Well Behaved Charged Generalization of Buchdahl’s Fluid Spheres

In the present article, we have obtained a class of well behaved charged analogues of Buchdahl (Phys. Rev. 116:1027–1034, 1959) neutral perfect fluid solution, which reduces to its neutral counter part in the absence of charge. The solutions so obtained are utilized to depict the super-dense stars models such as models for neutron stars and strange star. It is observed that the models are well behaved for restricted range of the parameter K (1<K≤1.64). Over all the maximum mass and corresponding radius is 2.4495M _Θ and 16.7289 respectively and moment of inertia . Also the pulsars character of the super-dense stars so obtained and has been analyzed with the help of moment of inertia. The analysis of the models reveals both vela and crab pulsars.     

Higher Dimensional Extension of Charged and Neutral Fluid Spheres with Pressure

General exact higher-dimensional (n+2), n>2 solutions in general theory of relativity of Einstein-Maxwell field equations for spherically symmetric distribution of charged pressure perfect fluid are expressed in terms of pressure extending 4-dimensional solutions presented by Bijalwan (Astrophys. Space Sci. 2011, doi:). Subsequently, metrics (e ^λ and e ^υ ), matter density and electric intensity are expressible in terms of pressure. Consequently, Pressure is found to be an invertible arbitrary function of ω (=c ₁+c ₂ r ²), where c ₁ and c ₂ (≠0) are arbitrary constants, and r is the radius of star, i.e. p=p(ω). We present a general solution for charged pressure fluid in terms for ω. We list and discuss some old and new solutions which fall in this category. Also, these solutions satisfy barotropic equation of state relating the radial pressure to the energy density. But we noticed that none of these solutions in terms of pressure for charged fluids has a well behaved neutral counter part for a spatial component of metric e ^λ i.e. choosing same spatial component for charged and neutral fluid. To illustrate the approach, we discovered a new solution for extended charged analogues of Schwarzschild interior solution in higher dimensions which is found to be well behaved only for n=2. The maximum mass found to be 1.512 M _Θ with linear dimension 14.964 km. Physical quantities pressure, energy density, red-shift, velocity of sound and p/c ² ρ are well behaved and monotonically decreasing towards the surface while adiabatic index and charge density are monotonically increasing. For brevity we don’t discuss the numerical results in detailed.     

Charged sphere of shear-free fluids with $$\frac{\partial}{\rho} \partial r \leq 0$$

The Einstein-Maxwell equations for non-static charged shear-free spherically symmetric perfect fluid distribution reduce to a second-order non-linear differential equation in the radial parameter. Several solutions of this equation have been obtained in earlier work without considering the general requirement for physical relevance of the solutions. Generally physically acceptable relativistic fluid models demand that the solutions satisfy the reality conditions ρ ≥ 0, p ≥ 0, ρ _r ≤ 0, etc. throughout the fluid model. In this article the expression for density gradient ρ _x (or ρ _r ) has been utilized to produce charged shear-free relativistic fluid models with non-positive density gradient (NDG)ρ _r ≤ 0. Eventually, we have found that none of the Riccati solutions have NDG including Vaidya metric. Also, the solutions with NDG neither possess Lie-symmetries nor Painlevé property. Further, it is observed that the solutions with NDG have no uncharged analogue.     

Relativistic stellar models

We obtain a class of solutions to the Einstein–Maxwell equations describing charged static spheres. Upon specifying particular forms for one of the gravitational potentials and the electric field intensity, the condition for pressure isotropy is transformed into a hypergeometric equation with two free parameters. For particular parameter values we recover uncharged solutions corresponding to specific neutron star models. We find two charged solutions in terms of elementary functions for particular parameter values. The first charged model is physically reasonable and the metric functions and thermodynamic variables are well behaved. The second charged model admits a negative energy density and violates the energy conditions.     

