In this paper, model of charged gravastar under $f(T)$ modified gravity is obtained. The model has been explored by taking the diagonal tetrad field of static spacetime together with electric charge. To solve the Einstein-Maxwell field equations, along with $f(T)$ gravity, we assume the existence of a conformal Killing vector which relates between geometry and matter through the Einstein-Maxwell field equations by an inheritance symmetry. We study several cases of interest to explore physically valid features of the solutions. Some physical properties of the model are discussed and we match our interior spacetime to the exterior Reissner-Nordström spacetime in presence of thin shell.
In this work, we study the Mazur and Mottola gravastar model within the context of Randall-Sundrum II type braneworld scenario, based on the fact that our four dimensional space-time is a three-brane, embedded in a five dimensional bulk. We present exact solutions of the modified field equations in each of the three regions making up the gravastar, namely, (I) the core, (II) the shell, and (III) the vacuum exterior. The junction conditions at each interface are fulfilled and we further explore interesting physical properties such as length and energy and entropy of the spherical distribution.
We propose a new model of a {\it gravastar} admitting conformal motion. While retaining the framework of the Mazur-Mottola model, the gravastar is assumed to be internally charged, with an exterior defined by a Reissner-Nordstr{ö}m rather than a Schwarzschild line element. The solutions obtained involve (i) the interior region, (ii) the shell, and (iii) the exterior region of the sphere. Of these three cases the first case is of primary interest since the total gravitational mass vanishes for vanishing charge and turns the total gravitational mass into an {\it electromagnetic mass} under certa…
This paper investigates the influence of charge on physical features of gravastars in the framework of energy-momentum squared gravity. A gravastar is an alternate model to a black hole that comprises of three distinct regions, namely the intermediate shell, inner and outer sectors. Different values of the barotropic equation of state parameter provide the mathematical formulation for these regions. We construct the structure of a gravastar admitting conformal motion for a specific model of energy-momentum squared gravity. The field equations are formulated for a spherically symmetric spacetim…
This paper studies the effects of charge on a peculiar stellar object, recognized as gravastar, under the influence of $f(R,T)$ gravity by considering the conjecture of Mazur and Mottola in general relativity. The gravastar is also known as an alternative to a black hole and is expressed by three distinct domains named as (i) the interior domain, (ii) the intermediate shell and (iii) the exterior domain. We analyze these domains for a specific $f(R,T)$ gravity model conceding the conformal Killing vectors. In the interior domain, we assume that pressure is equal to negative energy density whic…
We provide a new class of interior solutions for anisotropic stars admitting conformal motion. The Einstein's field equations in this construction are solved for specific choices of the density/mass functions. We analyze the behavior of the model parameters like radial and transverse pressures, density and surface tension.
Space-times admitting a 3-dimensional Lie group of conformal motions $C_3$ acting on null orbits are studied. Coordinate expressions for the metric and the conformal Killing vectors (CKV) are then provided (irrespectively of the matter content) and all possible perfect fluid solutions are found, although none of them verifies the weak and dominant energy conditions over the whole space-time manifold.
We provide a set of exact spherically symmetric solutions describing the interior of a relativistic star under f(T) modified gravity. To tackle the problem with lucidity we also assume the existence of a conformal Killing vector field within this f(T) gravity. We study several cases of interest to explore physically valid features of the solutions.
An exact analytical solution describing the interior of a charged strange quark star is found under the assumption of spherical symmetry and the existence of a one-parameter group of conformal motions. The solution describes a unique static charged configuration of quark matter with radius $R=9.46$ km and total mass $M=2.86M_{\odot}$.
This paper has been removed by arXiv administrators because it plagiarizes astro-ph/0611537, astro-ph/0506256, astro-ph/0203033, astro-ph/0311128, gr-qc/0505144, astro-ph/0611460, and astro-ph/0610840.
Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic nor Killing), all such space-times are classified according to the structure of their corresponding three-dimensional conformal Lie group and the nature of their corresponding orbits (that are assumed to be non-null). Each metric is then explicitly displayed in coordinates adapted to the symmetry vectors. Attention is then restricted to the diagonal case, an…
We have investigated the emerging conformal field theory behavior on the interior interface of the region near the cosmological event horizon on an example of massless Dirac fermions. Indeed, we have constructed and verified the emerging de Sitter/CFT correspondence for the near cosmological event horizon region. It is in this near horizon region where the infinitely thin shell of matter with the stiffest equation of state (Zeldovich's matter) is placed in the model for a thermodynamically stable `would be black hole' which is sometimes called a gravastar or a dark energy star. We put forward …
When Morris and Thorne first proposed that traversable wormholes may be actual physical objects, they concentrated on the geometry by specifying the shape and redshift functions. This mathematical approach necessarily raises questins regarding the determination of the required stress-energy tensor. This paper discusses a natural way to obtain a complete wormhole solution by assuming that the wormhole (1) is supported by generalized Chaplygin gas and (2) admits conformal Killing vectors.
We study charged fluid spheres under the 4-dimensional Einstein-Maxwell space-time. The solutions thus obtained admitting conformal motion. We also investigate whether the solutions set provide electromagnetic mass models such that the physical parameters including the gravitational mass arise from the electromagnetic field alone. In this connection three cases are studied here in detail with the propositions: (1) $p = - ρ$, (2) $σe^{λ/2} = σ_0$ and (3) $8 πp - E^2 = p_0$ where $ρ$, $p$, $σ$ are respectively the usual matter density, fluid pressure and charge density of the spherical distribut…
In this article, we study the possibility of sustaining a static and spherically symmetric traversable wormhole geometries admitting conformal motion in Einstein gravity, which presents a more systematic approach to search a relation between matter and geometry. In wormhole physics, the presence of exotic matter is a fundamental ingredient and we show that this exotic source can be dark energy type which support the existence of wormhole spacetimes. In this work we model a wormhole supported by dark energy which admits conformal motion. We also discuss the possibility of detection of wormholes…
We discuss the interior solutions of fluid Sphere in f(R,T) gravity admitting conformal killing vectors, where R is Ricci scalar and T is trace of energy momentum tensor. The solutions corresponding to isotropic and anisotropic configurations have been investigated explicitly. Further, the anisotropic case has been dealt by the utilization of linear equation of state. The results for both cases have been interpreted graphically. The equation of state parameter, integration constants and other parameters of the theory have been chosen to find the central density equal to standard value of centr…
It has been argued that wormholes are as good a prediction of Einstein's theory as black holes but the theoretical construction requires a reverse strategy, specifying the desired geometric properties of the wormhole and leaving open the determination of the stress-energy tensor. We begin by confirming an earlier result by the author showing that a complete wormhole solution can be obtained by adopting the equation of state $p=ωρ$ and assuming that the wormhole admits a one-parameter group of conformal motions. The main purpose of this paper is to use the assumption of conformal symmetry to sh…
When Morris and Thorne first proposed the possible existence of traversable wormholes, they adopted the following strategy: maintain complete control over the geometry, thereby leaving open the determination of the stress-energy tensor. In this paper we determine this tensor by starting with a noncommutative-geometry background and assuming that the static and spherically symmetric spacetime admits conformal motions. This had been established in a previous collaboration with Rahaman et al. using a slightly different approach. Accordingly, the main purpose of this paper is to show that the worm…
We address the problem of finding static and spherically symmetric anisotropic compact stars in general relativity that admit conformal motions. The study is framed in the language of f(R) gravity theory in order to expose opportunity for further study in the more general theory. Exact solutions of compact stars are found under the assumption that spherically symmetric spacetimes which admits conformal motion with matter distribution anisotropic in nature. In this work, two cases have been studied for the existence of such solutions: first, we consider the model given by f(R) = R and then f(R)…
To explain the reason of accelerated expansion of our universe dark energy is a suitable candidate. Motivated by this concept in the present paper we have obtained a new model of an anisotropic superdense star which admits conformal motions in presence of quintessence field which is characterized by a parameter $omega$ with omega lies in the range -1 to -1/3.The model has been developed by choosing Vaidya-Titekar ansatz [P C Vaidya and R Tikekar (1982)J. Astrophys .Astron. 3 325].Our model satisfy all the physical requirements.We have analyze our result analytically as well as with the help of…
