Bulk Duals for Generic Static, Scale-Invariant Holographic CFT States

Near horizon geometries have been widely studied, and have found many applications. Certain static, near horizon geometries are now understood to be bulk duals to CFTs with static scale-invariant sources under the AdS/CFT correspondence. However, static near-horizon geometries aren't just scale-invariant, they have extra `enhanced' symmetry. This means that they can only be the bulk duals for a special class of static, scale-invariant sources that share this enhanced symmetry. The purpose of this paper is to consider bulk duals for more generic static, scale-invariant sources, without this extra symmetry. These solutions are quite different to near-horizon geometries. In place of the extremal horizon they have a null singularity. We find specific examples of such bulk geometries numerically for the cases of pure gravity, and for an abelian gauge field

Effects of thermal conduction in sonoluminescence

Current experimental results indicate that sonoluminescence is largely thermal in origin, with the spectra showing a direct relation between luminous intensity and the temper ature s generated inside the collapsing cavitation bubbles. In the present paper the strong dependence of the luminous intensity on the nature of the gas dissolved in the liquid is explained in terms of thermal conduction. Provided the cavitation bubbles are sufficiently small, loss of heat from the bubble into the liquid can significantly reduce the temperatures attained during collapse, so that there is a consequent reduction in the luminous intensity. This process is demonstrated analytically by means of a numerical solution of the equations of motion of a gas inside a collapsing cavitation bubble. The agreement between the theory and the observed luminous intensities for different dissolved gases is good

An Analysis of Echoes from a Solid Elastic Sphere in Water

It is well-known in sonar work that the pulse form of a direct echo from a target bears little relation to the form of the original signal. This is true even for regularly shaped bodies, such as a sphere. In this paper, the case of a homogeneous elastic sphere in water is examined theoretically and it is shown in comparison with experimental results, that the observed effects originate from vibrations induced in the sphere by the incident sound. Calculated results are presented for a variety of solid materials and it seems that echo forms could possibly provide information about the size and constitution of a sonar target

The collapse of a spherical cavity in a compressible liquid

This paper presents numerical solutions for the flow in the vicinity of a collapsing spherical bubble in water. The bubble is assumed to contain a small amount of gas and the solutions are taken beyond the point where the bubble reaches its minimum radius up to the stage where a pressure wave forms and propagates outwards into the liquid. The motion up to the point where the minimum radius is attained, is found by solving the equations of motion both in the Lagrangian and in the characteristic forms. These are in good agreement with each other and also with the approximate theory of Gilmore which is demonstrated to be accurate over a wide range of Mach number. The liquid flow after the minimum radius has been attained is determined from a solution of the Lagrangian equations. It is shown that an acoustic approximation is quite valid for fairly high pressures and this fact is used to determine the peak intensity of the pressure wave at a distance from the center of collapse. It is estimated in the case of typical cavitation bubbles that such intensities are sufficient to cause cavitation damage

Bounds on the local energy density of holographic CFTs from bulk geometry

The stress tensor is a basic local operator in any field theory; in the context of AdS/CFT, it is the operator which is dual to the bulk geometry itself. Here we exploit this feature by using the bulk geometry to place constraints on the local energy density in static states of holographic $(2+1)$-dimensional CFTs living on a closed (but otherwise generally curved) spatial geometry. We allow for the presence of a marginal scalar deformation, dual to a massless scalar field in the bulk. For certain vacuum states in which the bulk geometry is well-behaved at zero temperature, we find that the bulk equations of motion imply that the local energy density integrated over specific boundary domains is negative. In the absence of scalar deformations, we use the inverse mean curvature flow to show that if the CFT spatial geometry has spherical topology but non-constant curvature, the local energy density must be positive somewhere. This result extends to other topologies, but only for certain types of vacuum; in particular, for a generic toroidal boundary, the vacuum's bulk dual must be the zero-temperature limit of a toroidal black hole.Comment: 14+2 pages, 2 figures. v2: fixed equations (51) and (52

Uniform Distributions of Sound Sources on the Surface of a Rigid Sphere and Some Applications

A study is made of certain elementary source distributions on the surface of a rigid sphere for a fairly extensive range of frequencies. The elementary systems considered consist of a point source, uniformly vibrating caps and rings, and plane line sources. Results are given for typical cases of the far zone sound fields and acoustic impedances of caps and rings, and also for the far zone sound field of a particular plane line source. Combinations of the elementary rings and caps are examined with a view to producing desired directional patterns and the results for a particular directional beam are presented. Taking a sphere as a model for the human head, the results for a point source are used to examine possible mechanisms for the binaural localization of sources of sound. These results indicate that, due to non-linear variation of phase with frequency, a pulsed sound should appear in a somewhat different form at each ear. It is suggested that localization is achieved by the brain in reconciling such pulse forms and that time and intensity differences are elements in a much more general process. Another possible application of the results involves the particular line source considered which could be taken to represent a human mouth