Kinematic Self-Similar Cylindrically Symmetric Solutions

This paper is devoted to find out cylindrically symmetric kinematic self-similar perfect fluid and dust solutions. We study the cylindrically symmetric solutions which admit kinematic self-similar vectors of second, zeroth and infinite kinds, not only for the tilted fluid case but also for the parallel and orthogonal cases. It is found that the parallel case gives contradiction both in perfect fluid and dust cases. The orthogonal perfect fluid case yields a vacuum solution while the orthogonal dust case gives contradiction. It is worth mentioning that the tilted case provides solution both for the perfect as well as dust cases.Comment: 22 pages, accepted for publication in Int. J. of Mod. Phys.

The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models

The purpose of this paper is to further investigate the solution space of self-similar spherically symmetric perfect-fluid models and gain deeper understanding of the physical aspects of these solutions. We achieve this by combining the state space description of the homothetic approach with the use of the physically interesting quantities arising in the comoving approach. We focus on three types of models. First, we consider models that are natural inhomogeneous generalizations of the Friedmann Universe; such models are asymptotically Friedmann in their past and evolve fluctuations in the energy density at later times. Second, we consider so-called quasi-static models. This class includes models that undergo self-similar gravitational collapse and is important for studying the formation of naked singularities. If naked singularities do form, they have profound implications for the predictability of general relativity as a theory. Third, we consider a new class of asymptotically Minkowski self-similar spacetimes, emphasizing that some of them are associated with the self-similar solutions associated with the critical behaviour observed in recent gravitational collapse calculations.Comment: 24 pages, 12 figure

Near-Critical Gravitational Collapse and the Initial Mass Function of Primordial Black Holes

The recent discovery of critical phenomena arising in gravitational collapse near the threshold of black hole formation is used to estimate the initial mass function of primordial black holes (PBHs). It is argued that the universal scaling relation between black hole mass and initial perturbation found for a variety of collapsing space-times also applies to PBH formation, indicating the possibility of the formation of PBHs with masses much smaller than one horizon mass. Owing to the natural fine-tuning of initial conditions by the exponential decline of the probability distribution for primordial density fluctuations, sub-horizon mass PBHs are expected to form at all epochs. This result suggests that the constraints on the primordial fluctuation spectrum based on the abundance of PBHs at different mass scales may have to be revisited.Comment: 4 pages, uses revtex, also available at http://bigwhirl.uchicago.edu/jcn/pub_pbh.html . To appear in Phys. Rev. Let

Unbinding of giant vortices in states of competing order

Funding: EPSRC (UK) via Grants No. EP/I031014/1 and No. EP/H049584/1.We consider a two-dimensional system with two order parameters, one with O(2) symmetry and one with O(M), near a point in parameter space where they couple to become a single O(2+M) order. While the O(2) sector supports vortex excitations, these vortices must somehow disappear as the high symmetry point is approached. We develop a variational argument which shows that the size of the vortex cores diverges as 1/root Delta and the Berezinskii-Kosterlitz-Thouless transition temperature of the O(2) order vanishes as 1/1n(1/Delta), where Delta denotes the distance from the high-symmetry point. Our physical picture is confirmed by a renormalization group analysis which gives further logarithmic corrections, and demonstrates full symmetry restoration within the cores.Publisher PDFPeer reviewe

Timelike self-similar spherically symmetric perfect-fluid models

Einstein's field equations for timelike self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively using the theory of dynamical systems.Comment: 23 pages, 6 eps-figure

Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity

A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state $P=\rho$. A wide class of self-similar solutions turn out to be unstable against kink mode perturbation. According to the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be a critical solution for the spherical collapse of a stiff fluid if we allow sufficiently small discontinuity in the density gradient field in the initial data sets. The self-similar scalar-field solution, which was recently found numerically by Brady {\it et al.} (2002 {\it Class. Quantum. Grav.} {\bf 19} 6359), is also unstable. Both the flat Friedmann universe with a scalar field and that with a stiff fluid suffer from kink instability at the particle horizon scale.Comment: 15 pages, accepted for publication in Classical and Quantum Gravity, typos correcte

Comparison of porcine thorax to gelatine blocks for wound

Published online first in International Journal of Legal Medicine. The support of EPSRC and The Home Office are recognised. Open Access, this article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http:/ /creativecommons.org/licenses/by/4.0/)Tissue simulants are typically used in ballistic testing as substitutes for biological tissues. Many simulants have been used, with gelatine amongst the most common. While two concentrations of gelatine (10 and 20 %) have been used extensively, no agreed standard exists for the preparation of either. Comparison of ballistic damage produced in both concentrations is lacking. The damage produced in gelatine is also questioned, with regards to what it would mean for specific areas of living tissue. The aim of the work discussed in this paper was to consider how damage caused by selected pistol and rifle ammunition varied in different simulants. Damage to gelatine blocks 10 and 20 % in concentration were tested with 9 mm Luger (9 × 19 full metal jacket; FMJ) rounds, while damage produced by .223 Remington (5.56 × 45 Federal Premium® Tactical® Bonded®) rounds to porcine thorax sections (skin, underlying tissue, ribs, lungs, ribs, underlying tissue, skin; backed by a block of 10 % gelatine) were compared to 10 and 20 % gelatine blocks. Results from the .223 Remington rifle round, which is one that typically expands on impact, revealed depths of penetration in the thorax arrangement were significantly different to 20 % gelatine, but not 10 % gelatine. The level of damage produced in the simulated thoraxes was smaller in scale to that witnessed in both gelatine concentrations,though greater debris was produced in the thoraxes.The support of EPSRC and The Home Office are recognised