scholarly journals CHARGED PERFECT FLUID CONFIGURATIONS WITH A DILATON FIELD

2005 ◽  
Vol 20 (11) ◽  
pp. 821-831 ◽  
Author(s):  
STOYTCHO S. YAZADJIEV
Keyword(s):  
Equation Of State ◽  
Nonlinear Equation ◽  
Helmholtz Equation ◽  
Linear Equation ◽  
Perfect Fluid ◽  
Constant Curvature ◽  
Interior Solution ◽  
Dilaton Field ◽  
Field Equations ◽  
Interior Solutions

We examine static charged perfect fluid configurations in the presence of a dilaton field. A method for construction of interior solutions is given. An explicit example of an interior solution which matches continuously the external Gibbons–Maeda–Garfinkle–Horowitz–Strominger solution is presented. Extremely charged perfect fluid configurations with a dilaton are also examined. We show that there are two types of extreme configurations. For each type the field equations are reduced to a single nonlinear equation on a space of a constant curvature. In the particular case of a perfect fluid with a linear equation of state, the field equations of the first type configurations are reduced to a Helmholtz equation on a space with a constant curvature. An explicit example of an extreme configuration is given and discussed.

Exact solutions of the Einstein–Maxwell equations with linear equation of state

2012 ◽  
Vol 90 (12) ◽  
pp. 1179-1183 ◽  
Author(s):  
Tooba Feroze
Keyword(s):  
Equation Of State ◽  
Linear Equation ◽  
Maxwell Equations ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Fluid Distribution ◽  
Spherically Symmetric ◽  
Field Equations ◽  
General Linear Equation ◽  
Energy Momentum Conservation

Two new classes of solutions of the Einstein–Maxwell field equations are obtained by substituting a general linear equation of state into the energy–momentum conservation equation. We have considered static, anisotropic, and spherically symmetric charged perfect fluid distribution of matter with a particular form of gravitational potential. Expressions for the mass–radius ratio, the surface, and the central red shift horizons are given for these solutions.

scholarly journals On Schwarzschild’s Interior Solution and Perfect Fluid Star Model

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1669
Author(s):  
Elisabetta Barletta ◽  
Sorin Dragomir ◽  
Francesco Esposito
Keyword(s):  
Gravitational Field ◽  
Perfect Fluid ◽  
Interior Solution ◽  
Star Model ◽  
Abelian Integrals ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Gravitational Field Equations ◽  
Radially Symmetric Solutions ◽  
Legendre Form

We solve the boundary value problem for Einstein’s gravitational field equations in the presence of matter in the form of an incompressible perfect fluid of density ρ and pressure field p(r) located in a ball r≤r0. We find a 1-parameter family of time-independent and radially symmetric solutions ga,ρa,pa:−2m<a<a1 satisfying the boundary conditions g=gS and p=0 on r=r0, where gS is the exterior Schwarzschild solution (solving the gravitational field equations for a point mass M concentrated at r=0) and containing (for a=0) the interior Schwarzschild solution, i.e., the classical perfect fluid star model. We show that Schwarzschild’s requirement r0>9κM/(4c2) identifies the “physical” (i.e., such that pa(r)≥0 and pa(r) is bounded in 0≤r≤r0) solutions {pa:a∈U0} for some neighbourhood U0⊂(−2m,+∞) of a=0. For every star model {ga:a0<a<a1}, we compute the volume V(a) of the region r≤r0 in terms of abelian integrals of the first, second, and third kind in Legendre form.

Bianchi type-II universe with linear equation of state

Open Physics ◽  
2014 ◽  
Vol 12 (8) ◽  
Author(s):  
Kishor Adhav ◽  
Ishwar Pawade ◽  
Abhijit Bansod
Keyword(s):  
General Relativity ◽  
Equation Of State ◽  
Cosmological Model ◽  
Linear Equation ◽  
Bianchi Type ◽  
Type Ii ◽  
Field Equations ◽  
Expansion Scalar ◽  
Shear Scalar

AbstractWe have studied anisotropic and homogeneous Bianchi type-II cosmological model with linear equation of state (EoS) p = αρ−β, where α and β are constants, in General Relativity. In order to obtain the solutions of the field equations we have assumed the geometrical restriction that expansion scalar θ is proportional to shear scalar σ. The geometrical and physical aspects of the model are also studied.

scholarly journals LRS Bianchi I model with perfect fluid equation-of-state

2019 ◽  
Vol 28 (03) ◽  
pp. 1950056 ◽  
Author(s):  
Vijay Singh ◽  
Aroonkumar Beesham
Keyword(s):  
Equation Of State ◽  
General Solution ◽  
Perfect Fluid ◽  
Vacuum Energy ◽  
Energy Model ◽  
Field Equations ◽  
Systematic Treatment ◽  
Fluid Equation ◽  
Stiff Matter ◽  
Bianchi I

