Modelling the dynamics of global monopoles

A thin wall approximation is exploited to describe a global monopole coupled to gravity. The core is modelled by de Sitter space; its boundary by a thin wall with a constant energy density; its exterior by the asymptotic Schwarzschild solution with negative gravitational mass $M$ and solid angle deficit, $\Delta\Omega/4\pi = 8\pi G\eta^2$, where $\eta$ is the symmetry breaking scale. The deficit angle equals $4\pi$ when $\eta=1/\sqrt{8\pi G} \equiv M_p$. We find that: (1) if $\eta <M_p$, there exists a unique globally static non-singular solution with a well defined mass, $M_0<0$. $M_0$ provides a lower bound on $M$. If $M_0<M<0$, the solution oscillates. There are no inflating solutions in this symmetry breaking regime. (2) if $\eta \ge M_p$, non-singular solutions with an inflating core and an asymptotically cosmological exterior will exist for all $M<0$. (3) if $\eta$ is not too large, there exists a finite range of values of $M$ where a non-inflating monopole will also exist. These solutions appear to be metastable towards inflation. If $M$ is positive all solutions are singular. We provide a detailed description of the configuration space of the model for each point in the space of parameters, $(\eta, M)$ and trace the wall trajectories on both the interior and the exterior spacetimes. Our results support the proposal that topological defects can undergo inflation.Comment: 44 pages, REVTeX, 11 PostScript figures, submitted to the Physical Review D. Abstract's correcte

Volume element structure and roton-maxon-phonon excitations in superfluid helium beyond the Gross-Pitaevskii approximation

We propose a theory which deals with the structure and interactions of volume elements in liquid helium II. The approach consists of two nested models linked via parametric space. The short-wavelength part describes the interior structure of the fluid element using a non-perturbative approach based on the logarithmic wave equation; it suggests the Gaussian-like behaviour of the element's interior density and interparticle interaction potential. The long-wavelength part is the quantum many-body theory of such elements which deals with their dynamics and interactions. Our approach leads to a unified description of the phonon, maxon and roton excitations, and has noteworthy agreement with experiment: with one essential parameter to fit we reproduce at high accuracy not only the roton minimum but also the neighboring local maximum as well as the sound velocity and structure factor.Comment: 9 pages, 6 figure

A New Class of Exact Hairy Black Hole Solutions

We present a new class of black hole solutions with minimally coupled scalar field in the presence of a negative cosmological constant. We consider a one-parameter family of self-interaction potentials parametrized by a dimensionless parameter $g$. When $g=0$, we recover the conformally invariant solution of the Martinez-Troncoso-Zanelli (MTZ) black hole. A non-vanishing $g$ signals the departure from conformal invariance. All solutions are perturbatively stable for negative black hole mass and they may develop instabilities for positive mass. Thermodynamically, there is a critical temperature at vanishing black hole mass, where a higher-order phase transition occurs, as in the case of the MTZ black hole. Additionally, we obtain a branch of hairy solutions which undergo a first-order phase transition at a second critical temperature which depends on $g$ and it is higher than the MTZ critical temperature. As $g\to 0$, this second critical temperature diverges.Comment: 18 pages, 6 figures, minor changes, references added, published versio

Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences

Within the framework of a generic generally covariant quantum theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra governed by this non-linear correction. It turns out that such time parametrization is essentially energy-dependent and becomes global only asymptotically - when the energies get very small comparing to the effective quantum gravity scale. We show how the logarithmic non-linearity deforms the vacuum wave dispersion relations and explains certain features of the astrophysical data coming from recent observations of high-energy cosmic rays. In general, the estimates imply that ceteris paribus the particles with higher energy propagate slower than those with lower one, therefore, for a high-energy particle the mean free path, lifetime in a high-energy state and, therefore, travel distance from the source can be significantly larger than one would expect from the conventional theory. © 2009 American Institute of Physics.Conference Pape