arXiv subjects

Megandhren Govender

Publications and source records attributed to Megandhren Govender.

13 recordsLinked to original sources

arXiv2026

Solutions for neutron stars in General Relativity from a complexity structure scalar boundary condition

A new condition involving the complexity factor, a structure scalar arising from the orthogonal splitting of the Riemann tensor, is generated at the boundary of a spherically symmetric anisotropic fluid. This condition leads to the generation of a model, without invoking any further constraints on geometry or matter variables. The model generated is physically reasonable and suggests that there is a non-zero, positive minimum constraint on the complexity scalar value evaluated at the surface. This suggests that vanishing complexity is a globalized constraint which does not apply at the boundary, specifically for compact objects in the strong-gravity regime.

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arXiv2026

Relativistic stellar collapse of initially static configurations

We study the dynamics of a radiating relativistic star in the presence of the electromagnetic field and the cosmological constant. The evolution of the model originates from an initially static configuration. The temporal behaviour of the system is governed by a nonlinear second order equation which is studied using a phase plane analysis. We show that in the general case, with all physical parameters present, fold bifurcations arise which are related to nonzero charge and cosmological constant. Our treatment clarifies earlier results and we extend our study to the general solution space. We obtain a more comprehensive understanding of the temporal evolution for a shear-free configuration during collapse.

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arXiv2026

Exploration of Zero-Complexity Compact Stars in Higher Dimensions under the Finch-Skea Background

Motivated by the recent extension of Herrera's gravitational complexity to arbitrary higher-dimensional spacetimes, we investigate exact compact-star models that satisfy the vanishing-complexity condition within the Finch--Skea geometry in $(n+2)$-dimensional Einstein gravity. By combining the higher-dimensional Einstein field equations with the generalized complexity formalism, we obtain a new class of exact interior solutions describing anisotropic fluid spheres with zero complexity. The physical properties of these models are evaluated by analyzing the behavior of the matter variables, pressure anisotropy, and equilibrium conditions, alongside the standard requirements of regularity, energy conditions, causality, and stability. We further explore the influence of spacetime dimensionality on the structural characteristics of the stellar configurations, demonstrating that the presence of extra dimensions significantly modifies the internal matter distribution while preserving physical viability. The solutions presented here represent the first exact higher-dimensional Finch--Skea compact-star models constructed within this recently developed generalized complexity framework \cite{choudas}. These results provide a natural extension of zero-complexity stellar configurations beyond four-dimensional General Relativity and offer a robust framework for investigating self-gravitating systems in higher- dimensional gravity.

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arXiv2023

An Eternal gravitational collapse in $f(R)$ theory of gravity and their astrophysical implications

In this work, we explore the eternal collapsing phenomenon of a stellar system (e.g., a star) within the framework of $f(R)$ gravity and investigate some new aspects of the continued homogeneous gravitational collapse with perfect fluid distribution. The exact solutions of field equations have been obtained in an independent way by the parameterization of the expansion scalar ($\Theta$) governed by the interior spherically symmetric FLRW metric. We impose the Darmois junction condition required for the smooth matching of the interior region to the Schwarzschild exterior metric across the boundary hypersurface of the star. The junction conditions demand that the pressure is non-vanishing at the boundary and is proportional to the non-linear terms of $f(R)$ gravity, and the mass function $m(t, r)$ is equal to Schwarzschild mass $M$. The eight massive stars, namely $Westerhout 49-2, BAT99-98, R136a1, R136a2, WR 24, Pismis 24-1$, $\lambda- Cephei$, and $\beta -Canis Majoris$ with their known astrophysical data (masses and radii) are used to estimate the numerical values of the model parameters which allows us to study the solutions numerically and graphically. Here we have discussed two $f(R)$ gravity models describing the collapse phenomenon. The singularity analysis of models is discussed via the apparent horizon and we have shown that stars tend to collapse for an infinite co-moving time in order to attain the singularity (an eternal collapsing phenomenon). We have also shown that our models satisfy the energy conditions and stability requirements for stellar systems.

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arXiv2023

Black hole formation in gravitational collapse and their astrophysical implications

In this work, we have investigated a novel aspect of black hole (BH) formation during the collapse of a self-gravitating configuration. The exact solution of the Einstein field equations is obtained in a model-independent way by considering a parametrization of the expansion scalar ($\Theta$) in the background of spherically symmetric space-time geometry governed by the FLRW metric. Smooth matching of the interior solution with the Schwarzschild exterior metric across the boundary hypersurface of the star, together with the condition that the mass function $m(t,r)$ is equal to Schwarzschild mass $M$, is used to obtain all the physical and geometrical parameters in terms of the stellar mass. The four known massive stars namely $R136a3$, $Melnick$, $R136c$, and $R136b$ with their known astrophysical data (mass, radius, and present age) are used to study the physics of the model both numerically and graphically. We demonstrate that the formation of the apparent horizon occurs earlier than the singular state that is, the model of massive stars would inevitably lead to the formation of a BH as their end state. We have conducted an analysis indicating that the lifespans of massive stars are closely related to their respective masses. Our findings demonstrate that more massive stars exhibit considerably shorter lifespans in comparison to their lighter counterparts. Thus, the presented model corresponds to the evolutionary stages of astrophysical stellar objects and theoretically predicts their possible lifespan. We have also shown that our model satisfies the energy conditions and stability requirements via Herrera's cracking method.

