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 distribution. Based on these assumptions several features are explored which seems physically very interesting.
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…
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.
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 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 ou…
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…
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…
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 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 consider source-free electromagnetic fields in spacetimes possessing a non-null Killing vector field, $ξ^a$. We assume further that the electromagnetic field tensor, $F_{ab}$, is invariant under the action of the isometry group induced by $ξ^a$. It is proved that whenever the two potentials associated with the electromagnetic field are functionally independent the entire content of Maxwell's equations is equivalent to the relation $\n^aT_{ab}=0$. Since this relation is implied by Einstein's equation we argue that it is enough to solve merely Einstein's equation for these electrovac spacetim…
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…
We investigate properties of higher-dimensional generally rotating black-hole spacetimes, so called Kerr-NUT-(A)dS spacetimes, as well as a family of related spaces which share the same explicit and hidden symmetries. In these spaces, we study a particle motion in the presence of a weak electromagnetic field and compare it with its operator analogies. First, we find general commutativity conditions for classical observables and for their operator counterparts, then we investigate a fulfillment of these conditions in the Kerr-NUT-(A)dS and related spaces. We find the most general form of the we…
We find a new property in $W^2$-conformal gravity in spherical symmetry. We demonstrate that the charge of the electromagnetic field varies with respect to the partial scaling symmetry (conformal transformations in subspaces of a spacetime) in the conformal gravity. We find that the electric and magnetic charges can vanish or appear via partial conformal transformations for the on-shell configurations in the conformal gravity. We find a solution of a Yang-Mills SU(2)-charged black hole in the conformal gravity, and further demonstrate that the SU(2) charge has similar properties with electroma…
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.
The exact analytical solutions for vacuum electromagnetic fields of slowly rotating magnetized compact stars in conformal gravity have been studied. Taking the realistic dipolar magnetic field configuration for the star, analytical solutions of the Maxwell equations for the near zone magnetic and the electric fields exterior to a slowly rotating magnetized relativistic star in conformal gravity are obtained. In addition, the dipolar electromagnetic radiation and energy losses from the rotating magnetized compact star in conformal gravity have been studied. With the aim to find observational co…
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.
Maxwell's equations are invariant under both duality rotations and conformal transformations. Recently Bandos, Lechner, Sorokin, and Townsend have found a nonlinear generalisation of electrodynamics which possesses both of these symmetries. We couple this theory to General Relativity and explore self-gravitating configurations with a clear physical interpretation. We find charged black holes and exact gravitational waves. The black hole geometry is Reissner-Nordström, however, the non-linearity parameter acts as a screening factor allowing extremal configurations where the mass of the black ho…
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…
"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…
Using a C-metric-type ansatz, we obtain an exact solution to conformal gravity coupled to a Maxwell electromagnetic field. The solution resembles a C-metric spacetime carrying an electromagnetic charge. The metric is cast in a factorised form which allows us to study the domain structure of its static coordinate regions. This metric reduces to the well-known Mannheim-Kazanas metric under an appropriate limiting procedure, and also reduces to the (Anti-)de Sitter C-metric of Einstein gravity for a particular choice of parameters.
We study scalar and electromagnetic perturbations of a family of nonsingular nonrotating black hole spacetimes that are solutions in a large class of conformally invariant theories of gravity. The effective potential for scalar perturbations depends on the exact form of the scaling factor. Electromagnetic perturbations do not feel the scaling factor, and the corresponding quasinormal mode spectrum is the same as in the Schwarzschild metric. We find that these black hole metrics are stable under scalar and electromagnetic perturbations. Assuming that the quasinormal mode spectrum for scalar per…
Penrose limits are considered in space-times admitting two abelian, space-like Killing vectors in vacuum as well as in the presence of an electromagnetic field. This type of space-times describe inhomogeneous cosmologies as well as colliding plane gravitational and electromagnetic waves. Following the work of Tod [1] the conditions for diagonal Penrose limits are investigated in these backgrounds. The twistor equation is considered in these space-times and solutions given in the Penrose limit.
As a simple application of special conformal transformations, we derive the electromagnetic field produced by an electric charge in hyperbolic motion. Unlike other purely algebraic derivations, here we develop a more intuitive geometrical description, based on Minkowski diagrams.
We extend our analysis for scalar fields in a Robertson-Walker metric to the electromagnetic field and Dirac fields by the method of invariants. The issue of the relation between conformal properties and particle production is re-examined and it is verified that the electromagnetic and massless spinor actions are conformal invariant, while the massless conformally coupled scalar field is not. For the scalar field case it is pointed out that the violation of conformal simmetry due to surface terms, although ininfluential for the equation of motion, does lead to effects in the quantized theory.
We consider electromagnetic fields and charged particle dynamics around non-singular black holes in conformal gravity immersed in an external, asymptotically uniform magnetic field. First, we obtain analytic solutions of the electromagnetic field equation around rotating non-singular black holes in conformal gravity. We show that the radial components of the electric and magnetic fields increase with the increase of the parameters $L$ and $N$ of the black hole solution. Second, we study the dynamics of charged particles. We show that the increase of the values of the parameters $L$ and $N$ and…
A new 8-dim conformal gauging solves the auxiliary field problem and eliminates unphysical size change from Weyl's electromagnetic theory. We derive the Maurer-Cartan structure equations and find the zero curvature solutions for the conformal connection. By showing that every one-particle Hamiltonian generates the structure equations we establish a correspondence between phase space and the 8-dim base space, and between the action and the integral of the Weyl vector. Applying the correspondence to generic flat solutions yields the Lorentz force law, the form and gauge dependence of the electro…
We present a conformal isometry for static extremal black hole solutions in all four-dimensional Einstein-Maxwell-scalar theories with electromagnetic duality groups `of type $E_7$'. This includes, but is not limited to, all supergravity theories with $\mathcal{N}>2$ supersymmetry and all $\mathcal{N}=2$ supergravity theories with symmetric scalar manifolds. The conformal isometry is valid for arbitrary electromagnetic charge configurations and relies crucially on the notion of Freudenthal duality.
Primordial magnetic fields are generated during inflation by considering actions that break the conformal invariance of the electromagnetic field. To break the conformal invariance, the electromagnetic fields are coupled either to the inflaton or to the scalar curvature. Also, a parity violating term is often added to the action in order to enhance the amplitudes of the primordial electromagnetic fields. In this work, we examine the effects of deviations from slow roll inflation on the spectra of non-helical as well as helical electromagnetic fields. We find that, in the case of the coupling t…
As is well known, both Weyl and Weitzenböck spacetimes were initially used as attempts to geometrize the electromagnetic field. In this letter, we prove that this field can also be regarded as a geometrical quantity in an extended version of the Weitzenböck spacetime. The new geometry encompasses features of both Weyl and Weitzenböck spacetimes. In addition, we obtain Einstein's field equations coupled to the Maxwell energy-momentum tensor from a purely geometrical action and, to exemplify the advantage of using this new geometry when dealing with conformal invariance, we construct a model tha…
