Scalar Synchrotron Radiation in the Schwarzschild-anti-de Sitter Geometry

We present a complete relativistic analysis for the scalar radiation emitted by a particle in circular orbit around a Schwarzschild-anti-de Sitter black hole. If the black hole is large, then the radiation is concentrated in narrow angles- high multipolar distribution- i.e., the radiation is synchrotronic. However, small black holes exhibit a totally different behavior: in the small black hole regime, the radiation is concentrated in low multipoles. There is a transition mass at $M=0.427 R$, where $R$ is the AdS radius. This behavior is new, it is not present in asymptotically flat spacetimes.Comment: 13 pages, 6 figures, published version. References adde

Polyhedral Analysis using Parametric Objectives

The abstract domain of polyhedra lies at the heart of many program analysis techniques. However, its operations can be expensive, precluding their application to polyhedra that involve many variables. This paper describes a new approach to computing polyhedral domain operations. The core of this approach is an algorithm to calculate variable elimination (projection) based on parametric linear programming. The algorithm enumerates only non-redundant inequalities of the projection space, hence permits anytime approximation of the output

Anti-de Sitter boundary in Poincare coordinates

We study the space-time boundary of a Poincare patch of Anti-de Sitter (AdS) space. We map the Poincare AdS boundary to the global coordinate chart and show why this boundary is not equivalent to the global AdS boundary. The Poincare AdS boundary is shown to contain points of the bulk of the entire AdS space. The Euclidean AdS space is also discussed. In this case one can define a semi-global chart that divides the AdS space in the same way as the corresponding Euclidean Poincare chart.Comment: In this revised version we add a discussion of the physical consequences of the choice of a coordinate system for AdS space. We changed figure 1 and added more references. Version to be published in Gen. Relat. Grav

Black hole collision with a scalar particle in four, five and seven dimensional anti-de Sitter spacetimes: ringing and radiation

In this work we compute the spectra, waveforms and total scalar energy radiated during the radial infall of a small test particle coupled to a scalar field into a $d$-dimensional Schwarzschild-anti-de Sitter black hole. We focus on $d=4, 5$ and 7, extending the analysis we have done for $d=3$. For small black holes, the spectra peaks strongly at a frequency $\omega \sim d-1$, which is the lowest pure anti-de Sitter (AdS) mode. The waveform vanishes exponentially as $t \to \infty$, and this exponential decay is governed entirely by the lowest quasinormal frequency. This collision process is interesting from the point of view of the dynamics itself in relation to the possibility of manufacturing black holes at LHC within the brane world scenario, and from the point of view of the AdS/CFT conjecture, since the scalar field can represent the string theory dilaton, and 4, 5, 7 are dimensions of interest for the AdS/CFT correspondence.Comment: 16 pages, 13 figures. Published versio

Properties of branes in curved spacetimes

A generic property of curved manifolds is the existence of focal points. We show that branes located at focal points of the geometry satisfy special properties. Examples of backgrounds to which our discussion applies are AdS_m x S^n and plane wave backgrounds. As an example, we show that a pair of AdS_2 branes located at the north and south pole of the S^5 in AdS_5 x S^5 are half supersymmetric and that they are dual to a two-monopole solution of N=4 SU(N) SYM theory. Our second example involves spacelike branes in the (Lorentzian) plane wave. We develop a modified lightcone gauge for the open string channel, analyze in detail the cylinder diagram and establish open-closed duality. When the branes are located at focal points of the geometry the amplitude acquires most of the characteristics of flat space amplitudes. In the open string channel the special properties are due to stringy modes that become massless.Comment: 41 pages; v2:typos corrected, ref adde

Bound States in the AdS/CFT Correspondence

We consider a massive scalar field theory in anti-de Sitter space, in both minimally and non-minimally coupled cases. We introduce a relevant double-trace perturbation at the boundary, by carefully identifying the correct source and generating functional for the corresponding conformal operator. We show that such relevant double-trace perturbation introduces changes in the coefficients in the boundary terms of the action, which in turn govern the existence of a bound state in the bulk. For instance, we show that the usual action, containing no additional boundary terms, gives rise to a bound state, which can be avoided only through the addition of a proper boundary term. Another notorious example is that of a conformally coupled scalar field, supplemented by a Gibbons-Hawking term, for which there is no associated bound state. In general, in both minimally and non-minimally coupled cases, we explicitly compute the boundary terms which give rise to a bound state, and which ones do not. In the non-minimally coupled case, and when the action is supplemented by a Gibbons-Hawking term, this also fixes allowed values of the coupling coefficient to the metric. We interpret our results as the fact that the requirement to satisfy the Breitenlohner-Freedman bound does not suffice to prevent tachyonic behavior from existing in the bulk, as it must be supplemented by additional conditions on the coefficients in the boundary terms of the action.Comment: 32 pages, Latex. v2: added comments and clarifications, minor changes. v3: corrected wrong result in the non-minimally coupled case, added reference, minor changes. v4: Added new results and discussions, parts of the paper are rewritten. Final version to be published in Phys.Rev.

Protecting the conformal symmetry via bulk renormalization on Anti deSitter space

The problem of perturbative breakdown of conformal symmetry can be avoided, if a conformally covariant quantum field phi on d-dimensional Minkowski spacetime is viewed as the boundary limit of a quantum field Phi on d+1-dimensional anti-deSitter spacetime (AdS). We study the boundary limit in renormalized perturbation theory with polynomial interactions in AdS, and point out the differences as compared to renormalization directly on the boundary. In particular, provided the limit exists, there is no conformal anomaly. We compute explicitly the "fish diagram" on AdS_4 by differential renormalization, and calculate the anomalous dimension of the composite boundary field phi^2 with bulk interaction Phi^4.Comment: 40 page

Perturbations of brane worlds

We consider cosmological models where the universe, governed by Einstein's equations, is a piece of a five dimensional double-sided anti-de Sitter spacetime (that is, a "$Z_2$-symmetric bulk") with matter confined to its four dimensional Robertson-Walker boundary or "brane". We study the perturbations of such models. We use conformally minkowskian coordinates to disentangle the contributions of the bulk gravitons and of the motion of the brane. We find the restrictions put on the bulk gravitons when matter on the brane is taken to be a scalar field and we solve in that case the brane perturbation equations.Comment: 19 pages, no figures, RevTex, version to appear in Phys.Rev.D; minor changes in chap.V, polarisation tensor at page 13 correcte

On exact solutions for quantum particles with spin S= 0, 1/2, 1 and de Sitter event horizon

Exact wave solutions for particles with spin 0, 1/2 and 1 in the static coordinates of the de Sitter space-time model are examined in detail. Firstly, for a scalar particle, two pairs of linearly independent solutions are specified explicitly: running and standing waves. A known algorithm for calculation of the reflection coefficient $R_{\epsilon j}$ on the background of the de Sitter space-time model is analyzed. It is shown that the determination of R_{\epsilon j} requires an additional constrain on quantum numbers \epsilon \rho / \hbar c >> j, where \rho is a curvature radius. When taken into account of this condition, the R_{\epsilon j} vanishes identically. It is claimed that the calculation of the reflection coefficient R_{\epsilon j} is not required at all because there is no barrier in an effective potential curve on the background of the de Sitter space-time. The same conclusion holds for arbitrary particles with higher spins, it is demonstrated explicitly with the help of exact solutions for electromagnetic and Dirac fields.Comment: 30 pages. This paper is an updated and more comprehensive version of the old paper V.M. Red'kov. On Particle penetrating through de Sitter horizon. Minsk (1991) 22 pages Deposited in VINITI 30.09.91, 3842 - B9