Analyticity Properties of Graham-Witten Anomalies

Analytic properties of Graham-Witten anomalies are considered. Weyl anomalies according to their analytic properties are of type A (coming from $\delta$-singularities in correlators of several energy-momentum tensors) or of type B (originating in counterterms which depend logarithmically on a mass scale). It is argued that all Graham-Witten anomalies can be divided into 2 groups: internal and external, and that all external anomalies are of type B, whereas among internal anomalies there is one term of type A and all the rest are of type B. This argument is checked explicitly for the case of a free scalar field in a 6-dimensional space with a 2-dimensional submanifold.Comment: 2 typos correcte

Dynamical vs. Auxiliary Fields in Gravitational Waves around a Black Hole

The auxiliary/dynamic decoupling method of hep-th/0609001 applies to perturbations of any co-homogeneity 1 background (such as a spherically symmetric space-time or a homogeneous cosmology). Here it is applied to compute the perturbations around a Schwarzschild black hole in an arbitrary dimension. The method provides a clear insight for the existence of master equations. The computation is straightforward, coincides with previous results of Regge-Wheeler, Zerilli and Kodama-Ishibashi but does not require any ingenuity in either the definition of variables or in fixing the gauge. We note that the method's emergent master fields are canonically conjugate to the standard ones. In addition, our action approach yields the auxiliary sectors.Comment: 26 page

An orbital radar mapper of venus in the 1980's: Mission design and analysis

The examination of Venus topography, obscured for photographic imaging, is reported in the application of airborne radar mapping systems to an orbiter mission about the planet. Extrapolating the improving capabilities of earth-based radar study of Venus into the 1980's is reported which suggests that only a non-uniform, poorly resolved surface profile will be possible relative to the potential for 100% coverage at 100 meter resolution with an orbital radar. The intent of this paper is: to define mission opportunities favorable for a Venus orbital mapper during the 1980's, to examine orbit design problems associated with mapping radar systems, to establish with flexibility exists for an adaptive mapping strategy, to contribute to the sizing of particular spacecraft systems, and to suggest a reference mission design and demonstrate feasibility

High and Low Dimensions in The Black Hole Negative Mode

The negative mode of the Schwarzschild black hole is central to Euclidean quantum gravity around hot flat space and for the Gregory-Laflamme black string instability. We analyze the eigenvalue as a function of space-time dimension by constructing two perturbative expansions: one for large d and the other for small d-3, and determining as many coefficients as we are able to compute analytically. Joining the two expansions we obtain an interpolating rational function accurate to better than 2% through the whole range of dimensions including d=4.Comment: 17 pages, 4 figures. v2: added reference. v3: published versio

Analytic Evidence for Continuous Self Similarity of the Critical Merger Solution

The double cone, a cone over a product of a pair of spheres, is known to play a role in the black-hole black-string phase diagram, and like all cones it is continuously self similar (CSS). Its zero modes spectrum (in a certain sector) is determined in detail, and it implies that the double cone is a co-dimension 1 attractor in the space of those perturbations which are smooth at the tip. This is interpreted as strong evidence for the double cone being the critical merger solution. For the non-symmetry-breaking perturbations we proceed to perform a fully non-linear analysis of the dynamical system. The scaling symmetry is used to reduce the dynamical system from a 3d phase space to 2d, and obtain the qualitative form of the phase space, including a non-perturbative confirmation of the existence of the "smoothed cone".Comment: 25 pages, 4 figure

On rolling, tunneling and decaying in some large N vector models

Various aspects of time-dependent processes are studied within the large N approximation of O(N) vector models in three dimensions. These include the rolling of fields, the tunneling and decay of vacua. We present an exact solution for the quantum conformal case and find a solution for more general potentials when the total change of the value of the field is small. Characteristic times are found to be shorter when the time dependence of the field is taken into account in constructing the exact large N effective potentials. We show that the different approximations yield the same answers in the regions of the overlap of the validity. A numerical solution of this potential reveals a tunneling in which the bubble that separates the true vacuum from the false one is thick

Analytic evidence for the Gubser-Mitra conjecture

A simple master equation for the static perturbation of charged black strings is derived while employing the gauge proposed by Kol. As the charge is varied it is found that the potential in the master equation for the perturbations becomes positive exactly when the specific heat turns positive thus forbidding a bound state and the onset of the Gregory-Laflamme instability. It can safely be said that this is the first analytic and explicit evidence for the Gubser-Mitra conjecture, correlating the classical and thermodynamic instabilities of black branes. Possible generalizations of the analysis are also discussed.Comment: 9 pages, 2 figures, typos fixed, to appear in Phys. Lett.