All hypersurface homogeneous locally rotationally symmetric spacetimes which admit conformal symmetries are determined and the symmetry vectors are given explicitly. It is shown that these spacetimes must be considered in two sets. One set containing Ellis Class II and the other containing Ellis Class I, III LRS spacetimes. The determination of the conformal algebra in the first set is achieved by systematizing and completing results on the determination of CKVs in 2+2 decomposable spacetimes. In the second set new methods are developed. The results are applied to obtain the classification of …
In this work, we discuss the configuration of a gravastar (gravitational vacuum stars) in the context of $f(R, \,T )$ gravity by employing the Mazur-Mottola conjecture [P. Mazur and E. Mottola, Report No. LA-UR-01-5067; P. Mazur and E. Mottola, Proc. Natl. Acad. Sci. USA $101$, $9545$ ($2004$)]. Gravastar is conceptually a substitute for a black hole theory as available in literature and it has three regions with different equation of states. By assuming that the gravastar geometry admits conformal killing vector, the Einstein-Maxwell field equations have been solved in different regions of gr…
New solutions for $(2+1)$-dimensional Einstein-Maxwell space-time are found for a static spherically symmetric charged fluid distribution with the additional condition of allowing conformal killing vectors (CKV). We discuss physical properties of the fluid parameters. Moreover, it is shown that the model actually represents two structures, namely (i) Gravastar as an alternative of black hole and (ii) Electromagnetic Mass model depending on the nature of the equation state of the fluid. Here the gravitational mass originates from electromagnetic field alone. The solutions are matched with the e…
The theoretical construction of a traversable wormhole proposed by Morris and Thorne maintains complete control over the geometry by assigning both the shape and redshift functions, thereby leaving open the determination of the stress-energy tensor. This paper examines the effect of introducing the linear barotropic equation of state $p_r=ωρ$ on the theoretical construction. If either the energy density or the closely related shape function is known, then the Einstein field equations do not ordinarily yield a finite redshift function. If, however, the wormhole admits a one-parameter group of c…
Methods are presented for finding Killing-Yano tensors, conformal Killing-Yano tensors, and conformal Killing vectors in spacetimes with a hypersurface orthogonal Killing vector. These methods are similar to a method developed by the authors for finding Killing tensors. In all cases one decomposes both the tensor and the equation it satisfies into pieces along the Killing vector and pieces orthogonal to the Killing vector. Solving the separate equations that result from this decomposition requires less computing than integrating the original equation. In each case, examples are given to illust…
In this manuscript, we explore the existence of wormhole solutions exhibiting spherical symmetry in a modified gravity namely $f(R,T)$ theory by involving some aspects of non-commutative geometry. For this purpose, we consider the anisotropic matter contents along with the well-known Gaussian and Lorentizian distributions of string theory. For the sake of simplicity in analytic discussions, we take a specific form of $f(R,T)$ function given by $f(R,T)=R+λT$. For both these non-commutative distributions, we get exact solutions in terms of exponential and hypergeometric functions. By taking some…
We carry on a general study on non--static spherically symmetric fluids admitting a conformal Killing vector (CKV). Several families of exact analytical solutions are found for different choices of the CKV, in both, the dissipative and the adiabatic regime. To specify the solutions, besides the fulfillment of the junction conditions on the boundary of the fluid distribution, different conditions are imposed, such as vanishing complexity factor and quasi--homologous evolution. A detailed analysis of the obtained solutions, its prospective applications to astrophysical scenarios, as well as alte…
In this paper, we investigate conformal Killing's vectors (CKVs) admitted by some plane symmetric spacetimes. Ten conformal Killing's equations and their general forms of CKVs are derived along with their conformal factor. The existence of conformal Killing's symmetry imposes restrictions on the metric functions. The conditions imposing restrictions on these metric functions are obtained as a set of integrability conditions. Considering the cases of time-like and inheriting CKVs, we obtain spacetimes admitting plane conformal symmetry. Integrability conditions are solved completely for some kn…
We study the space-times admitting a null conformal Killing-Yano tensor whose divergence defines a Killing vector. We analyze the similitudes and differences with the recently studied non null case (Gen. Relativ. Grav. (2015) {\bf 47} 1911). The results by Barnes concerning the Birkhoff theorem for the case of null orbits are analyzed and generalized.
