arXiv subjects

Sudan Hansraj

Publications and source records attributed to Sudan Hansraj.

30 records · Page 2Linked to original sources

arXiv2018

Deflection of light by black holes and massless wormholes in massive gravity

Weak gravitational lensing by black holes and wormholes in the context of massive gravity (Bebronne and Tinyakov 2009) theory is studied. The particular solution examined is characterized by two integration constants, the mass $M$ and an extra parameter $S$ namely `scalar charge'. These black hole reduce to the standard Schwarzschild black hole solutions when the scalar charge is zero and the mass is positive. In addition, a parameter $λ$ in the metric characterizes so-called 'hair'. The geodesic equations are used to examine the behavior of the deflection angle in four relevant cases of the parameter $λ$. Then, by introducing a simple coordinate transformation $r^λ=S+v^2$ into the black hole metric, we were able to find a massless wormhole solution of Einstein-Rosen (ER) \cite{Einstein} type with scalar charge $S$. The programme is then repeated in terms of the Gauss--Bonnet theorem in the weak field limit after a method is established to deal with the angle of deflection using different domains of integration depending on the parameter $λ$. In particular, we have found new analytical results corresponding to four special cases which generalize the well known deflection angles reported in the literature. Finally, we have established the time delay problem in the spacetime of black holes and wormholes, respectively.

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arXiv2018

Role of pressure anisotropy on relativistic compact stars

We investigate a compact spherically symmetric relativistic body with anisotropic particle pressure profiles. The distribution possesses characteristics relevant to modeling compact stars within the framework of general relativity. For this purpose, we consider a spatial metric potential of Korkina and Orlyanskii [Ukr. Phys. J. 36, 885 (1991)] type in order to solve the Einstein field equations. An additional prescription we make is that the pressure anisotropy parameter takes the functional form proposed by Lake [Phys. Rev. D 67, 104015 (2003)]. Specifying these two geometric quantities allows for further analysis to be carried out in determining unknown constants and obtaining a limit of the mass-radius diagram, which adequately describes compact strange star candidates like Her X-1 and SMC X-1. Using the anisotropic Tolman-Oppenheimer-Volkoff equations, we explore the hydrostatic equilibrium and the stability of such compact objects. Then, we investigate other physical features of this models, such as the energy conditions, speeds of sound and compactness of the star in detail and show that our results satisfy all the required elementary conditions for a physically acceptable stellar model. The results obtained are useful in analyzing the stability of other anisotropic compact objects like white dwarfs, neutron stars, and gravastars.

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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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arXiv2017

Inverse square law isothermal property in relativistic charged static distributions

We analyse the impact of the inverse square law fall-off of the energy density in a charged isotropic spherically symmetric fluid. Initially we impose a linear barotropic equation of state $p=αρ$ but this leads to an intractable differential equation. Next we consider the neutral isothermal metric of Saslaw, Maharaj and Dadhich (1996) in an electric field and the usual inverse square law of energy density and pressure results thus preserving the equation of state. Additionally, we discard a linear equation of state and endeavour to find new classes of solutions with the inverse square law fall off of density. Certain prescribed forms of the spatial and temporal gravitational forms result in new exact solutions. An interesting result that emerges is that while isothermal fluid spheres are unbounded in the neutral case, this is not so when charge is involved. Indeed it was found that barotropic equations of state exist and hypersurfaces of vanishing pressure exist establishing a boundary in practically all models. One model was studied in depth and found to satisfy other elementary requirements for physical admissability such as a subluminal sound speed as well as gravitational surface redshifts smaller than 2. The Buchdahl (1959), Bohmer and Harko (2007) and Andreasson (2009) mass-radius bounds were also found to be satisfied. Graphical plots utilising constants selected from the boundary conditions established that the model displayed characteristics consistent with physically viable models.

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arXiv2017

Generalised spheroidal spacetimes in 5-D Einstein--Maxwell--Gauss--Bonnet gravity

The field equations for static EGBM gravity are obtained and transformed to an equivalent form through a coordinate redefinition. A form for one of the metric potentials that generalises the spheroidal ansatz of Vaidya--Tikekar superdense stars and additionally prescribing the electric field intensity yields viable solutions. Some special cases of the general solution are considered and analogous classes in the Einstein framework are studied. In particular the Finch--Skea ansatz is examined in detail and found to satisfy the elementary physical requirements. These include positivity of pressure and density, the existence of a pressure free hypersurface marking the boundary, continuity with the exterior metric, a subluminal sound speed as well as the energy conditions. Moreover, the solution possesses no coordinate singularities. It is found that the impact of the Gauss--Bonnet term is to correct undesirable features in the pressure profile and sound speed index when compared to the equivalent Einstein gravity model. Furthermore graphical analyses suggest that higher densities are achievable for the same radial values when compared to the 5--dimensional Einstein case. The case of a constant gravitational potential, isothermal distribution as well as an incompressible fluid are studied. All exact solutions derived exhibit an equation of state explicitly.

