arXiv subjects

S. D. Maharaj

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

At least 19 recordsLinked to original sources

arXiv2020

Emergent Universe Scenario in Modified Gauss-Bonnet Gravity

We present modified Gauss-Bonnet gravity without matter in four dimensions which accommodates flat emergent universe (EU) obtained in Einstein's general theory of gravity with a non-linear equation of state. The EU model is interesting which is free from big-bang singularity with other observed features of the universe. It is assumed that the present universe emerged out from a static Einstein universe phase exists in the infinite past. To obtain a flat EU model we reconstructed mimetic modified $f(G)$-gravity ($G$ representing Gauss-Bonnet terms) without matter. The functional form of f(G)-gravity is determined which accommodates the early inflation and late accelerating phases without matter.

astro-ph.CO↗

arXiv2017

Anisotropic fluid spheres of embedding class one using Karmarkar condition

We obtain a new anisotropic solution for spherically symmetric spacetimes by analysing of the Karmarkar embedding condition. For this purpose we construct a suitable form of one of the gravitational potentials to obtain a closed form solution. This form of the remaining gravitational potential allows us to solve the embedding equation and integrate the field equations. The resulting new anisotropic solution is well behaved which can be utilized to construct realistic static fluid spheres. Also we estimated masses and radii of fluid spheres for LMC X-4 and EXO 1785-248 by using observational data sets values. The obtained masses and radii show that our anisotropic solution can represent fluid spheres to a very good degree of accuracy.

physics.gen-ph↗

arXiv2017

Exact solutions for scalar field cosmology in f(R) gravity

We look for exact solutions in scalar field cosmology. To achieve this we use $f(R)$ modified gravity with a scalar field and do not specify the the form of the $f(R)$ function. In particular, we study Friedmann universe assuming that acceleration of the scalar curvature is negligible. We first present solutions for special cases and then the general solution. Using initial conditions which represent the universe at the present epoch, we evaluated the constants of integration. This allows for the comparison of the scale factor in the new solutions with that of the $ΛCDM$ solution, thereby affecting the age of the universe in $f(R)$ gravity.

gr-qc↗

arXiv2016

New charged anisotropic compact models

We find new exact solutions to the Einstein-Maxwell field equations which are relevant in the description of highly compact stellar objects. The relativistic star is charged and anisotropic with a quark equation of state. Exact solutions of the field equations are found in terms of elementary functions. It is interesting to note that we regain earlier quark models with uncharged and charged matter distributions. A physical analysis indicates that the matter distributions are well behaved and regular throughout the stellar structure. A range of stellar masses are generated for particular parameter values in the electric field. In particular the observed mass for a binary pulsar is regained.

gr-qc↗

arXiv2016

Anisotropic charged core envelope star

We study a charged compact object with anisotropic pressures in a core envelope setting. The equation of state is quadratic in the core and linear in the envelope. There is smooth matching between the three regions: the core, envelope and the Reissner-Nordström exterior. We show that the presence of the electric field affects the masses, radii and compactification factors of stellar objects with values which are in agreement with previous studies. We investigate in particular the effect of electric field on the physical features of the pulsar PSR J1614-2230 in the core envelope model. The gravitational potentials and the matter variables are well behaved within the stellar object. We demonstrate that the radius of the core and the envelope can vary by changing the parameters in the speed of sound.

gr-qc↗

arXiv2016

Radiating stars with exponential Lie symmetries

We analyze the general model of a radiating star in general relativity. A group analysis of the under determined, nonlinear partial differential equation governing the model's gravitational potentials is performed. This analysis is an extension of previous group analyses carried out and produces new group invariant solutions. We find that the gravitational potentials depend on exponential functions owing to the choice of the Lie symmetry generator. The fundamental boundary equation to be solved is in general a Riccati equation. Several new exact families of solutions to the boundary condition are generated. Earlier models of Euclidean stars and generalized Euclidean stellar models are regained as special cases. Linear equations of state can be found for shear-free and shearing spacetimes.

gr-qc↗

arXiv2016

Riccati equations for bounded radiating systems

We systematically analyze the nonlinear partial differential equation that determines the behaviour of a bounded radiating spherical mass in general relativity. Four categories of solution are possible. These are identified in terms of restrictions on the gravitational potentials. One category of solution can be related to the horizon function transformation which was recently introduced. A Lie symmetry analysis of the resulting Riccati equation shows that several new classes of exact solutions are possible. The relationship between the horizon function, Euclidean star models and other earlier investigations is clarified.

gr-qc↗

arXiv2016

A family of Finch and Skea relativistic stars

Several new families of exact solution to the Einstein-Maxwell system of differential equations are found for anisotropic charged matter. The spacetime geometry is that of Finch and Skea which satisfies all criteria for physical acceptability. The exact solutions can be expressed in terms of elementary functions, Bessel functions and modified Bessel functions. When a parameter is restricted to be an integer then the special functions reduce to simple elementary functions. The uncharged model of Finch and Skea (Class. Quantum Grav. 6, 467 (1989)) and the charged model of Hansraj and Maharaj (Int. J. Mod. Phys. D 8, 1311 (2006)) are regained as special cases. The solutions found admit a barotropic equation of state. A graphical analysis indicates that the matter and electric quantities are well behaved.

gr-qc↗

arXiv2015

A group theoretic approach to shear-free radiating stars

A systematic analysis of the junction condition, relating the radial pressure with the heat flow in a shear-free relativistic radiating star, is undertaken. This is a highly nonlinear partial differential equation in general. We obtain the Lie point symmetries that leave the boundary condition invariant. Using a linear combination of the symmetries, we transform the junction condition into ordinary differential equations. We present several new exact solutions to the junction condition. In each case we can identify the exact solution with a Lie point generator. Some of the solutions obtained satisfy the linear barotropic equation of state. As a special case we regain conformally flat models which were found previously. Our analysis highlights the interplay between Lie algebras, nonlinear differential equations and application to relativistic astrophysics.

