Scalar Deformations of Schwarzschild Holes and Their Stability

We construct two solutions of the minimally coupled Einstein-scalar field equations, representing regular deformations of Schwarzschild black holes by a self-interacting, static, scalar field. One solution features an exponentially decaying scalar field and a triple-well interaction potential; the other one is completely analytic and sprouts Coulomb-like scalar hair. Both evade the no-hair theorem by having partially negative potential, in conflict with the dominant energy condition. The linear perturbation theory around such backgrounds is developed in general, and yields stability criteria in terms of effective potentials for an analog Schr\"odinger problem. We can test for more than half of the perturbation modes, and our solutions prove to be stable against those.Comment: 24 pp, 16 figs, Latex; version published in Int. J. Mod. Phys.

Matching characteristic codes: exploiting two directions

Combining incoming and outgoing characteristic formulations can provide numerical relativists with a natural implementation of Einstein's equations that better exploits the causal properties of the spacetime and gives access to both null infinity and the interior region simultaneously (assuming the foliation is free of caustics and crossovers). We discuss how this combination can be performed and illustrate its behavior in the Einstein-Klein-Gordon field in 1D.Comment: 10 pages, 9 postscript figures. To appear in Int. Journ. of Mod. Phys.

New Critical Behavior in Einstein-Yang-Mills Collapse

We extend the investigation of the gravitational collapse of a spherically symmetric Yang-Mills field in Einstein gravity and show that, within the black hole regime, a new kind of critical behavior arises which separates black holes formed via Type I collapse from black holes formed through Type II collapse. Further, we provide evidence that these new attracting critical solutions are in fact the previously discovered colored black holes with a single unstable mode.Comment: 13 pages, 4 figure

THE EFFECT OF FINANCIAL LEVERAGE TO THE PROFITABILITY AT SUB- SECTORS OF FOOD AND BEVERAGE COMPANIES LISTED ON INDONESIA STOCK EXCHANGE IN 2010-2014

ABSTRACT  This study examined the effect of financial leverage to the profitability at Sub-Sectors of Food and Beverage Companies listed on Indonesia Stock Exchange in 2010 – 2014 simultaneously and partially. Financial leverage seen from debt ratio and debt to equity ratio, then profitabilitas seen from return on equity.The result of the study revealed debt ratio and debt to equity ratio affected the profitability when it simultaneous. However, when it partial debt ratio did not affect the profitability positively, while debt to equity ratio affected the profitability positively. Keywords : financial leverage, debt ratio, debt to equity ratio, profitability, return on equity.   PENGARUH FINANCIAL LEVERAGE TERHADAP PROFITABILITAS PADA PERUSAHAAN SUB SEKTOR MAKANAN DAN MINUMAN YANG TERDAFTAR DI BURSA EFEK INDONESIA PERIODE 2010-2014 ABSTRAK  Penelitian ini bertujuan untuk mengetahui pengaruh financial levarage terhadap profitabilitas pada perusahaan sub sektor makanan dan minuman yang terdaftar di Bursa Efek Indonesia periode 2010-2014 baik secara simultan maupun secara parsial. Financial leverage dapat dilihat melalui debt ratiodan debt to equity ratio, sedangkan profitabilitas dapat dilihat melalui return on equity.Hasil penelitian menunjukkan bahwa secara simultan kedua variabel independen, yaitu debt ratio dan debt to equity ratio secara bersama-sama berpengaruh terhadap profitabilitas. Untuk pengaruh secara parsial, hasil penelitian menunjukkan bahwa debt ratio tidak berpengaruh positif terhadap profitabilitas, sedangkan debt to equity ratio berpengaruh positif terhadap profitabilitas. Kata kunci : financial leverage, debt ratio, debt to equity ratio, profitabilitas, return on equity

Critical behavior of gravitating sphalerons

We examine the gravitational collapse of sphaleron type configurations in Einstein--Yang--Mills--Higgs theory. Working in spherical symmetry, we investigate the critical behavior in this model. We provide evidence that for various initial configurations, there can be three different critical transitions between possible endstates with different critical solutions sitting on the threshold between these outcomes. In addition, we show that within the dispersive and black hole regimes, there are new possible endstates, namely a stable, regular sphaleron and a stable, hairy black hole.Comment: Latex, 14 pages, 8 figure

Black Hole--Scalar Field Interactions in Spherical Symmetry

We examine the interactions of a black hole with a massless scalar field using a coordinate system which extends ingoing Eddington-Finkelstein coordinates to dynamic spherically symmetric-spacetimes. We avoid problems with the singularity by excising the region of the black hole interior to the apparent horizon. We use a second-order finite difference scheme to solve the equations. The resulting program is stable and convergent and will run forever without problems. We are able to observe quasi-normal ringing and power-law tails as well an interesting nonlinear feature.Comment: 16 pages, 26 figures, RevTex, to appear in Phys. Rev.

Late-time evolution of nonlinear gravitational collapse

We study numerically the fully nonlinear gravitational collapse of a self-gravitating, minimally-coupled, massless scalar field in spherical symmetry. Our numerical code is based on double-null coordinates and on free evolution of the metric functions: The evolution equations are integrated numerically, whereas the constraint equations are only monitored. The numerical code is stable (unlike recent claims) and second-order accurate. We use this code to study the late-time asymptotic behavior at fixed $r$ (outside the black hole), along the event horizon, and along future null infinity. In all three asymptotic regions we find that, after the decay of the quasi-normal modes, the perturbations are dominated by inverse power-law tails. The corresponding power indices agree with the integer values predicted by linearized theory. We also study the case of a charged black hole nonlinearly perturbed by a (neutral) self-gravitating scalar field, and find the same type of behavior---i.e., quasi-normal modes followed by inverse power-law tails, with the same indices as in the uncharged case.Comment: 14 pages, standard LaTeX, 18 Encapsulated PostScript figures. A new convergence test and a determination of QN ringing were added, in addition to correction of typos and update of reference

Black Hole Data via a Kerr-Schild Approach

We present a new approach for setting initial Cauchy data for multiple black hole spacetimes. The method is based upon adopting an initially Kerr-Schild form of the metric. In the case of non-spinning holes, the constraint equations take a simple hierarchical form which is amenable to direct numerical integration. The feasibility of this approach is demonstrated by solving analytically the problem of initial data in a perturbed Schwarzschild geometry.Comment: 13 pages, RevTeX forma

On free evolution of self gravitating, spherically symmetric waves

We perform a numerical free evolution of a selfgravitating, spherically symmetric scalar field satisfying the wave equation. The evolution equations can be written in a very simple form and are symmetric hyperbolic in Eddington-Finkelstein coordinates. The simplicity of the system allow to display and deal with the typical gauge instability present in these coordinates. The numerical evolution is performed with a standard method of lines fourth order in space and time. The time algorithm is Runge-Kutta while the space discrete derivative is symmetric (non-dissipative). The constraints are preserved under evolution (within numerical errors) and we are able to reproduce several known results.Comment: 15 pages, 15 figure