Solutions Of Einstein Field Equations Research Articles

Reciprocal NUT spacetimes

In this paper, we study the Ehlers' transformation (sometimes called gravitational duality rotation) for reciprocal static metrics. First, we introduce the concept of reciprocal metric. We prove a theorem which shows how we can construct a certain new static solution of Einstein field equations using a seed metric. Later, we investigate the family of stationary spacetimes of such reciprocal metrics. The key here is a theorem from Ehlers', which relates any static vacuum solution to a unique stationary metric. The stationary metric has a magnetic charge. The spacetime represents Newman-Unti-Tamburino (NUT) solutions. Since any stationary spacetime can be decomposed into a 1 + 3 time-space decomposition, Einstein field equations for any stationary spacetime can be written in the form of Maxwell's equations for gravitoelectromagnetic fields. Further, we show that this set of equations is invariant under reciprocal transformations. An additional point is that the NUT charge changes the sign. As an instructive example, by starting from the reciprocal Schwarzschild as a spherically symmetric solution and reciprocal Morgan–Morgan disk model as seed metrics we find their corresponding stationary spacetimes. Starting from any static seed metric, performing the reciprocal transformation and by applying an additional Ehlers' transformation we obtain a family of NUT spaces with negative NUT factor (reciprocal NUT factors).

Errata: “New black hole solutions of Einstein field equations and their Riemann curvature tensors”

Errata: “New black hole solutions of Einstein field equations and their Riemann curvature tensors”

Relativistic Modelling of Stable Anisotropic Super-Dense Star

In the present article we have obtained new set of exact solutions of Einstein field equations for anisotropic fluid spheres by using the Herrera et al.[1] algorithm. The anisotropic fluid solution so obtained join continuously to Schwarzschild exterior solution across the pressure free boundary. It is observed that most of the new anisotropic solutions are well behaved and utilized to construct the super-dense star models such as neutron star and pulsars.

Magnetized Emergent Universe with Null Radiation Flow

In this paper, we study the Bianchi type-I cosmological model in a different basic form incorporating with null radiation flow with the perfect fluid in the presence as well as absence of a source free magnetic field. A set of new exact solutions of Einstein field equations are obtained in both the cases. We observe that the emergent universe model with null radiation flow approaches to de-sitter universe at late time obeying the same rate of expansion in presence and absence of the magnetic field.

Bianchi Type-I Cosmological Model with Null Radiation Flow

The present paper deals with the Bianchi type-I cosmological models in a different basic form incorporating with null radiation flow with the perfect fluid. A set of new exact solutions of Einstein field equations has been obtained. Thermodynamical properties and the entropy distribution have been studied. The energy condition of the model has also been discussed.

New black hole solutions of Einstein field equations and their Riemann curvature tensors

Here, we are going to discuss some new cases of cylindrically symmetric black hole solutions of Einstein field equations (EFEs). These are new solutions which we have not seen in the literature. We also listed their Riemann curvature tensors.

Some special solutions in Bianchi type VI0 cosmological models with modified chaplygin gas in general relativity

In the present paper, the role of modified chaplygin gas models in relation with the Bianchi type VI0 universe is examined. For obtaining complete solution of Einstein field equations, it is assumed that expansion scalar in the model is proportional to shear scalar and equation of state of this modified model is valid from the radiation era to the Lambda cold dark matter (ΛCDM) model. State finder and various physical, geometrical properties have also been discussed.

Some new similarity solutions of Einstein field equations for spherical symmetric metric of class two

Some spherical symmetric perfect fluid model of embedding class two has been investigated by constructing a fluid sphere of variable pressure and density with property that the pressure and density vanishes at the boundary beyond which Schwarzschild exterior solution prevails. New general solution has been obtained using similarity transformation method; the solution so obtained is new.

Connection between Lense–Thirring precession, Ernst potential and Thorne multipoles

For stationary axially symmetric spacetimes we find a simple expression for the Lense–Thirring precession in terms of two scalar quantities, the real and imaginary parts of the Ernst potential. Its weak-field approximation is expressed in terms of Thorne multipoles and used to compute the major non-spherical contributions to the precession of a gyroscope orbiting around the Earth. We reproduce previously known results and give a new estimation for non-spherical contributions. We believe the present work has important applications in the interpretation of approximate as well as exact solutions of Einstein field equations.

Hypersurface-Homogeneous Cosmological Models with Matter and Dark Energy

We have presented exact solutions of Einstein field equations for a hypersurface-homogeneous space time in the presence of a perfect fluid with constant EoS parameter. One solution corresponds to a cosmological model filled with stiff matter which may be useful for the description of the early stages of the universe. The other two solutions represent recent accelerating expanding models filled with dark energy and negative EoS parameter. The physical and kinematical properties of the models are discussed.

Bianchi Type-II String Cosmological Models with Bulk Viscous Fluid in Lyra Geometry

A oneparameter family of totally anisotropic Bianchi type-II string cosmological models with bulk viscous fluid in Lyra geometry is investigated. Exact solutions of Einstein field equations have been obtained by constraining the the constant deceleration parameter which yields power-law form of the average scale factor. Some physical and geometrical properties of the models along with the physical acceptability have been also discussed.

