(2,2)-Formalism of General Relativity: An Exact Solution

I discuss the (2,2)-formalism of general relativity based on the (2,2)-fibration of a generic 4-dimensional spacetime of the Lorentzian signature. In this formalism general relativity is describable as a Yang-Mills gauge theory defined on the (1+1)-dimensional base manifold, whose local gauge symmetry is the group of the diffeomorphisms of the 2-dimensional fibre manifold. After presenting the Einstein's field equations in this formalism, I solve them for spherically symmetric case to obtain the Schwarzschild solution. Then I discuss possible applications of this formalism.Comment: 2 figures included, IOP style file neede

Electronic Transport in the Oxygen Deficient Ferromagnetic Semiconducting TiO2−δ_{2-\delta}

TiO$_{2-\delta}$ films were deposited on (100) Lanthanum aluminates LaAlO$_{3}$ substrates at a very low oxygen chamber pressure $P\approx 0.3$ mtorr employing a pulsed laser ablation deposition technique. In previous work, it was established that the oxygen deficiency in these films induced ferromagnetism. In this work it is demonstrated that this same oxygen deficiency also gives rise to semiconductor titanium ion impurity donor energy levels. Transport resistivity measurements in thin films of TiO$_{2-\delta}$ are presented as a function of temperature and magnetic field. Magneto- and Hall- resistivity is explained in terms of electronic excitations from the titanium ion donor levels into the conduction band.Comment: RevTeX4, Four pages, Four Figures in ^.eps forma

New Hamiltonian formalism and quasi-local conservation equations of general relativity

I describe the Einstein's gravitation of 3+1 dimensional spacetimes using the (2,2) formalism without assuming isometries. In this formalism, quasi-local energy, linear momentum, and angular momentum are identified from the four Einstein's equations of the divergence-type, and are expressed geometrically in terms of the area of a two-surface and a pair of null vector fields on that surface. The associated quasi-local balance equations are spelled out, and the corresponding fluxes are found to assume the canonical form of energy-momentum flux as in standard field theories. The remaining non-divergence-type Einstein's equations turn out to be the Hamilton's equations of motion, which are derivable from the {\it non-vanishing} Hamiltonian by the variational principle. The Hamilton's equations are the evolution equations along the out-going null geodesic whose {\it affine} parameter serves as the time function. In the asymptotic region of asymptotically flat spacetimes, it is shown that the quasi-local quantities reduce to the Bondi energy, linear momentum, and angular momentum, and the corresponding fluxes become the Bondi fluxes. The quasi-local angular momentum turns out to be zero for any two-surface in the flat Minkowski spacetime. I also present a candidate for quasi-local {\it rotational} energy which agrees with the Carter's constant in the asymptotic region of the Kerr spacetime. Finally, a simple relation between energy-flux and angular momentum-flux of a generic gravitational radiation is discussed, whose existence reflects the fact that energy-flux always accompanies angular momentum-flux unless the flux is an s-wave.Comment: 36 pages, 3 figures, RevTex

Nano granular metallic Fe - oxygen deficient TiO2−δ_{2-\delta} composite films: A room temperature, highly carrier polarized magnetic semiconductor

Nano granular metallic iron (Fe) and titanium dioxide (TiO$_{2-\delta}$) were co-deposited on (100) lanthanum aluminate (LaAlO$_3$) substrates in a low oxygen chamber pressure using a pulsed laser ablation deposition (PLD) technique. The co-deposition of Fe and TiO$_2$ resulted in $\approx$ 10 nm metallic Fe spherical grains suspended within a TiO$_{2-\delta}$ matrix. The films show ferromagnetic behavior with a saturation magnetization of 3100 Gauss at room temperature. Our estimate of the saturation magnetization based on the size and distribution of the Fe spheres agreed well with the measured value. The film composite structure was characterized as p-type magnetic semiconductor at 300 K with a carrier density of the order of $10^{22} /{\rm cm^3}$. The hole carriers were excited at the interface between the nano granular Fe and TiO$_{2-\delta}$ matrix similar to holes excited in the metal/n-type semiconductor interface commonly observed in Metal-Oxide-Semiconductor (MOS) devices. From the large anomalous Hall effect directly observed in these films it follows that the holes at the interface were strongly spin polarized. Structure and magneto transport properties suggested that these PLD films have potential nano spintronics applications.Comment: 6 pages in Latex including 8 figure

Rotating Black Hole Entropy from Two Different Viewpoints

Using the brick-wall method, we study the entropy of Kerr-Newman black hole from two different viewpoints, a rest observer at infinity and zero angular momentum observer near horizon. We investigate this with scalar field in the canonical quantization approach. An observer at infinity can take one of the two possible frequency ranges; one is with positive frequencies only and the other is with the whole range including negative frequencies. On the other hand, a zero angular momentum observer near horizon can take positive frequencies only. For the observer at infinity the superradiant modes appear in either choice of the frequency ranges and the two results coincide. For the zero angular momentum observer superradiant modes do not appear due to absence of ergoregion. The resulting entropies from the two viewpoints turn out to be the same.Comment: LaTeX 18 pages, 2 figures, Minor modifications in section 3(ZAMO

Controlling internal barrier in low loss BaTiO3 supercapacitors

Supercapacitor behavior has been reported in a number of oxides including reduced BaTiO3 ferroelectric ceramics. These so-called giant properties are however not easily controlled. We show here that the continuous coating of individual BaTiO3 grains by a silica shell in combination with spark plasma sintering is a way to process bulk composites having supercapacitor features with low dielectric losses and temperature stability. The silica shell acts both as an oxidation barrier during the processing and as a dielectric barrier in the final composite

Free Energy Approach to the Formation of an Icosahedral Structure during the Freezing of Gold Nanoclusters

The freezing of metal nanoclusters such as gold, silver, and copper exhibits a novel structural evolution. The formation of the icosahedral (Ih) structure is dominant despite its energetic metastability. This important phenomenon, hitherto not understood, is studied by calculating free energies of gold nanoclusters. The structural transition barriers have been determined by using the umbrella sampling technique combined with molecular dynamics simulations. Our calculations show that the formation of Ih gold nanoclusters is attributed to the lower free energy barrier from the liquid to the Ih phases compared to the barrier from the liquid to the face-centered-cubic crystal phases