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arXiv2022

Lie symmetry approach to the time-dependent Karmarkar condition

We obtain solutions of the time-dependent Einstein Field Equations which satisfy the Karmarkar condition via the method of Lie symmetries. Spherically symmetric spacetime metrics are used with metric functions set to impose conformal flatness, Weyl-free collapse and shear-free collapse. In particular, a solution was found which satisfies the heat-flux boundary condition of Santos, and a radiating stellar model was then obtained and investigated. Solutions obtained which do not allow for the application of the junction conditions at a boundary surface may lend themselves to cosmological models. This is a first attempt in generating solutions satisfying the Karmarkar condition via the method of Lie symmetries and our example of a radiating model highlights the viability of this method.

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arXiv2022

Physical Implications of Pure Lovelock Geometry on Stellar Structure

We construct an exact anisotropic star model with a linear barotropic equation of state and with Finch-Skea potential within the framework of pure Lovelock gravity. A comparison with the corresponding Einstein model in a suitable limit is easily deduced. Evidently higher curvature effects induced by the Lovelock contributions generate lower densities, pressures, surface tensions and anisotropy factors when compared to its Einstein counterpart. The maximum moment of inertia is attained for the Einstein case and hence it may be inferred that Lovelock effects soften the equation of state. The model satisfies various stability tests.

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arXiv2022

Lie Symmetries, Painlevé analysis and global dynamics for the temporal equation of radiating stars

We study the temporal equation of radiating stars by using three powerful methods for the analysis of nonlinear differential equations. Specifically, we investigate the global dynamics for the given master ordinary differential equation to understand the evolution of solutions for various initial conditions as also to investigate the existence of asymptotic solutions. Moreover, with the application of Lie's theory, we can reduce the order of the master differential equation, while an exact similarity solution is determined. Finally, the master equation possesses the Painlevé property, which means that the analytic solution can be expressed in terms of a Laurent expansion.

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arXiv2022

Temporal evolution of a radiating star via Lie symmetries

In this work, we present for the first time the general solution of the temporal evolution equation arising from the matching of a conformally flat interior to the Vaidya solution. This problem was first articulated by Banerjee et al. (A. Banerjee, S. B. Dutta Choudhury, and Bidyut K. Bhui, Phys. Rev. D, 40 (670) 1989) in which they provided a particular solution to the temporal equation. This simple exact solution has been widely utilized in modeling dissipative collapse with the most notable result being a prediction of the avoidance of the horizon as the collapse proceeds. We study the dynamics of dissipative collapse arising from the general solution obtained via the method of symmetries and of the singularity analysis. We show that the end-state of collapse for our model is significantly different from the widely used linear solution.

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arXiv2021

Strange stars in the framework of higher curvature gravity

We study the influence of higher curvature effects on stellar structure and conclude that the properties of stars are greatly impacted when such terms are dynamic. In particular the surface gravitational redshift which is connected to the equation of state and also the mass-radius ratio differs greatly from the corresponding values in general relativity as evidenced through our empirical comparisons. A model of a superdense star with strange star equation of state is constructed within the framework of the Einstein--Gauss--Bonnet theory. Under these assumptions large classes of solutions are admitted by the field equations. We isolate a particular class with the ansatz of the Vaidya--Tikekar superdense star spatial gravitational potential. The model is found to satisfy elementary requirements for physical applicability and stability. The parameter values chosen are consistent with observed star models. A significant effect of the higher curvature terms is to reduce the speed of sound and to drastically reduce the values of the surface gravitational redshift compared to the Einstein counterpart. These latter results have implications for interpretations of observations in relativistic astrophysics which are often made against the background of the standard general theory of relativity.

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arXiv2021

All Conformally Flat Einstein--Gauss--Bonnet static Metrics

It is known that the standard Schwarzschild interior metric is conformally flat and generates a constant density sphere in any spacetime dimension in Einstein and Einstein--Gauss--Bonnet gravity. This motivates the questions: In EGB does the conformal flatness criterion yield the Schwarzschild metric? Does the assumption of constant density generate the Schwarzschild interior spacetime? The answer to both questions turn out in the negative in general. In the case of the constant density sphere, a generalised Schwarzschild metric emerges. When we invoke the conformal flatness condition the Schwarschild interior solution is obtained as one solution and another metric which does not yield a constant density hypersphere in EGB theory is found. For the latter solution one of the gravitational metrics is obtained explicitly while the other is determined up to quadratures in 5 and 6 dimensions. The physical properties of these new solutions are studied with the use of numerical methods and a parameter space is located for which both models display pleasing physical behaviour.

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arXiv2020

A new class of viable and exact solutions of EFE's with Karmarkar conditions: An application to cold star modeling

In this work we present a theoretical framework within Einstein's classical general relativity which models stellar compact objects such as PSR J1614-2230 and SAX J1808.4-3658. The Einstein field equations are solved by assuming that the interior of the compact object is described by a class I spacetime. The so-called Karmarkar condition arising from this requirement is integrated to reduce the gravitational behaviour to a single generating function. By appealing to physics we adopt a form for the gravitational potential which is sufficiently robust to accurately describe compact objects. Our model satisfies all the requirements for physically realistic stellar structures.

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arXiv2017

Expanding, shearing and accelerating isotropic plane symmetric universe with conformal Kasner geometry

We construct a model of a universe filled with a perfect fluid with isotropic particle pressure. The anisotropic plane symmetric Kasner spacetime is used as a seed metric and through a conformal mapping a perfect fluid is generated. The model is inhomogeneous, irrotational, shearing and accelerating. For negative time, the universe is expanding while for positive time it is collapsing. With the aid of graphical three dimensional plots it is established that the density and pressure hypersurfaces are smooth and singularity free. Additionally the sound-speed index is computed and the fluid obeys causality criterion.

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