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arXiv2017

Static trace free Einstein equations and stellar distributions

We construct models of static spherical distributions of perfect fluid in trace--free Einstein gravity theory. The equations governing the gravitational field are equivalent to the standard Einstein's equations however, their presentation is manifestly different which motivates the question whether new information would emerge due to the nonlinearity of the field equations. The incompressible fluid assumption does not lead to the well known Schwarzschild interior metric of Einstein gravity and a term denoting the presence of a cosmological constant is present on account of the integration process. The Schwarzschild interior is regained as a special case of a richer geometry. On the other hand, when the Schwarzschild geometry is prescribed, a constant density fluid emerges consistent with the standard equations. A complete model of an isothermal fluid sphere with pressure and density obeying the inverse square law is obtained. Corrections to the model previously presented in the literature by Saslaw {\it {et al}} are exhibited. The isothermal ansatz does not yield a constant gravitational potential in general but both potentials are position dependent. Conversely, it is shown that assuming a constant $g_{rr}$ gravitational potential does not yield an isothermal fluid in general as is the case in standard general relativity. The results of the standard Einstein equations are special cases of the models reported here. Noteworthy is the fact that whereas the previously reported isothermal solution was only of cosmological interest, the solution reported herein admit compact objects by virtue of the fact that a pressure-free hypersurface exists. Finally we analyze the consequences of selecting the Finch--Skea metric as the seed solution.

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arXiv2017

Compact objects in pure Lovelock theory

For static fluid interiors of compact objects in pure Lovelock gravity (involving ony one $N$th order term in the equation) we establish similarity in solutions for the critical odd and even $d=2N+1, 2N+2$ dimensions. It turns out that in critical odd $d=2N+1$ dimensions, there can exist no bound distribution with a finite radius, while in critical even $d=2N+2$ dimensions, all solutions have similar behavior. For exhibition of similarity we would compare star solutions for $N =1, 2$ in $d=4$ Einstein and $d=6$ in Gauss-Bonnet theory respectively. We also obtain the pure Lovelock analogue of the Finch-Skea model.

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arXiv2017

Anisotropic stellar models admitting conformal motion

We address the problem of finding static and spherically symmetric anisotropic compact stars in general relativity that admit conformal motions. The study is framed in the language of f(R) gravity theory in order to expose opportunity for further study in the more general theory. Exact solutions of compact stars are found under the assumption that spherically symmetric spacetimes which admits conformal motion with matter distribution anisotropic in nature. In this work, two cases have been studied for the existence of such solutions: first, we consider the model given by f(R) = R and then f(R) = aR+b. Finally, specific characteristics and physical properties have been explored by analytically along with graphical representations for conformally symmetric compact stars in f(R) gravity.

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arXiv2016

Stability analysis of Lower Dimensional Gravastars in noncommutative geometry

The Bañados, Teitelboim and Zanelli \cite{BTZ1992}, black hole solution is revamped from the Einstein field equations in (2 + 1)-dimensional anti-de Sitter spacetime, in a context of noncommutative geometry \cite{Rahaman(2013)}. In this article, we explore the exact gravastar solutions in three-dimension anti-de Sitter space given in the same geometry. As a first step we derive BTZ solution assuming the source of energy density as point-like structures in favor of smeared objects, where the particle mass M, is diffused throughout a region of linear size $\sqrtα$ and is described by a Gaussian function of finite width rather than a Dirac delta function. We matched our interior solution to an exterior BTZ spacetime at a junction interface situated outside the event horizon. Furthermore, stability analysis is carried out for the dynamic case for the specific case when $χ< 0. 214$ under radial perturbations about static equilibrium solutions. To give theoretical support we also trying to explore their physical properties and characteristics.

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arXiv2015

Exact EGB models for spherical static perfect fluids

We obtain a new exact solution to the field equations in the EGB modified theory of gravity for a 5-dimensional spherically symmetric static distribution. By using a transformation, the study is reduced to the analysis of a single second order nonlinear differential equation. In general the condition of pressure isotropy produces a first order differential equation which is an Abel equation of the second kind. An exact solution is found. The solution is examined for physical admissability. In particular a set of constants is found which ensures that a pressure-free hypersurface exists which defines the boundary of the distribution. Additionally the isotropic pressure and the energy density are shown to be positive within the radius of the sphere. The adiabatic sound speed criterion is also satisfied within the fluid ensuring a subluminal sound speed. Furthermore, the weak, strong and dominant conditions hold throughout the distribution. On setting the Gauss-Bonnet coupling to zero, an exact solution for 5-dimensional perfect fluids in the standard Einstein theory is obtained. Plots of the dynamical quantities for the Gauss-Bonnet and the Einstein case reveal that the pressure is unaffected while the the energy density increases under the influence of the Gauss-Bonnet term.

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arXiv2015

Exact barotropic distributions in Einstein-Gauss-Bonnet gravity

New exact solutions to the field equations in the Einstein--Gauss--Bonnet modified theory of gravity for a 5--dimensional spherically symmetric static distribution of a perfect fluid is obtained. The Frobenius method is used to obtain this solution in terms of an infinite series. Exact solutions are generated in terms of polynomials from the infinite series. The 5--dimensional Einstein solution is also found by setting the coupling constant to be zero. All models admit a barotropic equation of state. Linear equations of state are admitted in particular models with the energy density profile of isothermal distributions. We examine the physicality of the solution by studying graphically the isotropic pressure and the energy density. The model is well behaved in the interior and the weak, strong and dominant energy conditions are satisfied.

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arXiv2015

Universality of isothermal fluid spheres in Lovelock gravity

We show universality of isothermal fluid spheres in pure Lovelock gravity where the equation of motion has only one $N$th order term coming from the corresponding Lovelock polynomial action of degree $N$. Isothermality is characterized by the equation of state, $p = αρ$ and the property, $ρ\sim 1/r^{2N}$. Then the solution describing isothermal spheres, which exist only for the pure Lovelock equation, is of the same form for the general Lovelock degree $N$ in all dimenions $d \geq 2N+2$. We further prove that the necessary and sufficient condition for the isothermal sphere is that its metric is conformal to the massless global monopole or the solid angle deficit metric, and this feature is also universal.

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