Space-times admitting a 3-dimensional Lie group of conformal motions $C_3$ acting on null orbits are studied. Coordinate expressions for the metric and the conformal Killing vectors (CKV) are provided (irrespectively of the matter content) and then all possible perfect fluid solutions are found, although none of these verify the weak and dominant energy conditions over the whole space-time manifold.
Proper conformal symmetries in self-dual (SD) Einstein spaces are considered. It is shown, that such symmetries are admitted only by the Einstein spaces of the type [N]x[N]. Spaces of the type [N]x[-] are considered in details. Existence of the proper conformal Killing vector implies existence of the isometric, covariantly constant and null Killing vector. It is shown, that there are two classes of [N]x[-]-metrics admitting proper conformal symmetry. They can be distinguished by analysis of the associated anti-self-dual (ASD) null strings. Both classes are analyzed in details. The problem is r…
We study the stationary and axisymmetric non-convective differentially rotating perfect-fluid solutions of Einstein's field equations admitting one conformal symmetry. We analyse the two inequivalent Lie algebras not exhaustively considered in Mars and Senovilla, 1994, and show that the general solution for each Lie algebra depends on one arbitrary function of one of the coordinates while a set of three ordinary differential equations for four unknowns remains to be solved. The conformal Killing vector of these solutions is necessarily homothetic. We summarize in a table all the possible solut…
Many theories of gravity admit formulations in different, conformally related manifolds, known as the Jordan and Einstein conformal frames. Among them are various scalar-tensor theories of gravity and high-order theories with the Lagrangian $f(R)$ where $R$ is the scalar curvature and $f$ an arbitrary function. It may happen that a singularity in the Einstein frame corresponds to a regular surface S_trans in the Jordan frame, and the space-time is then continued beyond this surface. This phenomenon is called a conformal continuation (CC). We discuss the properties of vacuum static, spherically…
We consider static, spherically symmetric vacuum solutions to the equations of a theory of gravity with the Lagrangian f(R) where R is the scalar curvature and f is an arbitrary function. Using a well-known conformal transformation, the equations of f(R) theory are reduced to the ``Einstein picture'', i.e., to the equations of general relativity with a source in the form of a scalar field with a potential. We have obtained necessary and sufficient conditions for the existence of solutions admitting conformal continuations. The latter means that a central singularity that exists in the Einstein…
Conformal Killing equations and their integrability conditions for expanding hyperheavenly spaces with Lambda in spinorial formalism are studied. It is shown that any conformal Killing vector reduces to homothetic or isometric Killing vector. Reduction of respective Killing equation to one master equation is presented. Classification of homothetic and isometric Killing vectors is given. Type [D]x[any] is analysed in details and some expanding HH complex metrics of types [III, N]x[III, N] with Lambda admitting isometric Killing vectors are found.
