The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images The general results are illustrated with examples of spacetimes where the lensing features can be explicitly calculated, including the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane gravitational waves, and others

https://link.springer.com/content/pdf/10.12942%2Flrr-2004-9.pdf

Gravitational Lensing from a Spacetime Perspective

The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime. It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images. The general results are illustrated with examples of spacetimes where the lensing features can be explicitly calculated, including the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane gravitational waves, and others.

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 solutions. 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.

Charged anisotropic matter with a linear equation of state, Classical and Quantum Gravity

We obtain two new families of compact solutions for a spherically symmetric distribution of matter consisting of an electrically charged anisotropic fluid sphere joined to the Reissner–Nordstrom static solution through a zero pressure surface. The static inner region also admits a one parameter group of conformal motions. First, to study the effect of the anisotropy in the sense of the pressures of the charged fluid, besides assuming a linear equation of state to hold for the fluid, we consider the tangential pressure p
 ⊥
 to be proportional to the radial pressure p
 r
 , the proportionality factor C measuring the grade of anisotropy. We analyze the resulting charge distribution and the features of the obtained family of solutions. These families of solutions reproduce for the value C=1, the conformal isotropic solution for quark stars, previously obtained by Mak and Harko. The second family of solutions is obtained assuming the electrical charge inside the sphere to be a known function of the radial coordinate. The allowed values of the parameters pertained to these solutions are constrained by the physical conditions imposed. We study the effect of anisotropy in the allowed compactness ratios and in the values of the charge. The Glazer’s pulsation equation for isotropic charged spheres is extended to the case of anisotropic and charged fluid spheres in order to study the behavior of the solutions under linear adiabatic radial oscillations. These solutions could model some stage of the evolution of strange quark matter fluid stars.

Conformal anisotropic relativistic charged fluid spheres with a linear equation of state

Basic structures of fuzzy topology

Here in this paper we present a locally rotationally symmetric Bianchi type-II metric filled with dark matter and anisotropic modified holographic Ricci dark energy. To solve the Einstein’s field equations we have taken the hybrid expansion law (HEL) which exhibits a cosmic transition of the universe from decelerating to accelerating phase. We have investigated the physical and geometrical properties of the model. It is observed that the anisotropy of the universe and that of the modified holographic Ricci dark energy tends to zero at later times and the universe becomes homogeneous, isotropic and flat. We have also studied the cosmic jerk parameter.

Anisotropic modified holographic Ricci dark energy cosmological model with hybrid expansion law

Interior Schwarzschild-like solution in higher dimensions

In this paper we present a spatially homogeneous and anisotropic Bianchi type-VI0 space-time filled with interacting dark matter and modified holographic Ricci dark energy. We have taken here a sign-changeable interaction. Assuming the relation between the shear scalar and expansion scalar with a particular form of Hubble parameter we have obtained the exact solution of the Einstein’s field equations. The geometric and kinematic properties of the model have been investigated. Under suitable conditions it is observed that the universe becomes spatially homogeneous, isotropic and flat. The results are found to be consistent with the recent day observations.

Modified holographic Ricci dark energy model with sign-changeable interaction

The present study deals with spatially homogeneous and anisotropic axially symmetric Bianchi type-I cosmological model with time variable G and Λ in the presence of bulk viscous fluid. The coefficient of bulk viscosity ζ is considered as a quadratic function of Hubble parameter H (i.e. ζ = ζ
 0 + ζ
 1
 H + ζ
 2
 H
 2, where ζ
 0, ζ
 1 and ζ
 2 are constants). The Einstein’s field equations are solved explicitly by using a law of variation for the Hubble parameter, which gives a constant value of deceleration parameter. The law generates power law and exponential form of average scale factor in terms of cosmic time. The physical and kinematical properties of the models are discussed.

Axially Symmetric Bianchi Type-I Bulk Viscous Cosmological Model with Time Varying Gravitational and Cosmological Constants

We present in this paper a LRS Bianchi type I cosmological model with dark matter and anisotropic ghost dark energy in presence of magnetic field. We have solved the Einstein’s field equations with a particular form of Hubble parameter. The physical and geometrical behaviors of the model are discussed. It is observed that the anisotropy of the universe and that of the ghost dark energy tends to zero at late times and the universe becomes spatially homogeneous, isotropic and flat. The coincidence parameter increases with time. We have also studied the statefinder parameters. The results obtained are in agreement with the recent days observations.

Kanika Das

Papers

Anisotropic modified holographic Ricci dark energy cosmological model with hybrid expansion law

Interior Schwarzschild-like solution in higher dimensions

Modified holographic Ricci dark energy model with sign-changeable interaction

Axially Symmetric Bianchi Type-I Bulk Viscous Cosmological Model with Time Varying Gravitational and Cosmological Constants

Magnetized anisotropic ghost dark energy cosmological model