A Class of Well Behaved Charged Analogues of Schwarzchild’s Interior Solution

A class of well behaved charged analogues of Schwarzchild’s interior solution has been obtained using a particular electric intensity. The solutions of this class are utilized to depict a superdense star model with surface density 2×10¹⁴ g cm⁻³. The solution obtained is new and the pressure (p), density (c ² ρ), velocity of sound and (p/(c ² ρ)) are monotonically decreasing towards the pressure free interface. Moreover the adiabatic constant is found to be more than (4/3) which is necessary for stability under radial perturbation. Also the electric intensity increases monotonically towards the surface. The well behaved model has the maximum mass M=1.740793M _Θ , Radius 12.130308 km. The redshift at the center and on the surface is given by z ₀=0.384261 and z _a =0.292489. Out of the models of superdense star obtained couple of models represent Vela Pulsar for (i) α ²=1.03, b=0.33, , Radius=10.8566 km, M=1.18331M _Θ , I=0.642601×10⁴⁵, (ii) α ²=1.1, b=0.3, , Radius=11.197533 km, M=1.311438M _Θ , I=0.774508×10⁴⁵. All the solutions mentioned above are reducible to Schwarzchild interior solution in the absence of charge.     

Bounds on charged lepton mixing with exotic charged leptons

We examine the effects of mixing induced light heavy charged lepton neutral currents on the partial wave amplitude for the process l⁺l⁻ →ZZ (withl = e,μ or τ). By imposing the constraints that the amplitude should not exceed the perturbative unitarity limit at high energy (√s = Λ), we obtain bounds on light heavy charged lepton mixing parameter sin²(2θ _L ^a ) where θ _L ^a is the mixing angle of the ordinary charged lepton with its exotic partner. For Λ = 1 TeV, no bound is obtained on sin² (2θ _L ^a ) form _E < 0.69 TeV. However, sin² (2θ _L ^a ) ≤ 1.52×10⁻⁵ form _E = 5 TeV, sin² (2θ _L ^a ) ≤ 2.41 ×10⁻⁷ form _E = 10 TeV. Similarity for Λ = ∞ no bound is obtained on sin² (2θ _L ^a ) for m_E < 1.97 TeV and sin² (2θ _L ^a ) ≤ 0.15 form _E = 5 TeV and sin² (2θ _L ^a ) ≤ 3.88×10^-2 form _E = 10 TeV.     

A Class of Super Dense Stars Models Using Charged Analogues of Hajj-Boutros Type Relativistic Fluid Solutions

We present a spherically symmetric solution of the general relativistic field equations in isotropic coordinates for perfect charged fluid, compatible with a super dense star modeling. The solution is well behaved for all the values of Schwarzschild parameter u lying in the range 0 < u < 0.1727 for the maximum value of charge parameter K = 0.08163. The maximum mass of the fluid distribution is calculated by using stellar surface density as ρ _b = 4.6888×10¹⁴g cm^?3. Corresponding to K = 0.08 and u _max = 0.1732, the resulting well behaved solution has a maximum mass M = 0.9324M _⊙ and radius R = 8.00 and by assuming ρ _b = 2×10¹⁴g cm^?3 the solution results a stellar configuration with maximum mass M = 1.43M _⊙ and radius R _b = 12.25 km. The maximum mass is found increasing with increasing K up to 0.08. The well behaved class of relativistic stellar models obtained in this work might has astrophysical significance in the study of internal structure of compact star such as neutron star or self-bound strange quark star like Her X-1.     

On Charged Analogues of Matese and Whitman Interior Solutions in General Relativity

A set of three static fluid spheres once derived by Matese and Whitman (in Phys. Rev. D 22:1270, 1980) are charged by means of a particular electric intensity to obtain compact objects like white dwarfs, quark stars and neutron stars etc. The charged objects so obtain and their neutral counterparts are analysed on astrophysical grounds. This revealed that two of the charged spheres and one of the neutral seed solutions are well behaved. The corresponding red shift and adiabatic index together with other physical entities like pressure, density and velocity of sound through the star models are studied systematically.     

