The absence of the Kerr black hole in the Hořava–Lifshitz gravity

We show that the Kerr metric does not exist as a fully rotating black hole solution to modified Hořava–Lifshitz (HL) gravity with Λ _W =0 and λ=1. We do this by showing that the Kerr metric does not satisfy the full equations derived from modified HL gravity.     

Kerr property of cubic K0.95Li0.05Ta0.60Nb0.40O3 single crystal

The Kerr (quadratic electro-optic) property of K_0.95Li_0.05Ta_0.60Nb_0.40O₃ was measured by using an automated scanning Mach–Zehnder interferometer. K_0.95Li_0.05Ta_0.60Nb_0.40O₃ has large Kerr effect with R₁₁ = 7.2 × 10⁻¹⁶ m²/V² and R₁₂ = −1.2 × 10⁻¹⁶ m²/V² at 632.8 nm near its phase-transition temperature. The dielectric and Kerr properties as function of temperature were also investigated, thus the quadratic polarization-optic coefficients were calculated. The values of g₁₁ and g₁₂ are 0.083 m⁴/C² and −0.014 m⁴/C², respectively, and do not depend on temperature within the measurement accuracy of 5%.     

Which coordinate representations can give correct Hawking temperature of Kerr black hole by tunneling approach

Some authors found that, in different coordinates, the tunneling approach gives different Hawking temperature for the Schwarzschild black hole recently. In this paper, by studying the Hawking radiation of the Kerr black hole arising from the scalar and Dirac particles, we find that, to obtain the Hawking temperature by using tunneling effect, the coordinate representations for the stationary Kerr black hole should satisfy two conditions: (a) to keep the Killing vectors x_(t)^m{{\xi_{(t)}^\mu}} and x_(j)^m{{\xi_{(\varphi)}^\mu}} invariant; and (b) the radial coordinate transformation is a regular and non-zero function.     

Kerr-type solution in Brans-Dicke theory

The Kerr-type solution in the Brans-Dicke theory should contain three parameters: a massm, a rotational parametera ₀, and a coupling parameter It goes over to the Kerr solution in Einstein's theory of general relativity in the limit 8. Using these conditions, we construct a special solution from Bruckman's solutions which can be regarded as a Kerr-type solution in the Brans-Dicke theory.     

A Kerr-NUT metric

Using Galilean time and retarded distance as coordinates the usual Kerr metric is expressed in form similar to the Newman-Unti-Tamburino (NUT) metric. The combined Kerr-NUT metric is then investigated. In addition to the Kerr and NUT solutions of Einstein's equations, three other types of solutions are derived. These are (i) the radiating Kerr solution, (ii) the radiating NUT solution satisfyingR _ik= _{i k} , _i ⁱ = 0, and (iii) the associated Kerr solution satisfyingR _ik=0. Solution (i) is distinct from and simpler than the one reported earlier by two of us (P.C.V.; L.K.P) [6]. Solutions (ii) and (iii) give line elements which have the axis of symmetry as a singular line.     

The harmonic-map structure of the axially symmetric stationary Einstein equations

We systematically review the solutions of the vacuum Einstein equations for the axially symmetric stationary case which are harmonic maps. In particular, we show that the interesting part of the Kerr solution is a composition of a harmonic map intoH ₁ ² with a totally geodesic map fromH ₁ ² into SS(1,1). We also point out, relying on Sanchez' results, that there is an analogous structure for the Lorentz-domain cases involving cylindrical gravitational waves and colliding plane waves.     

Static and stationary axially symmetric gravitational fields of bounded sources. I. Solutions obtainable from the van Stockum metric

This paper shows that a new class of axially symmetric static electrovacuum solutions and the Kerr solution are obtainable from the van Stockum metric. The new class contains an infinite set of asymptotically flat solutions (in closed form), each of which involves an arbitrary set of parameters. The parameters have to be interpreted as functions of massm, chargee, and higher electric multipole moments _i of the particle. The casee= _i =0 leads to the Darmois metric. Well-known and new examples are given.     

Growth and optical properties of paraelectric K<Subscript>1-y</Subscript>Na<Subscript>y</Subscript>Ta<Subscript>1-x</Subscript>Nb<Subscript>x</Subscript>O<Subscript>3</Subscript> single crystals

We report the successful growth of an electroholographic crystal, potassium sodium tantalate niobate (KNTN), by a top-seeded solution growth method. Both blue and colorless crystals were obtained. The structure, optical absorption, and refractive dispersion properties of the as-grown crystals have been investigated. Furthermore, the Kerr coefficients R₁₁ and R₁₂ of paraelectric K_0.95Na_0.05Ta_0.61Nb_0.39O₃ single crystal were determined by using an automated scanning Mach–Zehnder interferometer. The crystal has large Kerr coefficients with R₁₁= 2.8×10^-16 m²/V² and R₁₂= -0.3×10^-16 m²/V² at the wavelength of 632.8 nm near its cubic–tetragonal phase boundary. PACS 81.10.Dn; 42.70.Nq     

