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S. D. Maharaj

Publications and source records attributed to S. D. Maharaj.

At least 55 records · Page 3Linked to original sources
arXiv2010

Mixed potentials in radiative stellar collapse

We study the behaviour of a radiating star when the interior expanding, shearing fluid particles are traveling in geodesic motion. We demonstrate that it is possible to obtain new classes of exact solutions in terms of elementary functions without assuming a separable form for the gravitational potentials or initially fixing the temporal evolution of the model unlike earlier treatments. A systematic approach enables us to write the junction condition as a Riccati equation which under particular conditions may be transformed into a separable equation. New classes of solutions are generated which allow for mixed spatial and temporal dependence in the metric functions. We regain particular models found previously from our general classes of solutions.

gr-qc↗
arXiv2010

Gravitating fluids with Lie symmetries

We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means of Lie point symmetries. The method utilised reduces the partial differential equation to an ordinary differential equation according to the Lie symmetry admitted. We show that a class of solutions found previously can be characterised by a particular Lie generator. Several new families of solutions are found explicitly. In particular we find the relevant ordinary differential equation for all one-dimensional optimal subgroups; in several cases the ordinary differential equation can be solved in general. We are in a position to characterise particular solutions with a linear barotropic equation of state.

gr-qc↗
arXiv2009

Charged relativistic spheres with generalized potentials

A new class of exact solutions of the Einstein-Maxwell system is found in closed form. This is achieved by choosing a generalised form for one of the gravitational potentials and a particular form for the electric field intensity. For specific values of the parameters it is possible to write the new series solutions in terms of elementary functions. We regain well known physically reasonable models. A physical analysis indicates that the model may be used to describe a charged sphere. The influence of the electromagnetic field on the gravitational interaction is highlighted.

gr-qc↗
arXiv2009

Some new static charged spheres

We present new exact solutions for the Einstein-Maxwell system in static spherically symmetric interior spacetimes. For a particular form of the gravitational potentials and the electric field intensity, it is possible to integrate the system in closed form. For specific parameter values it is possible to find new exact models for the Einstein-Maxwell system in terms of elementary functions. Our model includes a particular charged solution found previously; this suggests that our generalised solution could be used to describe a relativistic compact sphere. A physical analysis indicates that the solutions describe realistic matter distributions.

gr-qc↗
arXiv2009

Generalised 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 values obtained previously for quark stars when anisotropy and charge are present.

gr-qc↗
arXiv2009

Radiating relativistic matter in geodesic motion

We study the gravitational behaviour of a spherically symmetric radiating star when the fluid particles are in geodesic motion. We transform the governing equation into a simpler form which allows for a general analytic treatment. We find that Bernoulli, Riccati and confluent hypergeometric equations are possible. These admit solutions in terms of elementary functions and special functions. Particular models contain the Minkowski spacetime and the Friedmann dust spacetime as limiting cases. Our infinite family of solutions contains specific models found previously. For a particular metric we briefly investigate the physical features, derive the temperature profiles and plot the behaviour of the casual and acasual temperatures.

gr-qc↗
arXiv2008

Charged anisotropic matter with linear equation of state

We consider the general situation of a compact relativistic body with anisotropic pressures in the presence of the electromagnetic field. The equation of state for the matter distribution is linear and may be applied to strange stars with quark matter. Three classes of new exact solutions are found to the Einstein-Maxwell system. This is achieved by specifying a particular form for one of the gravitational potentials and the electric field intensity. We can regain anisotropic and isotropic models from our general class of solution. A physical analysis indicates that the charged solutions describe realistic compact spheres with anisotropic matter distribution. The equation of state is consistent with dark energy stars and charged quark matter distributions. The masses and central densities correspond to realistic stellar objects in the general case when anisotropy and charge are present.

gr-qc↗
arXiv2008

Nonlinear Shear-free Radiative Collapse

We study realistic models of relativistic radiating stars undergoing gravitational collapse which have vanishing Weyl tensor components. Previous investigations are generalised by retaining the inherent nonlinearity at the boundary. We transform the boundary condition to an Abel equation of the first kind. A variety of nonlinear solutions are generated all of which can be written explicitly. Several classes of infinite solutions exist.