Mean flow scaling along smooth and rough wall boundary layers

Effects of the upstream conditions and the degree of the wall roughness on the mean velocity profiles and some integral flow parameters in two dimensional zero-pressure-gradient boundary layer were characterized experimentally. The results were analyzed utilizing conventional and recent scaling flow parameters for 245< Re _θ ≤ 11·10³, where Re _θ is the Reynolds number based on the free stream velocity (Ū _∞) and the momentum thickness (θ). Good correlation of the quantity ΔŪ ⁺ as a function of the roughness parameter k ⁺ was obtained for sand roughness of 1.7 < k ⁺ ≤ 172, revealing a universality of the roughness effect, where ΔŪ ⁺ = = (Ū _∞ − Ū)/u _τ and K ⁺ = ku _τ /v.The mean flow structure of the outer flow was observed not to be influenced by the degree of the wall roughness, i. e., the outer flow of either the smooth or the rough surfaces scales similarly with the various scaling parameters regardless the degree of the wall roughness. However, it made flow confined to the wall region away from the classical universality, allowing similarity hypothesis not to be identical in the wall region at least for the current range of the Reynolds number.     

Effects of Hall current on unsteady MHD flows of a second grade fluid

The aim of this present paper is to construct exact solutions corresponding to the motion of magnetohydrodynamic (MHD) fluid in the presence of Hall current, due to cosine and sine oscillations of a rigid plate as well as those induced by an oscillating pressure gradient. A uniform magnetic field is applied transversely to the flow. By using Fourier sine transform steady state and transient solutions are presented. These solutions satisfy the governing equations and all associated initial and boundary conditions. The results for a hydrodynamic second grade fluid can be obtained as a limiting case when B ₀ → 0 and for a Newtonian fluid when α ₁ → 0.     

Conformal anisotropic relativistic charged fluid spheres with a linear equation of state

We obtain two new families of compact solutions for a spherically symmetric distribution of matter consisting of an electrically charged anisotropic fluid sphere joined to the Reissner–Nordstrom static solution through a zero pressure surface. The static inner region also admits a one parameter group of conformal motions. First, to study the effect of the anisotropy in the sense of the pressures of the charged fluid, besides assuming a linear equation of state to hold for the fluid, we consider the tangential pressure p _⊥ to be proportional to the radial pressure p _r , the proportionality factor C measuring the grade of anisotropy. We analyze the resulting charge distribution and the features of the obtained family of solutions. These families of solutions reproduce for the value C=1, the conformal isotropic solution for quark stars, previously obtained by Mak and Harko. The second family of solutions is obtained assuming the electrical charge inside the sphere to be a known function of the radial coordinate. The allowed values of the parameters pertained to these solutions are constrained by the physical conditions imposed. We study the effect of anisotropy in the allowed compactness ratios and in the values of the charge. The Glazer’s pulsation equation for isotropic charged spheres is extended to the case of anisotropic and charged fluid spheres in order to study the behavior of the solutions under linear adiabatic radial oscillations. These solutions could model some stage of the evolution of strange quark matter fluid stars.     

KNΛ and KNΣ coupling constants from the Chiral Bag Model

The KNΛ and KNΣ coupling constants have been calculated in the framework of the Chiral Bag Model(CBM). We find −3.88 ≤g _KNΛ≤−3.67 and 1.15 ≤g _KNΣ≤ 1.24 by taking into account pseudoscalar mesons (π, K) and vector mesons (ρ, ω, K ^*) field effects. Particularly, it is shown that vector mesons make significant contributions to the coupling constants g _KNΛ and g _KNΣ. Our values are existing within the experimental limits compared to the phenomenological values extracted from the kaon photoproduction and kaon-nucleon scattering experiments. Also, form factors are suggested for the πNN, πNΔ, KNΛ and KNΣ couplings. Received: 17 August 1998 / Revised version: 22 December 1998     