AG 2 II algebraically general twistfree vacuum spacetime

Several authors, e.g., Kerr and Debney (1970), Lun (1978), have obtained severalG ₂ II algebraically special vacuum solutions. NoG ₂ II algebraically general vacuum solutions in explicit form have been found before. In this paper, we start from a system of first order partial differential equations, obtained by using a triad formalism, which determines twistfree vacuum metrics with a spacelike Killing vector. The method of group-invariant solutions is then used and aG ₂ II algebraically general twistfree vacuum solution is obtained. The solution also admits a homothetic Killing vector and is non-geodesic. It is believed to be new. The following explicit solutions are also obtained: (1) A Petrov type II with aG ₁-group of motions solution which belongs to Kundt's class. (2) A Petrov type III,G ₃ Robinson-Trautman solution. All these solutions are known.     

Infinite Operator-Sum Representation of Density Operator for a Dissipative Cavity with Kerr Medium Derived by Virtue of Entangled State Representation

By using the thermo entangled state representation we solve the master equation for a dissipative cavity with Kerr medium to obtain density operators’ infinite operator-sum representation ρ(t)=∑ _m,n,l=0^∞ M _m,n,l ρ ₀ℳ _m,n,l ^† . It is noticeable that M _m,n,l is not Hermite conjugate to ℳ _m,n,l ^† , nevertheless the normalization ∑ _m,n,l=0^∞ℳ _n,m,l ^† M _m,n,l =1 still holds, i.e., they are trace-preserving in a general sense. This example may stimulate further studying if general superoperator theory needs modification.     

Precession of angular momentum vector in a slowly rotating Kerr metric

Specializing Penrose and Floyd's resultF _ab;c =F _[ab;c] to the Kerr metric, we explicitly construct the skew symmetric tensorF _ab and Carter's quadratic integral of geodesic motion.F _ab is then shown to be closely related to the orbital angular momentum encountered in Newtonian mechanics. Furthermore, F_ab can be decomposed additively intoL _ab andM _ab , whereL _ab has the character of angular momentum, andM _ab exists only for a nonzero rotation parameter,a, of the Kerr metric. It turns out that the equation of precession = _a ^b L _b has a nontrivial solution only for the case of a slowly rotating Kerr metric valid to first order in rotation parameter. In this case, Carter's integral can be interpreted as the squared length of the precessing angular momentum vectorL _a =L _a ^b P _b . The equation of precession is solved, and a vector ^a describing angular velocity of precession is derived.     

Kerr effect of molecular oxygen at λ=1064 nm

We report a new measurement of the Kerr effect of molecular oxygen at λ= 1064 nm. The experimental value reported for the anisotropy of the index of refraction Δ n_u^l, (3.15±0.85)×10^-25 m² V^-2 atm^-1, is in good agreement with the value of 3.4×10^-25 m² V^-2 atm^-1 obtained via an ab initio calculation. We show that the dependence of the effect on the pressure is not linear because of the presence of a collision-induced absorption band around 1060 nm due to the transition from the X³ Σ^-_g ground state to the ¹Δ_g state. We also give the value of the quadratic anisotropy Δn_u^q (-1.03±0.68)×10^-25 m² V^-2 atm^-2. We finally compare our ab initio theoretical and experimental results with previous existing data.     

GdFeCo磁光薄膜中RE-TM反铁磁耦合与激光感应超快磁化翻转动力学研究

使用飞秒时间分辨抽运-探测磁光克尔光谱技术,研究了激光加热GdFeCo磁光薄膜跨越铁磁补偿温度时稀土-过渡金属(RE-TM)反铁磁交换耦合行为和超快磁化翻转动力学. 实验观察到由于跨越铁磁补偿温度、净磁矩携带者交换而引起的磁化翻转反常克尔磁滞回线以及在同向外磁场下,反常回线上大于和小于矫顽力部分的饱和磁化强度不同,显示出GdFeCo中RE与TM之间的非完全刚性反铁磁耦合. 在含有Al导热底层的GdFeCo薄膜上观测到饱和磁场下激光感应磁化态翻转及再恢复的完整超快动力学过程. 与剩磁态的激光感应超快退磁化过 关键词： 补偿温度 磁化翻转 反铁磁耦合 GdFeCo     

Preparation and characterization of Y-Fe alloy nanowires by template-assisted electrodeposition from aqueous solution

