scholarly journals Stable and self-consistent charged gravastar model within the framework of $$f(R,\,T)$$ gravity

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Piyali Bhar ◽  
Pramit Rej
Keyword(s):  
Black Hole ◽  
Present Model ◽  
Killing Vector ◽  
Conformal Killing ◽  
Field Equations ◽  
Spherical Region ◽  
Equation Of States ◽  
Gravitational Vacuum ◽  
Specific Equation ◽  
The Stability

AbstractIn this work, we discuss the configuration of a gravastar (gravitational vacuum stars) in the context of $$f(R, \,T )$$ f ( R , T ) gravity by employing the Mazur–Mottola conjecture (Mazur and Mottola in Report No. LA-UR-01-5067, 2001; Mazur and Mottola, Proc Natl Acad Sci USA 101:9545, 2004). The gravastar is conceptually a substitute for a black hole theory as available in the literature and it has three regions with different equation of states. By assuming that the gravastar geometry admits a conformal Killing vector, the Einstein–Maxwell field equations have been solved in different regions of the gravastar by taking a specific equation of state as proposed by Mazur and Mottola. We match our interior spacetime to the exterior spherical region which is completely vacuum and described by the Reissner–Nordström geometry. For the particular choice of $$f(R,\,T)$$ f ( R , T ) of $$f(R, \,T )=R+2\gamma T$$ f ( R , T ) = R + 2 γ T , here we analyze various physical properties of the thin shell and also present our results graphically for these properties. The stability analysis of our present model is also studied by introducing a new parameter $$\eta $$ η and we explore the stability regions. Our proposed gravastar model in the presence of charge might be treated as a successful stable alternative of the charged black hole in the context of this version of gravity.

scholarly journals Fluid sphere: Stability problem and dimensional constraint

2015 ◽  
Vol 24 (07) ◽  
pp. 1550049 ◽  
Author(s):  
Farook Rahaman ◽  
Anirudh Pradhan ◽  
Nasr Ahmed ◽  
Saibal Ray ◽  
Bijan Saha ◽  
...  
Keyword(s):  
Killing Vector ◽  
Stellar System ◽  
Fluid Sphere ◽  
Conformal Killing ◽  
Stable Configuration ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
The Stability ◽  
Active Gravitational Mass

We study different dimensional fluids inspired by noncommutative geometry which admit conformal Killing vector (CKV). The solutions of the Einstein field equations were examined specifically for five different set of spacetime. We calculate the active gravitational mass and impose stability conditions of the fluid sphere. The analysis thus carried out immediately indicates that at four dimension only one can get a stable configuration for any spherically symmetric stellar system and any other dimension, lower or higher, becomes untenable as far as the stability of a system is concerned.

scholarly journals Black hole and naked singularity geometries supported by three-form fields

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Bruno J. Barros ◽  
Bogdan Dǎnilǎ ◽  
Tiberiu Harko ◽  
Francisco S. N. Lobo
Keyword(s):  
Black Hole ◽  
Killing Vector ◽  
Field Potential ◽  
Naked Singularity ◽  
Radial Coordinate ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Metric Tensor ◽  
Killing Horizon ◽  
Form Field

Abstract We investigate static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert–Einstein action with a Lagrangian constructed from a three-form field $$A_{\alpha \beta \gamma }$$Aαβγ, which is related to the field strength and a potential term. The field equations are obtained explicitly for a static and spherically symmetric geometry in vacuum. For a vanishing three-form field potential the gravitational field equations can be solved exactly. For arbitrary potentials numerical approaches are adopted in studying the behavior of the metric functions and of the three-form field. To this effect, the field equations are reformulated in a dimensionless form and are solved numerically by introducing a suitable independent radial coordinate. We detect the formation of a black hole from the presence of a Killing horizon for the timelike Killing vector in the metric tensor components. Several models, corresponding to different functional forms of the three-field potential, namely, the Higgs and exponential type, are considered. In particular, naked singularity solutions are also obtained for the exponential potential case. Finally, the thermodynamic properties of these black hole solutions, such as the horizon temperature, specific heat, entropy and evaporation time due to the Hawking luminosity, are studied in detail.

Conformally symmetric Friedmann–Robertson–Walker metric in f(R,T) gravity

2020 ◽  
Vol 35 (10) ◽  
pp. 2050067
Author(s):  
Dog̃ukan Taṣer
Keyword(s):  
Perfect Fluid ◽  
Conformal Symmetry ◽  
Killing Vector ◽  
Energy Condition ◽  
Gravitational Theory ◽  
Cosmic Acceleration ◽  
Energy Conditions ◽  
Conformal Killing ◽  
Field Equations ◽  
Frw Universe