Bianchi Type-III Cosmological Models with Time Dependent Displacement Vector for Barotropic Fluid Distribution in Lyra Geometry

Bianchi Type-III cosmological models for perfect fluid distribution with time dependent displacement field in the framework of Lyra geometry are investigated. To get the deterministic model of the universe, we have assumed two conditions (i) shear (σ) is proportional to the expansion (θ). This leads to B=C ⁿ where B and C are metric potentials and n is a constant. (ii) Universe is filled with barotropic fluid distribution which leads to p=γ ρ, 0≤γ≤1, p being isotropic pressure and ρ the energy density. The physical and geometrical aspects of the model with a special case and singularities in the models are also discussed.     

Pion and kaon electromagnetic form factors in a SUL(3) ⊗ SUR(3) effective Lagrangian

A SU(2) effective Lagrangian is extended to a SU _L(3) ⊗SU _R(3) by including the vector and axial vector meson. With this effective Lagrangian, electromagnetic form factors of charged pion and kaon are calculated in both time- and space-like regions. The pseudoscalar meson loops are taken into account. Good agreement with experimental data is obtained for those form factors and charged pseudoscalar meson radii. Decay widths of ρ→ππ and φ→K ⁺ K ^- are also calculated and shown to agree with experimental data very well. Received: 20 December 1999 / Accepted: 12 October 2000     

3D Visualization of the separated fluid flows

For the detailed investigation of the 3D unsteady incompressible viscous separated fluid flows around a sphere (for 200≤Re≤700) and a circular cylinder (for 200≤Re≤400) the direct numerical simulation and 3D visualization are used. For 3D visualization of the fluid flows around a sphere the definition of vortex core as a connected region containing two negative eigenvalues of theS ²+Ω ² tensor is used (whereS _i,j andΩ _ij are the rate of strain and the rate of rotation tensors). The formation mechanism of vortices in the sphere wake for Re=500 is described in detail. For 3D visualization of the fluid flows around a circular cylinder the 3D isosurfaces of the streamwise component of vorticity ω _x are used.     

Kinetics of triplet-triplet absorption of anionic water-soluble porphyrins

It was established that in aqueous solutions of anionic porphyrins the processes of triplet-triplet (T-T) annihilation are absent (K₂<2.5·10⁵ M⁻¹ sec⁻¹), while a delayed annihilation fluorescence can be detected for these porphyrins in methanol (K₂≊3.5·10⁷ M⁻¹ sec⁻¹) and for their lipophilic analogs in organic solutions (K ₂≊2.5·10⁹ M⁻¹ sec⁻¹), and the kinetics of absorption of the latter porphyrins in triplet states is dependent on the intensity of the exciting radiation. The extremely small constant of T-T annihilation of anionic porphyrins can be due to the formation of a relatively dense solvate shell consisting of water molecules around the charged groups of the porphyrin molecules, which increases steric barriers and thus prevents an exchange-resonance transfer of energy between triplet excited molecules in aqueous solutions. It is also shown that porphyrin molecules can electrostatically repel one another when in their structure there are charged groups. To whom correspondence should be addressed. Deceased. Institute of Molecular and Atomic Physics, National Academy of Sciences of Belarus, 70 F. Skorina Ave., Minsk, 220072, Belarus; e-mail: llum@imaph.bas-net.by. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 6, pp. 791–795, November–December, 1999.     

