subsequent dynamical collapse is studied in the linear perturbative regime. We find that anisotropic effects brought about by the differences in the radial and tangential pressures enhance the perturbations to the temperature, and that causal and non–causal cases yield identical profiles.