S D Maharaj
Articles written in Pramana – Journal of Physics
Volume 61 Issue 3 September 2003 pp 493-499
A charged spherically symmetric solution
K Moodley S D Maharaj K S Govinder
We find a solution of the Einstein-Maxwell system of field equations for a class of accelerating, expanding and shearing spherically symmetric metrics. This solution depends on a particular
Volume 66 Issue 2 February 2006 pp 313-324
A new algorithm for anisotropic solutions
We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic gravitational potential; and the integration can be completed exactly for particular isotropic seed metrics. A good feature of our approach is that the anisotropic solutions necessarily have an isotropic limit. We find two examples of anisotropic solutions which generalise the isothermal sphere and the Schwarzschild interior sphere. Both examples are expressed in closed form involving elementary functions only.
Volume 68 Issue 6 June 2007 pp 881-889 Research Articles
The role of pressure anisotropy on the maximum mass of cold compact stars
S Karmakar S Mukherjee S Sharma S D Maharaj
We study the physical features of a class of exact solutions for cold compact anisotropic stars. The effect of pressure anisotropy on the maximum mass and surface red-shift is analysed in the Vaidya–Tikekar model. It is shown that maximum compactness, red-shift and mass increase in the presence of anisotropic pressures; numerical values are generated which are in agreement with observation.
Volume 72 Issue 3 March 2009 pp 481-494 Research Articles
Generalized isothermal models with strange equation of state
We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein–Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal Universe. We show that the mass corresponds to the values obtained previously for quark stars when anisotropy and charge are present.
Volume 77 Issue 3 September 2011 pp 405-405
S D Maharaj K Pereira D P Mason
Volume 77 Issue 3 September 2011 pp 461-468
We obtain a class of solutions to the Einstein–Maxwell equations describing charged static spheres. Upon specifying particular forms for one of the gravitational potentials and the electric ﬁeld intensity, the condition for pressure isotropy is transformed into a hypergeometric equation with two free parameters. For particular parameter values we recover uncharged solutions corresponding to speciﬁc neutron star models. We ﬁnd two charged solutions in terms of elementary functions for particular parameter values. The ﬁrst charged model is physically reasonable and the metric functions and thermodynamic variables are well behaved. The second charged model admits a negative energy density and violates the energy conditions.
Volume 77 Issue 3 September 2011 pp 469-476
Temperature evolution during dissipative collapse
S D Maharaj G Govender M Govender
We investigate the gravitational collapse of a radiating sphere evolving into a ﬁnal static conﬁguration described by the interior Schwarzschild solution. The temperature proﬁles of this particular model are obtained within the framework of causal thermodynamics. The overall temperature evolution is enhanced by contributions from the temperature gradient induced by perturbations as well as relaxational effects within the stellar core.
Volume 77 Issue 3 September 2011 pp 477-482
We investigate the role of symmetries for charged perfect fluids by assuming that spacetime admits a conformal Killing vector. The existence of a conformal symmetry places restrictions on the model. It is possible to ﬁnd a general relationship for the Lie derivative of the electromagnetic ﬁeld along the integral curves of the conformal vector. The electromagnetic ﬁeld is mapped conformally under particular conditions. The Maxwell equations place restrictions on the form of the proper charge density.
Volume 81 Issue 4 October 2013 pp 557-567 Research Articles
Incompressible Einstein–Maxwell fluids with specified electric fields
S Hansraj S D Maharaj T Mthethwa
The Einstein–Maxwell equations describing static charged spheres with uniform density and variable electric field intensity are studied. The special case of constant electric field is also studied. The evolution of the model is governed by a hypergeometric differential equation which has a general solution in terms of special functions. Several classes of exact solutions are identified which may be considered as charged generalizations of the incompressible Schwarzschild interior model. An analysis of the physical features is undertaken for the uniform case. It is demonstrated that uniform density spheres with constant electric field intensity are not realizable with isotropic pressures. This highlights the necessity of studying the criteria for physical admissability of gravitating spheres in general relativity which are solutions to the Einstein–Maxwell equations.
Volume 86 Issue 1 January 2016 pp 49-58
Thermal evolution of the Kramer radiating star
M Govender S D Maharaj L Mkhize D B Lortan
The Kramer radiating star uses the interior Schwarzschild solution as a seed solution to generate a model of dissipative collapse. We investigate the thermal behaviour of the radiating star by employing a causal heat transport equation. The causal temperature is explicitly determined for the first time by integrating the transport equation. We further show that the dissipation of energy to the exterior space-time renders the core more unstable than the cooler surface layers.
Volume 94, 2020
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