The general solution of the field equations in LRS Bianchi-I spacetime with perfect fluid equation-of-state (EoS) is presented. The models filled with dust, vacuum energy, Zel’dovich matter and disordered radiation are studied in detail. A unified and systematic treatment of the solutions is presented, and some new solutions are found. The dust, stiff matter and disordered radiation models describe only a decelerated universe, whereas the vacuum energy model exhibits a transition from a decelerated to an accelerated phase.

scholarly journals Analytical model of dark energy stars

2020 ◽  
Vol 35 (10) ◽  
pp. 2050071
Author(s):  
Ayan Banerjee ◽  
M. K. Jasim ◽  
Anirudh Pradhan
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Energy Equation ◽  
Vacuum Solution ◽  
State Parameter ◽  
Accelerated Expansion ◽  
Energy Conditions ◽  
Interior Solution ◽  
Field Equations ◽  
Star Models

In this paper, we study the structure and stability of compact astrophysical objects which are ruled by the dark energy equation of state (EoS). The existence of dark energy is important for explaining the current accelerated expansion of the universe. Exact solutions to Einstein field equations (EFE) have been found by considering particularized metric potential, Finch and Skea ansatz. 1 The obtained solutions are relevant to the explanation of compact fluid sphere. Further, we have observed at the junction interface that the interior solution is matched with the Schwarzschild’s exterior vacuum solution. Based on that, we have noticed the obtained solutions are well in agreement with the observed maximum mass bound of [Formula: see text], namely, PSR J1416-2230, Vela X-1, 4U 1608-52, Her X-1 and PSR J1903+327, whose predictable masses and radii are not compatible with the standard neutron star models. Also, the stability of the stellar configuration has been discussed briefly, by considering the energy conditions, surface redshift, compactness, mass-radius relation in terms of the state parameter [Formula: see text]. Finally, we demonstrate that the features so obtained are physically acceptable and consistent with the observed/reported data.[Formula: see text] Thus, the present dark energy equation of state appears talented regarding the presence of several exotic astrophysical matters.

scholarly journals THE SCHWARZSCHILD'S BRANEWORLD SOLUTION

2010 ◽  
Vol 25 (39) ◽  
pp. 3323-3334 ◽  
Author(s):  
J. OVALLE
Keyword(s):  
Interior Solution ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Geometric Deformation ◽  
Weyl Functions ◽  
Interior Solutions ◽  
Deformation Approach

In the context of the Randall–Sundrum braneworld, the minimal geometric deformation approach, which has been successfully used to generate exact interior solutions to Einstein's field equations for static braneworld stars with local and nonlocal bulk terms, is used to obtain the braneworld version of the Schwarzschild's interior solution. Using this new solution, the behavior of the Weyl functions is elucidated in terms of the compactness for different stellar distributions.

HOMOGENEOUS PERFECT FLUID IN BRANS-DICKE-BIANCHI TYPE V COSMOLOGICAL MODEL

1996 ◽  
Vol 05 (01) ◽  
pp. 65-69 ◽  
Author(s):  
SUBENOY CHAKRABORTY ◽  
GOPAL CH. NANDY
Keyword(s):  
Equation Of State ◽  
Cosmological Model ◽  
Perfect Fluid ◽  
Analytical Solutions ◽  
Bianchi Type ◽  
Field Equations ◽  
Type V ◽  
Bianchi Type V

In this paper we have studied homogeneous perfect fluid for the Bianchi type V model in the Brans-Dicke theory. The equation of state is assumed to be [Formula: see text]. Some analytical solutions to the field equations are obtained for the radiation era.

scholarly journals f(R,T)-Gravity Model with Perfect Fluid Admitting Einstein Solitons

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 82
Author(s):  
Mohd Danish Siddiqi ◽  
Sudhakar K. Chaubey ◽  
Mohammad Nazrul Islam Khan
Keyword(s):  
Vector Field ◽  
Equation Of State ◽  
Perfect Fluid ◽  
Gravity Model ◽  
Ricci Tensor ◽  
Field Equations ◽  
Metric Tensor ◽  
Research Article ◽  
Phantom Barrier ◽  
Liouville’S Equation

f(R,T)-gravity is a generalization of Einstein’s field equations (EFEs) and f(R)-gravity. In this research article, we demonstrate the virtues of the f(R,T)-gravity model with Einstein solitons (ES) and gradient Einstein solitons (GES). We acquire the equation of state of f(R,T)-gravity, provided the matter of f(R,T)-gravity is perfect fluid. In this series, we give a clue to determine pressure and density in radiation and phantom barrier era, respectively. It is proved that if a f(R,T)-gravity filled with perfect fluid admits an Einstein soliton (g,ρ,λ) and the Einstein soliton vector field ρ of (g,ρ,λ) is Killing, then the scalar curvature is constant and the Ricci tensor is proportional to the metric tensor. We also establish the Liouville’s equation in the f(R,T)-gravity model. Next, we prove that if a f(R,T)-gravity filled with perfect fluid admits a gradient Einstein soliton, then the potential function of gradient Einstein soliton satisfies Poisson equation. We also establish some physical properties of the f(R,T)-gravity model together with gradient Einstein soliton.

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