gr-qc↗
arXiv2008

A Riccati equation in radiative stellar collapse

We model the behaviour of a relativistic spherically symmetric shearing fluid undergoing gravitational collapse with heat flux. It is demonstrated that the governing equation for the gravitational behaviour is a Riccati equation. We show that the Riccati equation admits two classes of new solutions in closed form. We regain particular models, obtained in previous investigations, as special cases. A significant feature of our solutions is the general spatial dependence in the metric functions which allows for a wider study of the physical features of the model, such as the behaviour of the causal temperature in inhomogeneous spacetimes.

gr-qc↗
arXiv2008

Classes of exact Einstein-Maxwell solutions

We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein-Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

gr-qc↗
arXiv2007

Analytical models for quark stars

We find two new classes of exact solutions to the Einstein-Maxwell system of equations. The matter content satisfies a linear equation of state consistent with quark matter; a particular form of one of the gravitational potentials is specified to generate solutions. The exact solutions can be written in terms of elementary functions, and these can be related to quark matter in the presence of an electromagnetic field. The first class of solutions generalises the Mak and Harko model. The second class of solutions does not admit any singularities in the matter and gravitational potentials at the centre.

gr-qc↗
arXiv2007

On surface tension for compact stars

In an earlier treatment it was demonstrated that general relativity gives higher values of surface tension in strange stars with quark matter than neutron stars.We generate the modified Tolman-Oppenheimer-Volkoff equation to incorporate anisotropic matter and use this to show that pressure anisotropy provides for a wide range of behaviour in the surface tension than is the case with isotropic pressures. In particular it is possible that anisotropy drastically decreases the value of the surface tension.

gr-qc↗
arXiv2007

The role of pressure anisotropy on the maximum mass of cold compact stars

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 redshift is analysed in the Vaidya-Tikekar model. It is shown that maximum compactness, redshift and mass increase in the presence of anisotropic pressures; numerical values are generated which are in agreement with observation.

gr-qc↗
arXiv2007

Generalised compact spheres in electric fields

We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with variable, rational coefficients. In an earlier treatment this condition was integrated by first transforming it to a hypergeometric equation. We demonstrate that it is possible to obtain a more general class of solutions to the Einstein-Maxwell system both in the form of special functions and elementary functions. Our results contain particular solutions found previously including models of charged relativistic spheres and uncharged neutron star models.

gr-qc↗
arXiv2007

Tikekar superdense stars in electric fields

We present exact solutions to the Einstein-Maxwell system of equations with a specified form of the electric field intensity by assuming that the hypersurface \{$t$ = constant\} are spheroidal. The solution of the Einstein-Maxwell system is reduced to a recurrence relation with variable rational coefficients which can be solved in general using mathematical induction. New classes of solutions of linearly independent functions are obtained by restricting the spheroidal parameter $K$ and the electric field intensity parameter $α$. Consequently it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions. Our result contains models found previously including the superdense Tikekar neutron star model [R. Tikekar, \emph{J. Math. Phys.} \textbf{31}, 2454 (1990)] when $K=-7$ and $α=0$. Our class of charged spheroidal models generalise the uncharged isotropic Maharaj and Leach solutions [S. D. Maharaj and P. G. L. Leach, \emph{J. Math. Phys.} \textbf{37}, 430 (1996)]. In particular, we find an explicit relationship directly relating the spheroidal parameter $K$ to the electromagnetic field.

gr-qc↗
arXiv2007

A class of relativistic stars with a linear equation of state

By assuming a particular mass function we find new exact solutions to the Einstein field equations with an anisotropic matter distribution. The solutions are shown to be relevant for the description of compact stars. A distinguishing feature of this class of solutions is that they admit a linear equation of state which can be applied to strange stars with quark matter.

gr-qc↗
arXiv2006

Emergent Universe with Exotic Matter

A general framework for an emergent universe scenario has been given which makes use of an equation of state. The general features of the model have also been studied and possible primordial composition of the universe have been suggested.

gr-qc↗