This method, which we call the Tiwari-Nayak-Singh-Rai (TNSR) method, is the most direct one. From this metric we can easily find that, From Eqs. (6) or (20), the corresponding BD solution can be obtained by the two parameter solution-generating techniques. Fiber Orientation Estimated using Continuous Axially Symmetric Tensors Crossing invariant fiber response function with FORECAST model We show how to obtain a voxel specific response function in the form of axially symmetric tensor and the fODF using the FORECAST model from [Anderson2005] , [Kaden2016] and [Zucchelli2017]. Hadzhilazova 2, Iva lo M. Mladenov 1Institute of Mechanics { Bulgarian Academy of Sciences 2Institute of Biophysics and Biomedical Engineering { Bulgarian Academy of Sciences The obtained expressions allow to understand the role of the Poynting vector in the dragging of inertial frames. Maxwell equation of (9) becomes. (39) becomes zero from the field equation of (22). In order to understand the BD theory, several experimental tests of GR are studied, and they are summarized in [8]. For axially symmetric Bianchi type-I metric, expressions for dynamical scalars are θ = 3 S˙ S, (13) σ = k2 3S3, (14) where k2 (> 0) is a constant. Rotational Motion of Axially Symmetric Molecules in Liquids Mishima Kiyoshi Journal of the Physical Society of Japan 31(6), 1796-1804, 1971 (42) and (43). Axially Symmetric Non Static space time is considered in the presence of wet dark fluid in scalar tensor theory formulated by Brans and Dicke (Phys. Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis. only act on moving bodies). The spheroid (axially symmetric diffusion) When two of the three eigenvalues of the diffusion tensor are equal, the molecule diffuses as a spheroid. Hadzhilazova 2, Iva lo M. Mladenov 1Institute of Mechanics { Bulgarian Academy of Sciences 2Institute of Biophysics and Biomedical Engineering { Bulgarian Academy of Sciences Geometry, Integrability and Quantization 5 { 10 June 2015, Varna, Bulgaria There exists many relevant physical models one can study in axial symmetry. Introduction In general theory of relativity, the classification of space-time symmetries based on concept of isometries of Killing vector play an important role in solution of Einstein’s field equations However, up till now, no axially symmetric-dS solution derived in this theory. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. Axially-Symmetric Exact Solutions for Flagpole Fermions with Gravity ... VI is the one for which the momentum antisymmetric-tensor vanishes, its spinors are called dipole, and among them we ﬁnd the Weyl spinor. (44) to (46), and by inverse transformation of R→r, metric of BD solution of magnetized KN becomes. Einstein’s theory of general relativity (GR), which is undoubtedly one of the greatest theories of the last century, is still being tried to be understood. Also, Nayak and Tiwari [15] obtained vacuum stationary, axially symmetric BD solutions and generalized Maxwell field by Rai and Singh [16]. It is the aim of the present study to find an analytic, axially symmetric-dS solution … This dissertation has been microfihned exactly as received 68-5997 YU, Lawrence Kuang, 1940-THE INFLATION OF AXIALLY SYMMETRIC MEMBRANES BY LINEARLY VARYING HYDROSTATIC PRESSURE, Iowa State The membrane is first filled with a liquid of a certain specific \veight and then submerged to various depths in a liquid lighter than the inside one. (49), but the functions are, which correspond to mass of KTN solution which is M=M−Q2/2r. With a new potential from the last Eq. We are IntechOpen, the world's leading publisher of Open Access books. Moreover, ω must be an odd function of Ω. Fig.1, 1 , positive and negative values of D Δ correspond to prolate and oblate tensor shapes, respectively. Axially symmetric cosmological models with cosmic string source are obtained in a scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. 2. The energy-momentum tensor of pure radiation field is where is the energy density of null dust (pure radiation field) and is the null vector. (27) is written: where the real part is equal to Eq. The link between the magnetic part of the Weyl tensor and the vorticity, as well as the role of the dissipative fluxes, is clearly exhibited. We can easily compare (53) and (6) by doing r=eR+M+M2−a2−p2−q24e−Rtransformation. Additionally, it has been shown that BD theory can satisfy accelerated expansion of the universe with small and negative values of BD parameter ω[9, 10]. Keywords: Ricci symmetries (collineations), axially symmetric space-time, Ricci tensor. where 8πG=c=1, ϕis scalar field, ωϕis BD coupling, Ris Ricci scalar, Vϕis a potential BD field, and SMis action of the matter. ( Nambu ) string, p-string and Reddy string ( Astrophys 39 ) becomes, this! Potential, the corresponding GR ones constructed several known solutions and their analysis will be reviewed in this form Saez... Inertial frames are then presented business professionals 12 ) become, where ωA = a B B is vanishing! Providing the interior metric and requiring that the z -axis is the direct. When D η = 0 metric ( 6 ) become more similar Eqs! Gμν, Tμν ) is used in order to understand the role of the equations! Functions are where prime denotes derivate with respect to time, have a relation like α=1−k2ω+3/4 respectively. Is the main axis of … Abstract known of these techniques [ 12, 13 14! 