The Thin-Wall Approximation in Vacuum Decay: a Lemma

The 'thin-wall approximation' gives a simple estimate of the decay rate of an unstable quantum field. Unfortunately, the approximation is uncontrolled. In this paper I show that there are actually two different thin-wall approximations and that they bracket the true decay rate: I prove that one is an upper bound and the other a lower bound. In the thin-wall limit, the two approximations converge. In the presence of gravity, a generalization of this lemma provides a simple sufficient condition for non-perturbative vacuum instability.Comment: technically contains 2 lemma

Application of granular mechanics to the analysis of solid propellants

In this paper a theoretical method is developed for analyzing the mechanical behavior of granular solid propellant materials. The granular nature of the material is specifically taken into account and, the analysis allows for a media composed of non-uniformly sized particles with random stacking configuration. The voids between the particles are assumed to be filled with an elastic, homogeneous binder material. Three types of internal forces are assumed to be acting; the normal and tangential contact forces between the granular particles and, the elastic stresses in the binder. The paper consists of three main parts. First a model is developed to represent a general granular medium. Subsequently, in the second part this model is used to analyze the response of a granular medium to hydrostatic pressure loading. Finally the stress-strain relations are derived for a general loading condition. Because of the presence of the non-conservative frictional forces between the granular particles, the deformation of such a medium depends on the loading history. Consequently the stress-strain relations are in a differential, or incremental form

Asset Forfeiture and Attorneys’ Fees: The Zero-Sum Game

The history of asset forfeiture law spans almost as long as the history of the United States. However, in the last thirty years, the number of crimes for which asset forfeiture can be levied has grown exponentially both on the federal and state levels. As a result, a growing number of defendants face asset forfeiture. When these criminal defendants seek legal representation, they place their attorneys in a difficult legal and ethical position. Asset forfeiture has developed in such a way that the criminal defense attorney cannot provide her client with zealous advocacy if the attorney seeks to retain her fees. Additionally, the law is designed to prevent these attorneys from withdrawing their representation once they learn that the funds being used to pay their fees are tainted. This Note examines these, and other, ethical dilemmas that arise for criminal defense attorneys whose clients may be subject to asset forfeiture. Ultimately, this Note proposes a statutory fix to resolve these ethical issues to ensure that lawyers retain their hard-earned fees and clients receive zealous advocates

The decay of hot KK space

The non-perturbative instabilities of hot Kaluza-Klein spacetime are investigated. In addition to the known instability of hot space (the nucleation of 4D black holes) and the known instability of KK space (the nucleation of bubbles of nothing by quantum tunneling), we find two new instabilities: the nucleation of 5D black holes, and the nucleation of bubbles of nothing by thermal fluctuation. These four instabilities are controlled by two Euclidean instantons, with each instanton doing double duty via two inequivalent analytic continuations; thermodynamic instabilities of one are shown to be related to mechanical instabilities of the other. I also construct bubbles of nothing that are formed by a hybrid process involving both thermal fluctuation and quantum tunneling. There is an exact high-temperature/low-temperature duality that relates the nucleation of black holes to the nucleation of bubbles of nothing.Comment: v2: minor improvements; new appendix on merger poin

Liberation of specific angular momentum through radiation and scattering in relativistic black-hole accretion discs

A key component of explaining the array of galaxies observed in the Universe is the feedback of active galactic nuclei, each powered by a massive black hole's accretion disc. For accretion to occur, angular momentum must be lost by that which is accreted. Electromagnetic radiation must offer some respite in this regard, the contribution for which is quantified in this paper, using solely general relativity, under the thin-disc regime. Herein, I calculate extremised situations where photons are entirely responsible for energy removal in the disc and then extend and relate this to the standard relativistic accretion disc outlined by Novikov & Thorne, which includes internal angular-momentum transport. While there is potential for the contribution of angular-momentum removal from photons to be >~1% out to ~10^4 Schwarzschild radii if the disc is irradiated and maximally liberated of angular momentum through inverse Compton scattering, it is more likely of order 10^2 Schwarzschild radii if thermal emission from the disc itself is stronger. The effect of radiation/scattering is stronger near the horizons of fast-spinning black holes, but, ultimately, other mechanisms must drive angular-momentum liberation/transport in accretion discs.Comment: 6 pages, 2 figures. Accepted for publication in PAS