In this paper, conformal symmetric Freidmann–Robertson–Walker (FRW) universe with perfect fluid in the framework of [Formula: see text] gravitational theory is investigated. Firstly, field equations of FRW universe with perfect fluid are obtained for [Formula: see text] modified theory of gravity. The field equations of the model have been revised to understand physical nature between matter and geometry by means of conformal symmetry in [Formula: see text] gravitational theory. The exact solutions of conformal FRW universe with perfect fluid are attained for matter part of the [Formula: see text] model in the case of [Formula: see text]. The [Formula: see text] gravitational theory is one of the acceptable modifications of General Relativity (GR) in order to expound cosmic acceleration of the universe with no needing any exotic component. Nevertheless, the obtained model indicates exotic matter distribution for the current selection of arbitrary constants. Also, different value selections of arbitrary constants for the obtained model are able to predicate expanding or contracting universe with zero deceleration. Besides, it is shown that the FRW universe under the influence of the conformal Killing vector preserves to isotropic nature. Energy conditions are investigated. Also, it is shown that the constructed model satisfies strong energy condition (SEC) in all cases.

scholarly journals Isotropic Stars in Higher-Order Torsion Scalar Theories

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Killing Vector ◽  
Higher Order ◽  
Stellar Model ◽  
The Other ◽  
Conformal Killing ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Torsion Scalar ◽  
Scalar Theories ◽  
Symmetric Spacetime

Two different nondiagonal tetrad spaces reproducing spherically symmetric spacetime are applied to the field equations of higher-order torsion scalar theories. Assuming the existence of conformal Killing vector, two isotropic solutions are derived. We show that the first solution is not stable while the second one confirms a stable behavior. We also discuss the construction of the stellar model and show that one of our solutions is capable of such construction while the other is not. Finally, we discuss the generalized Tolman-Oppenheimer-Volkoff and show that one of our models has a tendency to equilibrium.

scholarly journals Conformal and Disformal Structure of 3D Circularly Symmetric Static Metric in f(R) Theory of Gravity

2020 ◽  
Vol 39 (1) ◽  
pp. 111-116
Author(s):  
Muhammad Ramzan ◽  
Murtaza Ali ◽  
Fiaz Hussain
Keyword(s):  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Conformal Killing ◽  
Field Equations ◽  
Killing Vector Fields ◽  
Homothetic Vector ◽  
First Case ◽  
Conformal Vector Fields ◽  
Theory Of Gravity

Conformal vector fields are treated as generalization of homothetic vector fields while disformal vector fields are defined through disformal transformations which are generalization of conformal transformations, therefore it is important to study conformal and disformal vector fields. In this paper, conformal and disformal structure of 3D (Three Dimensional) circularly symmetric static metric is discussed in the framework of f(R) theory of gravity. The purpose of this paper is twofold. Firstly, we have found some dust matter solutions of EFEs (Einstein Field Equations) by considering 3D circularly symmetric static metric in the f(R) theory of gravity. Secondly, we have found CKVFs (Conformal Killing Vector Fields) and DKVFs (Disformal Killing Vector Fields) of the obtained solutions by means of some algebraic and direct integration techniques. A metric version of f(R) theory of gravity is used to explore the solutions and dust matter as a source of energy momentum tensor. This study reveals that no proper DVFs exists. Here, DVFs for the solutions under consideration are either HVFs (Homothetic Vector Fields) or KVFs (Killing Vector Fields) in the f(R) theory of gravity. In this study, two cases have been discussed. In the first case, both CKVFs and DKVFs become HVFs with dimension three. In the second case, there exists two subcases. In the first subcase, DKVFs become HVFs with dimension seven. In the second subcase, CKVFs and DKVFs become KVFs having dimension four.

Quintessence compact stars with Vaidya–Tikekar type grr for anisotropic fluid

2020 ◽  
Vol 98 (9) ◽  
pp. 869-876
Author(s):  
G. Abbas ◽  
M.R. Shahzad
Keyword(s):  
Killing Vector ◽  
Graphical Analysis ◽  
Compact Stars ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Conformal Killing ◽  
Field Equations ◽  
Anisotropic Matter ◽  
Quintessence Field ◽  
Analytical Expressions

The present study provides a new solution to the Einstein field equations for anisotropic matter configuration in static and spherically symmetric space–time. By taking benefit from the conformal Killing vector (CKV) technique and quintessence field specified by a parameter ωq as –1 < ωq < –1/3, we generate an exact solution to the field equations. For this investigation, we have used a specific form of metric potential taken fromVaidya–Tikekar (J. Astrophys. Astron. 3, 325 (1982)) geometry. To canvass the physical plausibility of the presented solution, we explored some analytical expressions such as energy conditions, the TOV equation, stability analysis, and equation of state parameters. We present graphical analysis of the necessary analytical expressions that revealed that our solution satisfies the necessary physical conditions.

scholarly journals Curvature tensor for the spacetime of general relativity

2017 ◽  
Vol 14 (05) ◽  
pp. 1750078 ◽  
Author(s):  
Zafar Ahsan ◽  
Musavvir Ali
Keyword(s):  
General Relativity ◽  
Perfect Fluid ◽  
Curvature Tensor ◽  
Vector Fields ◽  
Killing Vector ◽  
Conformal Killing ◽  
Field Equations ◽  
Text Structures ◽  
Conformal Killing Vector Fields ◽  
Perfect Fluid Spacetime

