Critical behavior in vacuum gravitational collapse in 4+1 dimensions

We show that the 4+1 dimensional vacuum Einstein equations admit gravitational waves with radial symmetry. The dynamical degrees of freedom correspond to deformations of the three-sphere orthogonal to the $(t,r)$ plane. Gravitational collapse of such waves is studied numerically and shown to exhibit discretely self-similar Type II critical behavior at the threshold of black hole formation.Comment: 4 pages, 7 figure

Codimension-two critical behavior in vacuum gravitational collapse

We consider the critical behavior at the threshold of black hole formation for the five dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial Bianchi IX ansatz. Exploiting a discrete symmetry present in this model we predict the existence of a codimension-two attractor. This prediction is confirmed numerically and the codimension-two attractor is identified as a discretely self-similar solution with two unstable modes.Comment: 4 pages, 5 figures, typos correcte

Anomalously small wave tails in higher dimensions

We consider the late-time tails of spherical waves propagating on even-dimensional Minkowski spacetime under the influence of a long range radial potential. We show that in six and higher even dimensions there exist exceptional potentials for which the tail has an anomalously small amplitude and fast decay. Along the way we clarify and amend some confounding arguments and statements in the literature of the subject.Comment: 13 page

On vacuum gravitational collapse in nine dimensions

We consider the vacuum gravitational collapse for cohomogeneity-two solutions of the nine dimensional Einstein equations. Using combined numerical and analytical methods we give evidence that within this model the Schwarzschild-Tangherlini black hole is asymptotically stable. In addition, we briefly discuss the critical behavior at the threshold of black hole formation.Comment: 4 pages, 4 figure

Formation of singularities for equivariant 2+1 dimensional wave maps into the two-sphere

In this paper we report on numerical studies of the Cauchy problem for equivariant wave maps from 2+1 dimensional Minkowski spacetime into the two-sphere. Our results provide strong evidence for the conjecture that large energy initial data develop singularities in finite time and that singularity formation has the universal form of adiabatic shrinking of the degree-one harmonic map from $\mathbb{R}^2$ into $S^2$.Comment: 14 pages, 5 figures, final version to be published in Nonlinearit

Colour-singlet strangelets at finite temperature

Considering massless $u$ and $d$ quarks, and massive (150 MeV) $s$ quarks in a bag with the bag pressure constant $B^{1/4} = 145$ MeV, a colour-singlet grand canonical partition function is constructed for temperatures $T = 1-30$ MeV. Then the stability of finite size strangelets is studied minimizing the free energy as a function of the radius of the bag. The colour-singlet restriction has several profound effects when compared to colour unprojected case: (1) Now bulk energy per baryon is increased by about $250$ MeV making the strange quark matter unbound. (2) The shell structures are more pronounced (deeper). (3) Positions of the shell closure are shifted to lower $A$-values, the first deepest one occuring at $A=2$, famous $H$-particle ! (4) The shell structure at $A=2$ vanishes only at $T\sim 30$ MeV, though for higher $A$-values it happens so at $T\sim 20$ MeV.Comment: Revtex file(8 pages)+6 figures(ps files) available on request from first Autho

Photon emission from bare quark stars

We investigate the photon emission from the electrosphere of a quark star. It is shown that at temperatures T\sim 0.1-1 MeV the dominating mechanism is the bremsstrahlung due to bending of electron trajectories in the mean Coulomb field of the electrosphere. The radiated energy for this mechanism is much larger than that for the Bethe-Heitler bremsstrahlung. The energy flux from the mean field bremsstrahlung exceeds the one from the tunnel e^{+}e^{-} pair creation as well. We demonstrate that the LPM suppression of the photon emission is negligible.Comment: 35 pages, 5 figure

Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem

We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB) equations, i.e. scalar conservation laws with diffusive-dispersive regularization. We review the existence of traveling wave solutions for these two classes of evolution equations. For classical equations the traveling wave problem (TWP) for a local KdVB equation can be identified with the TWP for a reaction-diffusion equation. In this article we study this relationship for these two classes of evolution equations with nonlocal diffusion/dispersion. This connection is especially useful, if the TW equation is not studied directly, but the existence of a TWS is proven using one of the evolution equations instead. Finally, we present three models from fluid dynamics and discuss the TWP via its link to associated reaction-diffusion equations

Strange Star Heating Events as a Model for Giant Flares of Soft Gamma-ray Repeaters

Two giant flares were observed on 5 March 1979 and 27 August 1998 from the soft gamma-ray repeaters SGR 0526-66 and SGR 1900+14, respectively. The striking similarity between these remarkable bursts strongly implies a common nature. We show that the light curves of the giant bursts may be easily explained in the model where the burst radiation is produced by the bare quark surface of a strange star heated, for example, by impact of a massive comet-like object.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. Letter