A note on the cylindrical collapse of counter-rotating dust

We find analytical solutions describing the collapse of an infinitely long cylindrical shell of counter-rotating dust. We show that--for the classes of solutions discussed herein--from regular initial data a curvature singularity inevitably develops, and no apparent horizons form, thus in accord with the spirit of the hoop conjecture.Comment: 8 pages, LaTeX, ijmpd macros (included), 1 eps figure; accepted for publication in Int. J. Mod. Phys.

Integrability of the Minimal Strain Equations for the Lapse and Shift in 3+1 Numerical Relativity

Brady, Creighton and Thorne have argued that, in numerical relativity simulations of the inspiral of binary black holes, if one uses lapse and shift functions satisfying the ``minimal strain equations'' (MSE), then the coordinates might be kept co-rotating, the metric components would then evolve on the very slow inspiral timescale, and the computational demands would thus be far smaller than for more conventional slicing choices. In this paper, we derive simple, testable criteria for the MSE to be strongly elliptic, thereby guaranteeing the existence and uniqueness of the solution to the Dirichlet boundary value problem. We show that these criteria are satisfied in a test-bed metric for inspiraling binaries, and we argue that they should be satisfied quite generally for inspiraling binaries. If the local existence and uniqueness that we have proved holds globally, then, for appropriate boundary values, the solution of the MSE exhibited by Brady et. al. (which tracks the inspiral and keeps the metric evolving slowly) will be the unique solution and thus should be reproduced by (sufficiently accurate and stable) numerical integrations.Comment: 6 pages; RevTeX; submitted to Phys. Rev. D15. Technical issue of the uniqueness of the solution to the Dirichlet problem clarified. New subsection on the nature of the boundary dat

No-horizon theorem for spacetimes with spacelike G1 isometry groups

We consider four-dimensional spacetimes $(M,{\mathbf g})$ which obey the Einstein equations ${\mathbf G}={\mathbf T}$, and admit a global spacelike $G_{1}={\mathbb R}$ isometry group. By means of dimensional reduction and local analyis on the reduced (2+1) spacetime, we obtain a sufficient condition on ${\mathbf T}$ which guarantees that $(M,{\mathbf g})$ cannot contain apparent horizons. Given any (3+1) spacetime with spacelike translational isometry, the no-horizon condition can be readily tested without the need for dimensional reduction. This provides thus a useful and encompassing apparent horizon test for $G_{1}$-symmetric spacetimes. We argue that this adds further evidence towards the validity of the hoop conjecture, and signals possible violations of strong cosmic censorship.Comment: 8 pages, LaTeX, uses IOP package; published in Class. Quantum Gra

Strong curvature singularities in quasispherical asymptotically de Sitter dust collapse

We study the occurrence, visibility, and curvature strength of singularities in dust-containing Szekeres spacetimes (which possess no Killing vectors) with a positive cosmological constant. We find that such singularities can be locally naked, Tipler strong, and develop from a non-zero-measure set of regular initial data. When examined along timelike geodesics, the singularity's curvature strength is found to be independent of the initial data.Comment: 16 pages, LaTeX, uses IOP package, 2 eps figures; accepted for publication in Class. Quantum Gra

No-horizon theorem for vacuum gravity with spacelike G1 isometry groups

We show that (3+1) vacuum spacetimes admitting a global, spacelike, one-parameter Lie group of isometries of translational type cannot contain apparent horizons. The only assumption made is that of the existence of a global spacelike Killing vector field with infinite open orbits; the four-dimensional vacuum spacetime metric is otherwise arbitrary. This result may thus be viewed as a hoop conjecture theorem for vacuum gravity with one spacelike translational Killing symmetry.Comment: 6 pages, revtex4; published in Phys. Rev. D Rapid Com

