Active tuning of high-Q dielectric metasurfaces

We demonstrate the active tuning of all-dielectric metasurfaces exhibiting high-quality factor (high-Q) resonances. The active control is provided by embedding the asymmetric silicon meta-atoms with liquid crystals, which allows the relative index of refraction to be controlled through heating. It is found that high quality factor resonances ($Q=270\pm30$) can be tuned over more than three resonance widths. Our results demonstrate the feasibility of using all-dielectric metasurfaces to construct tunable narrow-band filters.Comment: 4 pages, 6 figure

Electromagnetic Energy for a Charged Kerr Black Hole in a Uniform Magnetic Field

With the Komar mass formula we calculate the electromagnetic energy for a charged Kerr black hole in a uniform magnetic field. We find that the total electromagnetic energy takes the minimum when the Kerr black hole possesses a non-zero net charge $Q = 2\xi B_0 J_H$ where $B_0$ is the strength of the magnetic field, $J_H$ is the angular momentum of the black hole, $\xi$ is a dimensionless parameter determined by the spin of the black hole.Comment: 9 pages, 1 figur

Schwarzschild black hole levitating in the hyperextreme Kerr field

The equilibrium configurations between a Schwarzschild black hole and a hyperextreme Kerr object are shown to be described by a three-parameter subfamily of the extended double-Kerr solution. For this subfamily, its Ernst potential and corresponding metric functions, we provide a physical representation which employs as arbitrary parameters the individual Komar masses and relative coordinate distance between the sources. The calculation of horizon's local angular velocity induced in the Schwarzschild black hole by the Kerr constituent yields a simple expression inversely proportional to the square of the distance parameter.Comment: 6 pages, 1 figure; improved versio

Conserved Charges for Even Dimensional Asymptotically AdS Gravity Theories

Mass and other conserved Noether charges are discussed for solutions of gravity theories with locally Anti-de Sitter asymptotics in 2n dimensions. The action is supplemented with a boundary term whose purpose is to guarantee that it reaches an extremum on the classical solutions, provided the spacetime is locally AdS at the boundary. It is also shown that if spacetime is locally AdS at spatial infinity, the conserved charges are finite and properly normalized without requiring subtraction of a reference background. In this approach, Noether charges associated to Lorentz and diffeomorphism invariance vanish identically for constant curvature spacetimes. The case of zero cosmological constant is obtained as a limit of AdS, where $\Lambda$ plays the role of a regulator.Comment: 8 pages, RevTeX, no figures, two columns, references added and minor typos corrected, final version for Phys. Rev.

Planck Scale Physics of the Single Particle Schr\"{o}dinger Equation with Gravitational Self-Interaction

We consider the modification of a single particle Schr\"{o}dinger equation by the inclusion of an additional gravitational self-potential term which follows from the prescription that the' mass-density'that enters this term is given by $m |\psi (\vec {r},t)|^2$, where $\psi (\vec {r}, t)$ is the wavefunction and $m$ is the mass of the particle. This leads to a nonlinear equation, the ' Newton Schrodinger' equation, which has been found to possess stationary self-bound solutions, whose energy can be determined exactly using an asymptotic method. We find that such a particle strongly violates superposition and becomes a black hole as its mass approaches the Planck mass.Comment: 16 pages, Revtex, No figure, Submitted to Physics Letters

Conformal-thin-sandwich initial data for a single boosted or spinning black hole puncture

Sequences of initial-data sets representing binary black holes in quasi-circular orbits have been used to calculate what may be interpreted as the innermost stable circular orbit. These sequences have been computed with two approaches. One method is based on the traditional conformal-transverse-traceless decomposition and locates quasi-circular orbits from the turning points in an effective potential. The second method uses a conformal-thin-sandwich decomposition and determines quasi-circular orbits by requiring the existence of an approximate helical Killing vector. Although the parameters defining the innermost stable circular orbit obtained from these two methods differ significantly, both approaches yield approximately the same initial data, as the separation of the binary system increases. To help understanding this agreement between data sets, we consider the case of initial data representing a single boosted or spinning black hole puncture of the Bowen-York type and show that the conformal-transverse-traceless and conformal-thin-sandwich methods yield identical data, both satisfying the conditions for the existence of an approximate Killing vector.Comment: 13 pages, 2 figure

Conserved charges for gravity with locally AdS asymptotics

A new formula for the conserved charges in 3+1 gravity for spacetimes with local AdS asymptotic geometry is proposed. It is shown that requiring the action to have an extremum for this class of asymptotia sets the boundary term that must be added to the Lagrangian as the Euler density with a fixed weight factor. The resulting action gives rise to the mass and angular momentum as Noether charges associated to the asymptotic Killing vectors without requiring specification of a reference background in order to have a convergent expression. A consequence of this definition is that any negative constant curvature spacetime has vanishing Noether charges. These results remain valid in the limit of vanishing cosmological constant.Comment: 5 pages, 2 Columns, revtex. Last version for Phys. Rev. Let

Dirac-Schr\"odinger equation for quark-antiquark bound states and derivation of its interaction kerne

The four-dimensional Dirac-Schr\"odinger equation satisfied by quark-antiquark bound states is derived from Quantum Chromodynamics. Different from the Bethe-Salpeter equation, the equation derived is a kind of first-order differential equations of Schr\"odinger-type in the position space. Especially, the interaction kernel in the equation is given by two different closed expressions. One expression which contains only a few types of Green's functions is derived with the aid of the equations of motion satisfied by some kinds of Green's functions. Another expression which is represented in terms of the quark, antiquark and gluon propagators and some kinds of proper vertices is derived by means of the technique of irreducible decomposition of Green's functions. The kernel derived not only can easily be calculated by the perturbation method, but also provides a suitable basis for nonperturbative investigations. Furthermore, it is shown that the four-dimensinal Dirac-Schr\"odinger equation and its kernel can directly be reduced to rigorous three-dimensional forms in the equal-time Lorentz frame and the Dirac-Schr\"odinger equation can be reduced to an equivalent Pauli-Schr\"odinger equation which is represented in the Pauli spinor space. To show the applicability of the closed expressions derived and to demonstrate the equivalence between the two different expressions of the kernel, the t-channel and s-channel one gluon exchange kernels are chosen as an example to show how they are derived from the closed expressions. In addition, the connection of the Dirac-Schr\"odinger equation with the Bethe-Salpeter equation is discussed

Gauge conditions for binary black hole puncture data based on an approximate helical Killing vector

We show that puncture data for quasicircular binary black hole orbits allow a special gauge choice that realizes some of the necessary conditions for the existence of an approximate helical Killing vector field. Introducing free parameters for the lapse at the punctures we can satisfy the condition that the Komar and ADM mass agree at spatial infinity. Several other conditions for an approximate Killing vector are then automatically satisfied, and the 3-metric evolves on a timescale smaller than the orbital timescale. The time derivative of the extrinsic curvature however remains significant. Nevertheless, quasicircular puncture data are not as far from possessing a helical Killing vector as one might have expected.Comment: 11 pages, 6 figures, 2 table