Conservation laws of cylindrically symmetric vacuum solution of Einstein field equations

In this paper we present two vacuum solution of Einstein Field equations(EFEs) which we have not seen in the literature. We also present their conservation laws using the famous Noether theorem. This calculation will also help us in understanding the gravitational wave spacetimes.

Non-Trivial Linkup of Both Compact-Neutron-Object and Outer-Empty-Space Metrics

In 2011, Chinese researcher Ni found the solution of the Oppenheimer-Volkoff problem for a stable configuration of stellar object with no internal source of energy. The Ni’s solution is the nonrotating hollow sphere having not only an outer, but an inner physical radius as well. The upper mass of the object is not constrained. In our paper, we contribute to the description of the solution. Specifically, we give the explicit description of metrics inside the object and attempt to link it with that in the corresponding outer Schwarzschild solution of Einstein field equations. This task appears to be non-trivial. We discuss the problem and suggest a way how to achieve the continuous linkup of both object-interior and outer-Schwarzschild metrics. Our suggestion implies an important fundamental consequence: there is no universal relativistic speed limit, but every compact object shapes the adjacent spacetime and this action results in the specific speed limit for the spacetime dominated by the object. Regardless our suggestion will definitively be proved or the successful linkup will also be achieved in else, still unknown way, the success in the linkup represents a constraint for the physical acceptability of the models of compact objects.

Relativistic models of thin disks immersed in a Robertson-Walker type spacetime

Using the well known “displace, cut and reflect” method used to generate disks from given solutions of Einstein field equations, we construct somerelativistic models of time dependent thin disks of infinite extension made of a perfect fluid based on the Robertson-Walker metric. Two simple families of models of disks based on Robertson-Walker solutions admitting Matter and Ricci collineations are presented. We obtain disks that are inagreement with all the energy conditions.

Anisotropic Cosmological Models with Quintessence

In this paper anisotropic cosmological models with bulk viscosity and quintessence have been studied. Some exact solutions of Einstein field equations with bulk viscosity and quintessence on the background of anisotropic Bianchi Type I space-time are obtained. The new cosmological models approach to isotropy with evolution of the universe. Physical properties of these cosmological models have also been discussed.

On certain new exact solutions of the Einstein equations for axisymmetric rotating fields

We investigate the Einstein field equations corresponding to the Weyl—Lewis—Papapetrou form for an axisymmetric rotating field by using the classical symmetry method. Using the invariance group properties of the governing system of partial differential equations (PDEs) and admitting a Lie group of point transformations with commuting infinitesimal generators, we obtain exact solutions to the system of PDEs describing the Einstein field equations. Some appropriate canonical variables are characterized that transform the equations at hand to an equivalent system of ordinary differential equations and some physically important analytic solutions of field equations are constructed. Also, the class of axially symmetric solutions of Einstein field equations including the Papapetrou solution as a particular case has been found.

The Theory of Static Gravitational Field

The paper discusses in detail assumptions needed for the derivation of metric for the non-rotating centrally gravitating body, which is not based on Einstein field equations. The metric derivation is then generalized to any static mass configuration. It is shown that the Schwarzschild metric, which is the famous solution of Einstein field equations for the centrally gravitating body, is only a first order approximation of the correct metric and that the Einstein field equation concept is a wrong concept for finding any metric. Several examples of observations in support of the developed theory, which are not as easily explained in the main stream literature, are also presented in this paper.

New astrophysical aspects from Yukawa fractional potential correction to the gravitational potential in D dimensions

The aim of this paper is to generalize in D = d + 1 the Newtonian gravity by adding to the gravitational potential for fractal distribution of particles within the linearized theory, a propagating fractional correctional mode which have the form of Yukawa (exponential) fractional potential. Exact solutions of Einstein field equations are presented where many interested features are derived and discussed in some details.

Bianchi -V Space -Time with Anisotropic Dark Energy in General Relativity

In a spatially homogeneous and anisotropic Bianchi type-V space-time the consequences of the presence of dynamically anisotropic dark energy and perfect fluid with heat-conduction are studied. We assume that dark energy is minimally interacting with matter and has an equation of state which is modified in a consistent way with the conservation of energy momentum tensor. Exact solutions of Einstein field equations are obtained by taking constant value of deceleration parameter. We find that this assumption is reasonable for the observation of the present day universe. The physical and geometrical properties of the models, the behavior of the anisotropy of dark energy and the thermodynamical relations that govern such solutions are discussed in detail.

Bulk Viscous Bianchi Type V Cosmological Models with Decaying Cosmological Term Λ

We present bulk viscous Bianchi type V cosmological models with time-dependent cosmological term Λ. Exact solutions of Einstein field equations have been obtained by assuming shear scalar σ proportional to volume expansion θ. The coefficient of bulk viscosity is taken to be power function of energy density ρ or volume expansion θ. In these models cosmological term Λ come out to be negative. It is found that models obtained are expanding, shearing and non-rotating. They do not approach isotropy for large values of time t. Some observational parameters for the model have also been discussed.