In this study, a method was proposed for the preparation of Y-Fe alloy nanowires by PC membrane template-assisted electrodeposition from aqueous solution. Citric acid  acted as complexing agent was used into the solution to fabricate Y-Fe alloy nanowires. The electrolyte solution consisted of 5 g L^?1 YCl₃, 12.5 g L^?1 FeSO·6H₂O, different concentrations of citric acid , 25 g L^?1 boric acid in deionized water. The energy dispersive spectroscopy (EDS) found that the content of Y in the nanowires can be controlled by citric acid concentration and the current intensity, and the content of Y could reach up to 33.16 wt%. Scanning electron microscopy (SEM), BET specific surface area (BET), and X-ray diffraction (XRD) showed that there was a shift in the structure of nanowires from semicrystalline to amorphous due to the change of Y content, and their shapes were approximately 100 nm in diameter and 6 μm in length; the surface areas of nanowires were about 3.97 m²/g. Fourier transform infrared (FTIR) spectroscopy, UV–Vis diffuse reflectance spectroscopy, and X-ray photoelectron spectroscopy (XPS) indicated the formation of Y-Fe alloy, Y₂O₃ and Fe₂O₃   existed  in the outer layer of nanowires. The magnetic field applied both parallel and perpendicular to the nanowires by alternating gradient magnetometer (AGM) showed small magnetic anisotropy and low coercivity with easy axis of magnetization perpendicular to the nanowires. In addition, the magneto-optic Kerr effect (MOKE) was investigated, and a Kerr rotation angle of 29 mdeg was obtained.     

Light Quark Hadron Mass Scale

With a symmetry procedure based on Noether's theorem, the field equation of motion is obtained from the Dirac Hamiltonian H(D_μ) of a massless quark interacting with a gluon. The equation of motion is the Yang-Mills equation with external current which is spin-dependent and follows from the group algebra. In addition to the pure gauge solution we find a gauge covariant solution which follows from current conservation and sets the mass scale m₀/M = g². This gluon field is due to the density of dipole moments squared and represents four harmonic oscillators with quadratic constraints; the gluon can be written as a string potential or as a 1/x potential with a sharp cutoff. The chiral symmetry group G^spin × G^D gives the light quark hadron degenerate multiplet mass spectrum in terms of m₀[SU(2) × SU(2)] with the spinorial decomposition and the multipole breaks into dipoles. Scaling from atomic lengths it is found that g = em₀/nM for light quarks is the quark charge e/3 renormalized by m₀/M and g is magnetic. Thus quarks occur at the ends of spinning magnetic strings with dipole lengths ∼m₀⁻¹. The mass scale is that of a degenerate magnetic multipole with charge n = 3, 4… .     

A new technique for determination of melting temperature of poly(ethylene glycol) by ultrasonic velocimetry

Ultrasonic velocity and density of poly(ethylene glycol) (PEG) (mol. wt. 2000 and 8000) solutions in water and benzene have been studied as a function of temperature from which respective isentropic compressibility has also been calculated. The velocity (as well as isentropic compressibility) undergoes a sudden change near melting temperature, T _m, of the solute polymer. Normally, we expect only one peak in viscoelastic properties at the T _m of PEG. However, we see two peaks (T _m1 and T _m2) in the case of the aqueous solution of PEG while there is only one peak for the case of benzene solution. This has been interpreted on the basis that one of the peaks (T _m1) is for unsolvated PEG and the other peak (T _m2) is that of PEG with water solvation shell. Such solvation shell is not formed with the aprotic solvent (benzene).     

Mass dependence of nitride sputtering

A molecular dynamics simulation was performed to study the sputtering yield Y for BN, AlN and GaN polycrystals of wurtzite structure as a function of the masses m ₁ of bombarding ions with energies from 200 to 2000 eV. A nonmonotonic behavior of the Y(m ₁) curve was obtained for the irradiation by low-energy ions, the curve having a maximum with a position being dependent on m₂/m₁ (m₂ is the average mass of atoms in a compound). For AlN and GaN the maximum was observed at m₂/m₁ = 2, and for BN at m₂/m₁ = 1. The effect of the mass of bombarding ions on the mean energies and energy spectra of sputtered particles, the depth of sputtering origin, and the generation of emitted atoms for nitrides was also investigated and discussed.     

On frequency and temperature dependence of limiting efficiency in direct utilization of quasi-monochromatic radiation

The solution to the problem on limiting (thermodynamically permissible) efficiency η_m of direct conversion of energy of quasi-monochromatic radiation into work known from the literature leads to physically unacceptable results (η_m<0) in the range of small frequencies ν and temperatures T _ν of converted radiation. It is shown that the noted feature is a consequence of the approximate character of the mentioned solution obtained without taking into account background heat radiation: the exact solution obtained for η_m is valid for all ν and T _ν ≥ 0 and turns into the solution known earlier for $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ Fiziki, Vol. 70, No. 3, 2000, pp. 34–36.     

Magnetooptical properties and FMR in granular nanocomposites (Co84Nb14Ta2) x (SiO2)100? x

For nanodimensional magnetically inhomogeneous amorphous granular films of the system (Co₈₄Nb₁₄Ta₂) _x (SiO₂)_100−x , 30≤x≤60 at.% the concentration dependences of the magnetooptical Kerr effect (MOKE) spectra and FMR have been investigated. The observed changes in the MOKE and FMR spectra are associated with transformations of microstructure and topology of the nanocomposites. For the compositions within the percolation region the transversal Kerr effect increases by an order of magnitude.