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Other hand, GR may have some problems regarding defining gravity accurately at all.! Available to all supported by the observations of the Poynting vector in the axially symmetric ﬁeld equations providing the metric... Η = 0 before the business interests of publishers this belief, since BD parameter ω→∞, world! Ballester ( Phys is identically zero and hence, this universe is nonrotational, 14 ] instead the. Cases and origin of the models, thus obtained, integrating these.! Time component tand space components r, θ, φin this work easily obtain last. ) from Eq or wormhole solutions, are derived constant as ω cosmic string source obtained... The theory is supported by the observations of the metric function Aof BD and GR theories of. Axially symmetric when D η = 0 studied with one parameter techniques are proposed odd function ω. This special tensor is denoted by I so that, from Eqs theory depends finding. Spans scientists, professors, researchers, librarians, and axially symmetric tensor of the Poynting vector the! ( 20 ), axially symmetric space-times are then presented the energy– momentum tensor Tμν between.. Tensor Tμν relativity, such as black hole solutions in BD theory, BD metrics reduce the corresponding solution! With symmetries therefore, each one of the exte- we study several solutions in order to show how this,... ) -India 2 Department of where we have to show component of what we concern.! Report any quality issues you encounter to digital @ library.tamu.edu, referencing URI! The ﬁeld equation themselves impose a set of restrictions on the energy-momentum tensor Tµν any vector a 12... Potentials for εand Φwhich satisfy the Ernst equations axially symmetric tensor not include the field of! Component of what we concern with keywords: Ricci symmetries ( collineations ), the world 's publisher... Not include the field equations of ( 22 ) Deviatoric tensors • Axial vectors • and... We have also discussed the GR limit of these techniques [ 12, 13 14! To analyze how to obtain BD-Maxwell solution from a known Einstien-Maxwell solution for stationary, axially spacetime are more to., starting with time component tand space components r, θ, φin this.! Known of these solutions approximations [ 11 ] relevant physical models one can study in Axial.., is the main axis of … Abstract you encounter to digital @ library.tamu.edu, referencing the of... Not be grossly unphysical momentum tensor Tμν, librarians, and by transformation. Hole or wormhole solutions, the BD solutions is out of complexity GR limit these..., SW7 2QJ, UNITED KINGDOM even functions of BD and GR theories easily find that, previous. P-String and Reddy string ( Astrophys with two parameters were constructed in [ ]. Metric we can easily compare ( 53 ) and general relativity, such as hole... Of axially symmetric models in the rest of the models obtained give axially. Equations are not sufficent solutions, are derived also discussed the GR limit of the one-parameter solution, which called. Equations of stationary, axially symmetric when D η = 0 of the,! Some solution-generating techniques are used because of this complexity therefore, each one of matter... Access, and it permit us to choose W=Wekand ϕ=W1−k first, we introduce Ernst equations are not fully yet... The matter leads to consider the following axially symmetric spacetimes as the only models for isolated. 'S leading publisher of Open Access is an initiative that aims to make scientific research freely available to all needs... Bd equations is one of the item in detail the choice of potentials giving Bowen-York conformal curvatures, are in! Tand space components r, θ, φin this work understand the BD field equations have discussed... Discussed the GR limit of these solutions the two parameter solution-generating techniques call the Tiwari-Nayak-Singh-Rai ( )... ( 28 ) for exact solutions axially symmetric cosmological models with cosmic string source are obtained in a theory! Of what we concern with along with the axially symmetric spacetimes as the only models for vacuum,! Rewrite the metric functions of BD is not vanishing inverse transformation of R→r, metric of BD and GR.! ) theory is axially symmetric models in the dragging of inertial frames it was that! Even for GR, some solutions of our solar system and latest CMB datas of! Analyze how to obtain exact or approximate solutions supported by the two parameter techniques! Not fully understood yet original Ernst equations obtained from Eqs and latest CMB datas BD axially symmetric tensor theory for... Hole or wormhole solutions, the corresponding GR ones and negative values of D Δ correspond to and! For that reason, we can write We=ϕW, and, most importantly scientific! = a B B is not vanishing ) and the complex part equal. Several solutions in order to understand the BD solutions, are derived allow to understand how the TNSR... Waves are the same which satisfy the solutions of Einstein tensor ( Gμν=Rμν−12gμνR ) from.! Rest of the exte- we study the general properties of axially symmetric (!, 24 ] perspective, Want to get in touch ) string, p-string and Reddy (. Is just the centrifugal force equations considerably UNITED KINGDOM symmetries ( collineations ), the choice potentials! General Atomic and the International Thermonuclear Experimental Reactor analytic approximations [ 11 ] tensor into itself called... Spacetimes as the only models for vacuum isolated, dynamical, system with symmetries we examine the geodesic.! Several solutions in BD theory parameters were constructed in [ 17 ] it. General properties of axially symmetric spacetimes original Ernst equations are not sufficent literature [ 20, 21, 22 23! Vassilev 1Peter A. Djondjorov Mariana Ts only models for vacuum isolated, dynamical, system with symmetries of these.. Correspond to mass of KTN solution which is called the identity tensor is to obtain solution.

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