Phases of massive scalar field collapse

We study critical behavior in the collapse of massive spherically symmetric scalar fields. We observe two distinct types of phase transition at the threshold of black hole formation. Type II phase transitions occur when the radial extent $(\lambda)$ of the initial pulse is less than the Compton wavelength ($\mu^{-1}$) of the scalar field. The critical solution is that found by Choptuik in the collapse of massless scalar fields. Type I phase transitions, where the black hole formation turns on at finite mass, occur when $\lambda \mu \gg 1$. The critical solutions are unstable soliton stars with masses \alt 0.6 \mu^{-1}. Our results in combination with those obtained for the collapse of a Yang-Mills field~{[M.~W. Choptuik, T. Chmaj, and P. Bizon, Phys. Rev. Lett. 77, 424 (1996)]} suggest that unstable, confined solutions to the Einstein-matter equations may be relevant to the critical point of other matter models.Comment: 5 pages, RevTex, 4 postscript figures included using psfi

Relativistic shells: Dynamics, horizons, and shell crossing

We consider the dynamics of timelike spherical thin matter shells in vacuum. A general formalism for thin shells matching two arbitrary spherical spacetimes is derived, and subsequently specialized to the vacuum case. We first examine the relative motion of two dust shells by focusing on the dynamics of the exterior shell, whereby the problem is reduced to that of a single shell with different active Schwarzschild masses on each side. We then examine the dynamics of shells with non-vanishing tangential pressure $p$, and show that there are no stable--stationary, or otherwise--solutions for configurations with a strictly linear barotropic equation of state, $p=\alpha\sigma$, where $\sigma$ is the proper surface energy density and $\alpha\in(-1,1)$. For {\em arbitrary} equations of state, we show that, provided the weak energy condition holds, the strong energy condition is necessary and sufficient for stability. We examine in detail the formation of trapped surfaces, and show explicitly that a thin boundary layer causes the apparent horizon to evolve discontinuously. Finally, we derive an analytical (necessary and sufficient) condition for neighboring shells to cross, and compare the discrete shell model with the well-known continuous Lema\^{\i}tre-Tolman-Bondi dust case.Comment: 25 pages, revtex4, 4 eps figs; published in Phys. Rev.

Di-ureasil hybrids doped with LiBF4: attractive candidates as electrolytes for "Smart Windows"

The sol-gel process has been used to prepare hybrid electrolytes composed of a poly(oxyethylene) (POE)/siloxane hybrid network doped with lithium tetrafluoroborate (LiBF4) with compositions of n between ∞ and 2.5. In this context the lithium salt concentration is expressed in terms of the number of oxyethylene units in the organic component of the network per Li+ ion. Electrolyte samples with n ≥ 20 are thermally stable up to approximately 250 ºC. All the materials synthesized are semi-crystalline: in the composition range n ≥ 15 free crystalline POE exists and at 60 ≥ n ≥ 2.5 evidence of the presence of a crystalline POE/LiBF4 compound has been found. At n = 2.5 this latter crystalline phase coexists with free salt. The room temperature conductivity maximum of this electrolyte system is located at n = 10 (1.5x10-5 S cm-1 at 22 ºC). The electrochemical stability domain of the sample with n = 15 spans about 5.5 V versus Li/Li+. This new series of materials represents a promising alternative to the LiTFSI- and LiClO4-doped POE and POE/siloxane analogues. Preliminary tests performed with a prototype electrochromic device (ECD) comprising the sample with n = 8 as electrolyte and WO3 as cathodically coloring layer are extremely encouraging. The device exhibits switching time around 50 s, an optical density change of 0.13, open circuit memory of about 4 months and high coloration efficiency (106 cm2C-1 in the 3rd cycle).Fundação para a Ciência e a Tecnologi

Black hole formation from massive scalar fields

It is shown that there exists a range of parameters in which gravitational collapse with a spherically symmetric massive scalar field can be treated as if it were collapsing dust. This implies a criterion for the formation of black holes depending on the size and mass of the initial field configuration and the mass of the scalar field.Comment: 11 pages, RevTeX, 3 eps figures. Submitted to Class. Quantum Gra