In the differential geometry of certain [Formula: see text]-structures, the role of [Formula: see text]-curvature tensor is very well known. A detailed study of this tensor has been made on the spacetime of general relativity. The spacetimes satisfying Einstein field equations with vanishing [Formula: see text]-tensor have been considered and the existence of Killing and conformal Killing vector fields has been established. Perfect fluid spacetimes with vanishing [Formula: see text]-tensor have also been considered. The divergence of [Formula: see text]-tensor is studied in detail and it is seen, among other results, that a perfect fluid spacetime with conserved [Formula: see text]-tensor represents either an Einstein space or a Friedmann-Robertson-Walker cosmological model.

scholarly journals Black Hole Algorithm for Sustainable Design of Counterfort Retaining Walls

2020 ◽  
Vol 12 (7) ◽  
pp. 2767 ◽  
Author(s):  
Víctor Yepes ◽  
José V. Martí ◽  
José García
Keyword(s):  
Black Hole ◽  
Sustainable Design ◽  
Retaining Walls ◽  
The Other ◽  
Trade Off ◽  
Construction Company ◽  
Geometric Variables ◽  
The Stability ◽  
The Cost ◽  
Black Hole Algorithm

The optimization of the cost and CO 2 emissions in earth-retaining walls is of relevance, since these structures are often used in civil engineering. The optimization of costs is essential for the competitiveness of the construction company, and the optimization of emissions is relevant in the environmental impact of construction. To address the optimization, black hole metaheuristics were used, along with a discretization mechanism based on min–max normalization. The stability of the algorithm was evaluated with respect to the solutions obtained; the steel and concrete values obtained in both optimizations were analyzed. Additionally, the geometric variables of the structure were compared. Finally, the results obtained were compared with another algorithm that solved the problem. The results show that there is a trade-off between the use of steel and concrete. The solutions that minimize CO 2 emissions prefer the use of concrete instead of those that optimize the cost. On the other hand, when comparing the geometric variables, it is seen that most remain similar in both optimizations except for the distance between buttresses. When comparing with another algorithm, the results show a good performance in optimization using the black hole algorithm.

Properties of strangelets at zero temperature in a new quark mass confinement model

2014 ◽  
Vol 23 (03) ◽  
pp. 1450013 ◽  
Author(s):  
Shiwu Chen ◽  
Qin Li ◽  
Jianfeng Xu ◽  
Li Gao ◽  
Chengjun Xia
Keyword(s):  
Quark Model ◽  
Quark Mass ◽  
Present Model ◽  
Baryon Number ◽  
Zero Temperature ◽  
Gluon Exchange ◽  
The Stability ◽  
Stable Radius ◽  
Confinement Model

We investigate the properties of strangelets at zero temperature with a new quark model in which the linear confinement and one-gluon-exchange (OGE) interactions are integrated as a whole. The charge, parameters dependence and the stability of strangelets are discussed. Our results showed that the OGE interaction lowers the energy of a strangelet, and consequently makes its stable radius smaller than that in the case of not including this interaction, and less than that of a nucleus with the same baryon number. Therefore, the strangelet in the present model has more chance to be absolutely stable.

Pseudo-Z symmetric space-times with divergence-free Weyl tensor and pp-waves

2016 ◽  
Vol 13 (02) ◽  
pp. 1650015 ◽  
Author(s):  
Carlo Alberto Mantica ◽  
Young Jin Suh
Keyword(s):  
Symmetric Space ◽  
Weyl Tensor ◽  
Killing Vector ◽  
Complete Classification ◽  
Space Time ◽  
Conformal Killing ◽  
Conformally Flat ◽  
Conformal Curvature ◽  
Wave Space ◽  
Divergence Free

In this paper we present some new results about [Formula: see text]-dimensional pseudo-Z symmetric space-times. First we show that if the tensor Z satisfies the Codazzi condition then its rank is one, the space-time is a quasi-Einstein manifold, and the associated 1-form results to be null and recurrent. In the case in which such covector can be rescaled to a covariantly constant we obtain a Brinkmann-wave. Anyway the metric results to be a subclass of the Kundt metric. Next we investigate pseudo-Z symmetric space-times with harmonic conformal curvature tensor: a complete classification of such spaces is obtained. They are necessarily quasi-Einstein and represent a perfect fluid space-time in the case of time-like associated covector; in the case of null associated covector they represent a pure radiation field. Further if the associated covector is locally a gradient we get a Brinkmann-wave space-time for [Formula: see text] and a pp-wave space-time in [Formula: see text]. In all cases an algebraic classification for the Weyl tensor is provided for [Formula: see text] and higher dimensions. Then conformally flat pseudo-Z symmetric space-times are investigated. In the case of null associated covector the space-time reduces to a plane wave and results to be generalized quasi-Einstein. In the case of time-like associated covector we show that under the condition of divergence-free Weyl tensor the space-time admits a proper concircular vector that can be rescaled to a time like vector of concurrent form and is a conformal Killing vector. A recent result then shows that the metric is necessarily a generalized Robertson–Walker space-time. In particular we show that a conformally flat [Formula: see text], [Formula: see text], space-time is conformal to the Robertson–Walker space-time.

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