Perfect Fluid Source Research Articles

Dark Energy Cosmological Model in a Modified Theory of Gravity

The dark energy model with equation of state (EoS) parameter is derived for a non-static plane symmetric space-time filled with a perfect fluid source in the framework of f (R, T) gravity (Harko et al., arXiv: 1104.2669v2 [gr-qc], 2011). To obtain a determinate solution, a special form of deceleration parameter (DP) is used. We have assumed that the relation between metric potentials and the EoS parameter is proportional to the skewness parameter. It is observed that the EoS parameter, and the skewness parameter in the model turn out to be functions of cosmic time. Some physical and kinematical properties of the model are also discussed.

Cosmological models filled with a perfect fluid source in the f(R,T) theory of gravity

We investigated the physical behavior of an LRS Bianchi type I cosmological model in the framework of the f(R,T) theory of gravity in the presence of a perfect fluid, where R is the Ricci scalar and T is the trace of the stress energy tensor of the matter. In order to obtain a deterministic solution of the field equations we assumed the special law of variation of the Hubble parameter proposed by Berman that yields the constant deceleration parameter. Some physical properties of the models are discussed.

Five dimensional radiating model in Brans-Dicke theory of gravitation

A five dimensional Kaluza-Klein space-time is considered in the presence of perfect fluid source in a scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). A cosmological model with a negative constant deceleration parameter is presented using a relation between the metric potentials and an equation of state. The model obtained can be considered as a five dimensional radiating universe in this theory. Some physical and kinematical properties of the model are also discussed.

New class of rotating perfect fluid black holes in three dimensional gravity

We obtain a new class of rotating black holes for Einstein theory with perfect fluid source in (2+1) dimensions. We conclude that these black hole solutions only depend on variable angular velocity $m(r)$. Some examples of these black holes are given explicitly. In particular, the unknown static black hole in this special background is obtained. In addition, the general properties including the horizon structure, energy conditions and equation of state, mass and angular momentum are explained in detail.

Axially symmetric cosmological model in f(R, T) gravity

An axially symmetric space-time is considered in the presence of a perfect fluid source in the framework of f (R, T) gravity, where R is the Ricci scalar and T is the trace of the energy-momentum tensor proposed by Harko et al. (Phys. Rev. D 84, 024020, (2011)). We assume the variation law of mean Hubble parameter to obtain the exact solutions of the field equations. The geometrical and physical parameters for both the models are studied.

Bianchi Type-II Dark Energy Model in f(R,T) Gravity

The spatially homogeneous and totally anisotropic Bianchi Type-II space-time dark energy model with EoS parameter is considered in the presence of a perfect fluid source in the framework of f(R,T) gravity proposed by Harko et al. (Phys. Rev. D, 84:024020, 2011). With the help of special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B, 74:182, 1983) a dark energy cosmological model is obtained in this theory. We consider f(R,T) model and investigate the modification R+f(T) in Bianchi type-II cosmology with an appropriate choice of a function f(T)=λT. We use the power law relation between average Hubble parameter H and average scale factor R to find the solution. The assumption of constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. Some physical and kinematical properties of the model are also discussed.

On the constraints problem for the Einstein–Yang–Mills–Higgs system

We provide proofs of some key propositions that were used in previous work by Dossa and Tadmon dealing with the characteristic initial value problem for the Einstein–Yang–Mills–Higgs (EYMH) system. The aforesaid proofs were missing, making the considered work difficult to understand. This work is presented with a view to have an almost self-contained paper. With this respect we completely recall the process of constructing initial data for the EYMH system on two intersecting smooth null hypersurfaces as done in the work of Dossa and Tadmon mentioned above. This is achieved by successfully adapting the hierarchical method set up by Rendall to solve the same problem for the Einstein equations in vacuum and with perfect fluid source. Many delicate calculations and expressions are given in details so as to address, in a forthcoming work, the issue of global resolution of the characteristic initial value problem for the EYMH system. The method obviously applies to the Einstein–Maxwell and the Einstein-scalar field models as well.

