Universal properties of distorted Kerr-Newman black holes

We discuss universal properties of axisymmetric and stationary configurations consisting of a central black hole and surrounding matter in Einstein-Maxwell theory. In particular, we find that certain physical equations and inequalities (involving angular momentum, electric charge and horizon area) are not restricted to the Kerr-Newman solution but can be generalized to the situation where the black hole is distorted by an arbitrary axisymmetric and stationary surrounding matter distribution.Comment: 7 page

Directed current in the Holstein system

We propose a mechanism to rectify charge transport in the semiclassical Holstein model. It is shown that localised initial conditions, associated with a polaron solution, in conjunction with a nonreversion symmetric static electron on-site potential constitute minimal prerequisites for the emergence of a directed current in the underlying periodic lattice system. In particular, we demonstrate that for unbiased spatially localised initial conditions, violation of parity prevents the existence of pairs of counter-propagating trajectories, thus allowing for a directed current despite the time-reversibility of the equations of motion. Occurrence of long-range coherent charge transport is demonstrated

Field of homogeneous Plane in Quantum Electrodynamics

We study quantum electrodynamics coupled to the matter field on singular background, which we call defect. For defect on the infinite plane we calculated the fermion propagator and mean electromagnetic field. We show that at large distances from the defect plane, the electromagnetic field is constant what is in agreement with the classical results. The quantum corrections determining the field near the plane are calculated in the leading order of perturbation theory.Comment: 16 page

Non-existence of stationary two-black-hole configurations: The degenerate case

In a preceding paper we examined the question whether the spin-spin repulsion and the gravitational attraction of two aligned sub-extremal black holes can balance each other. Based on the solution of a boundary value problem for two separate (Killing-) horizons and a novel black hole criterion we were able to prove the non-existence of the equilibrium configuration in question. In this paper we extend the non-existence proof to extremal black holes.Comment: 18 pages, 2 figure

Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices

In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of analyticity versus wave amplitude is observed. As a consequence of the discreteness, oscillatory linear instabilities, persisting for arbitrarily small amplitude in infinite lattices, appear for all wave numbers Q not equal to zero or \pi. Incommensurate analytic SWs with |Q|>\pi/2 may however appear as 'quasi-stable', as their instability growth rate is of higher order.Comment: 4 pages, 6 figures, to appear in Phys. Rev. Let

Hamiltonian Hopf bifurcations in the discrete nonlinear Schr\"odinger trimer: oscillatory instabilities, quasiperiodic solutions and a 'new' type of self-trapping transition

Oscillatory instabilities in Hamiltonian anharmonic lattices are known to appear through Hamiltonian Hopf bifurcations of certain time-periodic solutions of multibreather type. Here, we analyze the basic mechanisms for this scenario by considering the simplest possible model system of this kind where they appear: the three-site discrete nonlinear Schr\"odinger model with periodic boundary conditions. The stationary solution having equal amplitude and opposite phases on two sites and zero amplitude on the third is known to be unstable for an interval of intermediate amplitudes. We numerically analyze the nature of the two bifurcations leading to this instability and find them to be of two different types. Close to the lower-amplitude threshold stable two-frequency quasiperiodic solutions exist surrounding the unstable stationary solution, and the dynamics remains trapped around the latter so that in particular the amplitude of the originally unexcited site remains small. By contrast, close to the higher-amplitude threshold all two-frequency quasiperiodic solutions are detached from the unstable stationary solution, and the resulting dynamics is of 'population-inversion' type involving also the originally unexcited site.Comment: 25 pages, 11 figures, to be published in J. Phys. A: Math. Gen. Revised and shortened version with few clarifying remarks adde

Discreteness-Induced Oscillatory Instabilities of Dark Solitons

We reveal that even weak inherent discreteness of a nonlinear model can lead to instabilities of the localized modes it supports. We present the first example of an oscillatory instability of dark solitons, and analyse how it may occur for dark solitons of the discrete nonlinear Schrodinger and generalized Ablowitz-Ladik equations.Comment: 11 pages, 4 figures, to be published in Physical Review Letter