"Diagonal" spatially inhomogeneous (SI) models are introduced under the assumption of the existence of (proper) intrinsic symmetries and can be seen, in some sense, complementary to the Szekeres models. The structure of this class of spacetimes can be regarded as a generalization of the (twist-free) Locally Rotationally Symmetric (LRS) geometries without any global isometry containing, however, these models as special cases. We consider geometries where a six-dimensional algebra $\mathcal{IC}$ of Intrinsic Conformal Vector Fields (ICVFs) exists acting on a $2-$dimensional (pseudo)-Riemannian m…
We study the Einstein field equations for spacetimes admitting a maximal two-dimensional abelian group of isometries acting orthogonally transitively on spacelike surfaces and, in addition, with at least one conformal Killing vector. The three-dimensional conformal group is restricted to the case when the two-dimensional abelian isometry subalgebra is an ideal and it is also assumed to act on non-null hypersurfaces (both, spacelike and timelike cases are studied). We consider both, diagonal and non-diagonal metrics and find all the perfect-fluid solutions under these assumptions (except those …
Global properties of vacuum static, spherically symmetric configurations are studied in a general class of scalar-tensor theories (STT) of gravity in various dimensions. The conformal mapping between the Jordan and Einstein frames is used as a tool. Necessary and sufficient conditions are found for the existence of solutions admitting a conformal continuation (CC). The latter means that a singularity in the Einstein-frame manifold maps to a regular surface S_(trans) in the Jordan frame, and the solution is then continued beyond this surface. S_(trans) can be an ordinary regular sphere or a hor…
We determine conformal symmetry classes for the pp-wave spacetimes. This refines the isometry classification scheme given by Sippel and Goenner (1986 {\it Gen. Rel. Grav.} {\bf 18} 1229). It is shown that every conformal Killing vector for the null fluid type $N$ pp-wave spacetimes is a conformal Ricci collineation. The maximum number of proper non-special conformal Killing vectors in a type $N$ pp-wave spacetime is shown to be three, and we determine the form of a particular set of type $N$ pp-wave spacetimes admitting such conformal Killing vectors. We determine the conformal symmetries of e…
In this paper, we present a complete classification of Locally Rotationally Symmetric (LRS) Bianchi type I spacetimes according to their Conformal Ricci Collineations (CRCs). When the Ricci tensor is non-degenerate, a general form of the vector field generating CRCs is found, subject to some integrability conditions. Solving the integrability conditions in different cases, it is found that the LRS Bianchi type I spacetimes admit 7, 10, 11 or 15- dimensional Lie algebra of CRCs for the choice of non-degenerate Ricci tensor. Moreover, it is found that these spacetimes admit infinite number of CR…
Through an exhaustive search, we produce a 5-parameter family of propagation identities for the closed conformal Killing-Yano equation on 2-forms, which hold on an Einstein cosmological vacuum spacetime in any dimension $n>4$. It is well-known that spacetimes admitting a non-degenerate 2-form of this type are exhausted by the Kerr-NUT-(A)dS family of exact higher dimensional black hole solutions. As a consequence, we identify a set of necessary and sufficient conditions ensuring that the cosmological vacuum development of an initial data set for Einstein's field equations admits a closed confo…
In this paper a thorough study of the normal form and the first integrability conditions arising from {\em bi-conformal vector fields} is presented. These new symmetry transformations were introduced in {\em Class. Quantum Grav.}\textbf{21}, 2153-2177 and some of their basic properties were addressed there. Bi-conformal vector fields are defined on a pseudo-Riemannian manifold through the differential conditions $\lie P_{ab}=ϕP_{ab}$ and $\lieΠ_{ab}=χΠ_{ab}$ where $P_{ab}$ and $Π_{ab}$ are orthogonal and complementary projectors with respect to the metric tensor $\rmg_{ab}$. One of the main re…
The paper aims to investigate curvature inheritance symmetry in M-projectively flat spacetimes. It is shown that the curvature inheritance symmetry in M-projectively flat spacetime is a conformal motion. We have proved that M- projective curvature tensor follows the symmetry inheritance property along a vector field $ξ$, when spacetime admits the conditions of both curvature inheritance symmetry and conformal motion or motion along the vector field $ξ$. Also, we have derived some results for M-projectively flat spacetime with perfect fluid following the Einstein field equations with a cosmolog…
Considering the degenerate and non-degenerate cases, we provide a complete classification of static plane symmetric spacetimes according to conformal Ricci collineations (CRCs) and conformal matter collineations (CMCs). In case of non-degenerate Ricci tensor, a general form of vector field generating CRCs is found in terms of unknown functions of t and x, subject to some integrability conditions. The integrability conditions are then solved in different cases depending upon the nature of Ricci tensor and it is concluded that static plane symmetric spacetimes possess 7, 10 or 15-dimensional Lie…
In this paper we reconsider the existence of stealth fields during the evolution of our Universe by admitting more realistic nonminimal couplings to gravity than the conformal one. In the framework of the FRW cosmology we found that inhomogeneous stealths, as those enabled in the conformal case, are only allowed in de Sitter backgrounds. In particular, it is shown that the homogeneous stealths resulting from nonconformal couplings can coexist with each kind of matter dominant in the several phases characterizing the evolution of our Universe according to the $Λ$CDM model.