Black holes with metric and fields of the same form

We present two rotating black hole solutions with axion ξ, dilaton f{\phi} and two U(1) vector fields. Starting from a non-rotating metric with three arbitrary parameters, which we have found previously, and applying the “Newman–Janis complex coordinate trick” we get a rotating metric g _μν with four arbitrary parameters namely the mass M, the rotation parameter a and the charges electric Q _E and magnetic Q _M . Then we find a solution of the equations of motion having this g _μν as metric. Our solution is asymptotically flat and has angular momentum J = M a, gyromagnetic ratio g = 2, two horizons, the singularities of the solution of Kerr, axion and dilaton singular only when r = a cos θ = 0 etc. By applying to our solution the S-duality transformation we get a new solution, whose axion, dilaton and vector fields have one more parameter. The metrics, the vector fields and the quantity l = x+ie^-2f{\lambda=\xi+ie^{-2\phi}} of our solutions and the solution of: Sen for Q _E , Sen for Q _E and Q _M , Kerr–Newman for Q _E and Q _M , Kerr, Reference Kyriakopoulos [Class. Quantum Grav. 23:7591, 2006, Eqs. (54–57)], Shapere, Trivedi and Wilczek, Gibbons–Maeda–Garfinkle–Horowitz–Strominger, Reissner–Nordstr?m, Schwarzschild are the same function of a, and two functions ρ ² = r(r + b) + a ² cos² θ and Δ = r(r + b) − 2Mr + a ² + c, of a, b and two functions for each vector field, and of a, b and d respectively, where a, b, c and d are constants. From our solutions several known solutions can be obtained for certain values of their parameters. It is shown that our two solutions satisfy the weak the dominant and the strong energy conditions outside and on the outer horizon and that all solutions with a metric of our form, whose parameters satisfy some relations satisfy also these energy conditions outside and on the outer horizon. This happens to all solutions given in the “Appendix”. Mass formulae for our solutions and for all solutions which are mentioned in the paper are given. One mass formula for each solution is of Smarr’s type and another a differential mass formula. Many solutions with metric, vector fields and λ of the same functional form, which include most physically interesting and well known solutions, are listed in an “Appendix”.     

Electromagnetic Form Factors of Nucleons in a Relativistic Three-Quark Model

We study electromagnetic form factors of nucleons within a relativistic three-quark model with a Gaussian shape for the nucleon-quark vertex. The allowed regions for two adjustable parameters, the range parameter Λ _N in the Gaussian and the constituent quark mass m _q , are obtained from fitting the data for magnetic moments and electromagnetic radii of nucleons. It is found that these observables, when calculated with m _q = 420 MeV and Λ _N = 1.25 GeV, agree very well with the experimental data. For these parameter values, however, our model underestimates the electromagnetic form factors of the nucleon at high momentum transfers for the calculated range O ≤ Q²≤ 1 GeV². Received April 10, 1996; revised June 20, 1996; accepted for publication July 19, 1996     

Dielectric spectroscopy of PbZr1 ? xTixO3 solid solutions (0.495 ≤ x ≤ 0.51) in a temperature range of 100–300 K at frequencies from 1 × 10?2 to 2 × 107 Hz

The behavior of the relative permittivity ɛ/ɛ₀ of PbZr_{1 − x} Ti _x O₃ (PZT) solid solutions (0.495 ≤ x ≤ 0.51) in the temperature range of 100–300 K at frequencies from 1 × 10⁻² to 2 × 10⁷ Hz was investigated. Diffuse, strongly relaxing maxima at T = 230−260 K (x = 0.495−0.505) and 150–160 K (x = 0.510) were observed in the PZT studied. The relaxation processes are well described by the Vogel-Fulcher law, and the dielectric spectra are approximated by the Cole-Cole formula.     

Neutral perfect fluids of Majumdar-type in general relativity

We consider the extension of the Majumdar-type class of static solutions for the Einstein-Maxwell equations proposed by Ida to include charged perfect fluid sources. We impose the equation of state ρ+3p = 0 and discuss spherically symmetric solutions for the linear potential equation satisfied by the metric. In this particular case the fluid charge density vanishes and we locate the arising neutral perfect fluid in the intermediate region defined by two thin shells with respective charges Q and −Q. With its innermost flat and external (Schwarzschild) asymptotically flat spacetime regions, the resultant condenser-like geometries resemble solutions discussed by Cohen and Cohen in a different context. We explore this relationship and point out an exotic gravitational property of our neutral perfect fluid. We mention possible continuations of this study to embrace non-spherically symmetric situations and higher dimensional spacetimes.