gr-qc↗

arXiv2015

Analytical models for gravitating radiating systems

We analyse the gravitational behaviour of a relativistic heat conducting fluid in a shear-free spherically symmetric spacetime. We show that the isotropy of pressure is a consistency condition which realises a second order nonlinear ordinary differential equation with variable coefficients in the gravitational potentials. Several new classes of solutions are found to the governing equation by imposing various forms on one of the potentials. Interestingly, a complex transformation leads to an exact solution with only real metric functions. All solutions are written in terms of elementary functions. We demonstrate graphically that the fluid pressure, energy density and heat flux are well behaved for the model, and the model is consistent with a core-envelope framework.

gr-qc↗

arXiv2014

The Deng algorithm in higher dimensions

We extend an algorithm of Deng in spherically symmetric spacetimes to higher dimensions. We show that it is possible to integrate the generalised condition of pressure isotropy and generate exact solutions to the Einstein field equations for a shear-free cosmological model with heat flow in higher dimensions. Three new metrics are identified which contain results of four dimensions as special cases. We show graphically that the matter variables are well behaved and the speed of sound is causal.

gr-qc↗

arXiv2014

Some simple models for quark stars

We find two new classes of exact solutions for the Einstein-Maxwell equations. The solutions are obtained by considering charged anisotropic matter with a linear equation of state consistent with quark stars. The field equations are integrated by specifying forms for the measure of anisotropy and a gravitational potential which are physically reasonable. The solutions found generalize the Mark-Harko model and the Komathiraj-Maharaj model. A graphical analysis indicates that the matter variables are well behaved.

gr-qc↗

arXiv2014

Charged compact objects in the linear regime

Astrophysical compact stars provide a natural laboratory for testing theoretical models which are otherwise difficult to prove from an experimental setup. In our present work we analyse an exact solution to the Einstein-Maxwell system for a charged anisotropic compact body in the linear regime. The charged parameter may be set to zero which gives us the case of neutral solutions. We have tuned the model parameters for the uncharged case so as to match with recent updated mass-radius estimates for five different compact objects. Then we make a systematic study of the effect of charge for the different parameter set that fits the observed stars. The effect of charge is clearly illustrated in the increase of mass. We show that the physical quantities for the objects PSR J1614-2230, PSR J1903+327, Vela X-1, SMC X-1, Cen X-3 are well behaved.

gr-qc↗

arXiv2014

Stellar objects in the quadratic regime

We model a charged anisotropic relativistic star with a quadratic equation of state. Physical features of an exact solution of the Einstein-Maxwell system are studied by incorporating the effect of the nonlinear term from the equation of state. It is possible to regain the masses, radii and central densities for a linear equation of state in our analysis. We generate masses for stellar compact objects and perform a detailed study of PSR J1614-2230 in particular. We also show the influence of the nonlinear equation of state on physical features of the matter distribution. We demonstrate that it is possible to incorporate the effects of charge, anisotropy and a quadratic term in the equation of state in modelling a compact relativistic body.

gr-qc↗

arXiv2014

Geodesic models generated by Lie symmetries

We study the junction condition relating the pressure to the heat flux at the boundary of a shearing and expanding spherically symmetric radiating star when the fluid particles are travelling in geodesic motion. The Lie symmetry generators that leave the junction condition invariant are identified and the optimal system is generated. We use each element of the optimal system to transform the partial differential equation to an ordinary differential equation. New exact solutions, which are group invariant under the action of Lie point infinitesimal symmetries, are found. We obtain families of traveling wave solutions and self-similar solutions, amongst others. The gravitational potentials are given in terms of elementary functions, and the line elements can be given explicitly in all cases. We show that the Friedmann dust model is regained as a special case, and we can connect our results to earlier investigations.

gr-qc↗

arXiv2014

Generalized Euclidean stars with equation of state

We consider the general case of an accelerating, expanding and shearing model of a radiating relativistic star using Lie symmetries. We obtain the Lie symmetry generators that leave the equation for the junction condition invariant, and find the Lie algebra corresponding to the optimal system of the symmetries. The symmetries in the optimal system allow us to transform the boundary condition to ordinary differential equations. The various cases for which the resulting systems of equations can be solved are identified. For each of these cases the boundary condition is integrated and the gravitational potentials are found explicitly. A particular group invariant solution produces a class of models which contains Euclidean stars as a special case. Our generalized model satisfies a linear equation of state in general. We thus establish a group theoretic basis for our generalized model with an equation of state. By considering a particular example we show that the weak, dominant and strong energy conditions are satisfied.

gr-qc↗

arXiv2014

Lie symmetries for a conformally flat radiating star

We consider a relativistic radiating spherical star in conformally flat spacetimes. In particular we study the junction condition relating the radial pressure to the heat flux at the boundary of the star which is a nonlinear partial differential equation. The Lie symmetry generators that leave the equation invariant are identified and we generate an optimal system. Each element of the optimal system is used to reduce the partial differential equation to an ordinary differential equation which is further analysed. We identify new categories of exact solutions to the boundary conditions. Two classes of solutions are of interest. The first class depends on a self similar variable. The second class is separable in the spacetime variables.

gr-qc↗

arXiv2014

A relativistic algorithm with isotropic coordinates

We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a new solution if a particular solution is known. The algorithm leads to a nonlinear Bernoulli equation which can be integrated in terms of arbitrary functions. We use a conformally flat metric to show that the integrals may be expressed in terms of elementary functions. It is important to note that we utilise isotropic coordinates unlike other treatments.

gr-qc↗