Area-charge inequality for black holes

The inequality between area and charge $A\geq 4\pi Q^2$ for dynamical black holes is proved. No symmetry assumption is made and charged matter fields are included. Extensions of this inequality are also proved for regions in the spacetime which are not necessarily black hole boundaries.Comment: 21 pages, 2 figure

Baryon Content of Massive Galaxy Clusters (0.57 < z < 1.33)

We study the stellar, Brightest Cluster Galaxy (BCG) and intracluster medium (ICM) masses of 14 South Pole Telescope (SPT) selected galaxy clusters with median redshift $z=0.9$ and median mass $M_{500}=6\times10^{14}M_{\odot}$. We estimate stellar masses for each cluster and BCG using six photometric bands spanning the range from the ultraviolet to the near-infrared observed with the VLT, HST and Spitzer. The ICM masses are derived from Chandra and XMM-Newton X-ray observations, and the virial masses are derived from the SPT Sunyaev-Zel'dovich Effect signature. At $z=0.9$ the BCG mass $M_{\star}^{\textrm{BCG}}$ constitutes $0.12\pm0.01$% of the halo mass for a $6\times10^{14}M_{\odot}$ cluster, and this fraction falls as $M_{500}^{-0.58\pm0.07}$. The cluster stellar mass function has a characteristic mass $M_{0}=10^{11.0\pm0.1}M_{\odot}$, and the number of galaxies per unit mass in clusters is larger than in the field by a factor $1.65\pm0.2$. Both results are consistent with measurements on group scales and at lower redshift. We combine our SPT sample with previously published samples at low redshift that we correct to a common initial mass function and for systematic differences in virial masses. We then explore mass and redshift trends in the stellar fraction (fstar), the ICM fraction (fICM), the cold baryon fraction (fc) and the baryon fraction (fb). At a pivot mass of $6\times10^{14}M_{\odot}$ and redshift $z=0.9$, the characteristic values are fstar=$1.1\pm0.1$%, fICM=$9.6\pm0.5$%, fc=$10.4\pm1.2$% and fb=$10.7\pm0.6$%. These fractions all vary with cluster mass at high significance, indicating that higher mass clusters have lower fstar and fc and higher fICM and fb. When accounting for a 15% systematic virial mass uncertainty, there is no statistically significant redshift trend at fixed mass in these baryon fractions. (abridged)Comment: Accepted for publication in MNRA

A Study of The Formation of Stationary Localized States Due to Nonlinear Impurities Using The Discrete Nonlinear Schr\"odinger Equation

The Discrete Nonlinear Schr$\ddot{o}$dinger Equation is used to study the formation of stationary localized states due to a single nonlinear impurity in a Caley tree and a dimeric nonlinear impurity in the one dimensional system. The rotational nonlinear impurity and the impurity of the form $-\chi \mid C \mid^{\sigma}$ where $\sigma$ is arbitrary and $\chi$ is the nonlinearity parameter are considered. Furthermore, $\mid C \mid$ represents the absolute value of the amplitude. Altogether four cases are studies. The usual Greens function approach and the ansatz approach are coherently blended to obtain phase diagrams showing regions of different number of states in the parameter space. Equations of critical lines separating various regions in phase diagrams are derived analytically. For the dimeric problem with the impurity $-\chi \mid C \mid^{\sigma}$, three values of $\mid \chi_{cr} \mid$, namely, $\mid \chi_{cr} \mid = 2$, at $\sigma = 0$ and $\mid \chi_{cr} \mid = 1$ and $\frac{8}{3}$ for $\sigma = 2$ are obtained. Last two values are lower than the existing values. Energy of the states as a function of parameters is also obtained. A model derivation for the impurities is presented. The implication of our results in relation to disordered systems comprising of nonlinear impurities and perfect sites is discussed.Comment: 10 figures available on reques