Kaluza-Klein dark energy cosmological model in scale Co-variant Theory of Gravitation

A five dimensional Kaluza-Klein dark energy model with variable EoS parameter is investigated in the scale co-variant theory of gravitation proposed by Canuto et al. (in Phys. Rev. 39:429, 1977) in a five dimensional Kaluza-Klein space-time in the presence of perfect fluid source. Using the special law of variation for Hubble’s parameter proposed by Berman (in Nuovo Cimento B 74:183, 1983), we have obtained a determinate solution which represents a dark energy cosmological model in the theory. We have also used the result that the scalar expansion is proportional to shear scalar of the space-time. It is observed that the EoS parameter, skewness parameter in the model turn out to be functions of cosmic time. Some physical and Kinematical properties of the model are also discussed.

Some Kaluza-Klein cosmological models in f(R,T) gravity theory

Algorithms are derived for constructing five dimensional Kaluza-Klein cosmological space-times in the presence of a perfect fluid source in the framework of f(R,T) gravity theory proposed by Harko et al. (Phys. Rev. D 84:024020, 2011). Starting from the solution of Reddy et al. (Int. J. Theor. Phys 51:3222-3227, 2012b) some classes of new solutions are generated which correspond to accelerating models of the Universe. The physical and kinematical behaviors of the models are studied.

Late Time Isotropy Viewed Through Bianchi Type I Cosmological Models with Vacuum Energy

We investigate Bianchi type I cosmological models for perfect fluid source with time-dependent cosmological term Λ. We explore the possibility of cosmological models assuming the expansion anisotropy (the ratio σ/θ of the shear scalar σ to the volume expansion θ) to be a function of average scale factor R. The resulting models begin with initial anisotropy and approach isotropy at late times. The models evolve with decelerating expansion and enters into accelerating phase for large values of t.

Erratum to: An approximate global solution of Einstein’s equation for a rotating compact source with linear equation of state

We use analytic perturbation theory to present a new approximate metric for a rigidly rotating perfect fluid source with equation of state (EOS) \(\epsilon +(1-n)p=\epsilon _0\). This EOS includes the interesting cases of strange matter, constant density and the fluid of the Wahlquist metric. It is fully matched to its approximate asymptotically flat exterior using Lichnerowicz junction conditions and it is shown to be a totally general matching using Darmois–Israel conditions and properties of the harmonic coordinates. Then we analyse the Petrov type of the interior metric and show first that, in accordance with previous results, in the case corresponding to Wahlquist’s metric it can not be matched to the asymptotically flat exterior. Next, that this kind of interior can only be of Petrov types I, D or (in the static case) O and also that the non-static constant density case can only be of type I. Finally, we check that it can not be a source of Kerr’s metric.

An approximate global solution of Einstein’s equation for a rotating compact source with linear equation of state

We use analytic perturbation theory to present a new approximate metric for a rigidly rotating perfect fluid source with equation of state (EOS) \(\epsilon +(1-n)p=\epsilon _0\). This EOS includes the interesting cases of strange matter, constant density and the fluid of the Wahlquist metric. It is fully matched to its approximate asymptotically flat exterior using Lichnerowicz junction conditions and it is shown to be a totally general matching using Darmois–Israel conditions and properties of the harmonic coordinates. Then we analyse the Petrov type of the interior metric and show first that, in accordance with previous results, in the case corresponding to Wahlquist’s metric it can not be matched to the asymptotically flat exterior. Next, that this kind of interior can only be of Petrov types I, D or (in the static case) O and also that the non-static constant density case can only be of type I. Finally, we check that it can not be a source of Kerr’s metric.

FORM INVARIANCE SYMMETRY GENERATES A LARGE SET OF FRW COSMOLOGIES

We show that Einstein's field equations for spatially flat Friedmann–Robertson–Walker (FRW) spacetimes have a form invariance symmetry (FIS) realized by the form invariance transformations (FIT) which are indeed generated by an invertible function of the source energy density. These transformations act on the Hubble expansion rate, the energy density and pressure of the cosmic fluid; likewise such transformations are endowed with a Lie group structure. Each representation of this group is associated with a particular fluid and consequently a determined cosmology, so that, the FIS defines a set of equivalent cosmological models. We focus our seek in the FIT generated by a linear function because it provides a natural framework to express the duality and also produces large sets of cosmologies, starting from a seed one, in several contexts as for instance in the cases of a perfect fluid source and a scalar field driven by a potential depending linearly on the scalar field kinetic energy density.

Higher Dimensional Cosmological Models Filled with Perfect Fluid in f(R,T) Theory of Gravity

The new class of higher dimensional cosmological model of the early universe filled with perfect fluid source in the framework of f(R,T) theory of gravity (Harko et al. in Phys. Rev. D 84, 024020, 2011) is considered. A cosmological model with an appropriate choice of the function f(T) has been constructed. The physical behavior of the model is studied. The well known astrophysical phenomena, namely the Hubble parameter H(z), luminosity distance (d L ) and distance modulus μ(z) with redshift are discussed.

Conformally 2 + 2-decomposable perfect fluid spacetimes with constant curvature factor manifolds

Conformally 2 + 2-decomposable non-conformally flat spacetimes, which are the solutions of the Einstein field equations with a perfect fluid source, are discussed. These spacetimes are necessarily of Petrov-type D and, when the fluid velocity is aligned with the plane of principal null directions, form a subset of the LRSII class, determined up to two first-order partial differential equations. When, on the contrary, the fluid is non-aligned, the general solution can be given in terms of elementary functions.

Bianchi type-III Dark Energy Model in f(R,T) Gravity

A dark energy model with EoS parameter is investigated in f(R,T) gravity in Bianchi type-III space-time in the presence of perfect fluid source. To obtain a determinate solution special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B 74:183, 1983) is used. We have also assumed that the scalar expansion is proportional to shear and the EoS parameter is proportional to skewness parameter. It is observed that the EoS parameter, skewness parameters in the model turn out to be functions of cosmic time. Some physical and kinematical properties of the model are also discussed.

Bianchi Type V Universe Models with Specific Expansion Anisotropy

We investigate Bianchi type V cosmological models for perfect fluid source with time varying cosmological term Λ. We examine the possibility of cosmological models assuming the expansion anisotropy (the ratio σ/θ of the shear scalar σ to the volume expansion θ) to be a function of average scale factor R. The resulting models begin with initial anisotropy and approach isotropy at late times. Our models present an initial epoch with decelerating expansion followed by late time acceleration consistent with observations.

Bianchi type-III cosmological model in f(R,T) theory of gravity

A spatially homogeneous Bianchi type-III space-time is considered in the presence of perfect fluid source in the frame work of f(R,T) gravity (Harko et al. in Phys. Rev. D 84:024020, 2011) with the help of a special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento B 74:182, 1983). A cosmological model with an appropriate choice of the function f(T) has been constructed. The physical behavior of the model is studied.

Kaluza-Klein Cosmological Model in f(R,T) Gravity

A five dimensional Kaluza-Klein space-time is considered in the presence of perfect fluid source in f(R,T) gravity proposed by Harko et al. ( arXiv:1104.2669 [gr-qc], 2011). A cosmological model with a negative constant deceleration parameter with an appropriate choice of a function f(T) is presented. To find a determinate solution of the field equations it is assumed that scalar of expansion is proportional to the shear scalar of the space time. The physical behavior of the model is also studied.

Axially symmetric radiating cosmological model in a self-creation cosmology

An axially symmetric space time is considered in the presence of a perfect fluid source in Barbers (Gen. Relativ. Gravit. 14, 117, 1982) second self creation theory of gravitation. An exact radiating cosmological model is presented using a relation between the metric potentials. Some physical and kinematical properties of the model are also discussed.