Galileon Hairs of Dyson Spheres, Vainshtein's Coiffure and Hirsute Bubbles

We study the fields of spherically symmetric thin shell sources, a.k.a. Dyson spheres, in a {\it fully nonlinear covariant} theory of gravity with the simplest galileon field. We integrate exactly all the field equations once, reducing them to first order nonlinear equations. For the simplest galileon, static solutions come on {\it six} distinct branches. On one, a Dyson sphere surrounds itself with a galileon hair, which far away looks like a hair of any Brans-Dicke field. The hair changes below the Vainshtein scale, where the extra galileon terms dominate the minimal gradients of the field. Their hair looks more like a fuzz, because the galileon terms are suppressed by the derivative of the volume determinant. It shuts off the `hair bunching' over the `angular' 2-sphere. Hence the fuzz remains dilute even close to the source. This is really why the Vainshtein's suppression of the modifications of gravity works close to the source. On the other five branches, the static solutions are all {\it singular} far from the source, and shuttered off from asymptotic infinity. One of them, however, is really the self-accelerating branch, and the singularity is removed by turning on time dependence. We give examples of regulated solutions, where the Dyson sphere explodes outward, and its self-accelerating side is nonsingular. These constructions may open channels for nonperturbative transitions between branches, which need to be addressed further to determine phenomenological viability of multi-branch gravities.Comment: 29+1 pages, LaTeX, 2 .pdf figure

A variational approach to approximate controls for system with essential spectrum : Application to membranal arch

We address the numerical approximation of boundary controls for systems of the form $\boldsymbol{y^{\prime\prime}}+\boldsymbol{A_M}\boldsymbol{y}=\boldsymbol{0}$ which models dynamical elastic shell structure. The membranal operator $\boldsymbol{A_M}$ is self-adjoint and of mixed order, so that it possesses a non empty and bounded essential spectrum $\sigma_{ess}(\boldsymbol{A_M})$. Consequently, the controllability does not hold uniformly with respect to the initial data. Thus the numerical computation of controls by the way of dual approachs and gradient methods may fail, even if the initial data belongs to the orthogonal of the space spanned by the eigenfunctions associated with $\sigma_{ess}(\boldsymbol{A_M})$. In that work, we adapt a variational approach introduced in [Pablo Pedregal, \textit{Inverse Problems} (26) 015004 (2010)] for the wave equation and obtain a robust method of approximation. This approach does not require any information on the spectrum of the operator $\boldsymbol{A_M}$. We also show that it allows to extract, from any initial data $(\boldsymbol{y^0},\boldsymbol{y^1})$, a controllable component for the mixed order system. We illustrate these properties with some numerical experiments in the full controllability context as well as a partial controllability one

Bubble collisions and measures of the multiverse

To compute the spectrum of bubble collisions seen by an observer in an eternally-inflating multiverse, one must choose a measure over the diverging spacetime volume, including choosing an "initial" hypersurface below which there are no bubble nucleations. Previous calculations focused on the case where the initial hypersurface is pushed arbitrarily deep into the past. Interestingly, the observed spectrum depends on the orientation of the initial hypersurface, however one's ability observe the effect rapidly decreases with the ratio of inflationary Hubble rates inside and outside one's bubble. We investigate whether this conclusion might be avoided under more general circumstances, in particular placing the observer's bubble near the initial hypersurface. We find that it is not. As a point of reference, a substantial appendix reviews relevant aspects of the measure problem of eternal inflation.Comment: 24 pages, two figures, plus 16-page appendix with one figure; v2: minor improvements and clarifications, conclusions unchanged (version to appear in JCAP

The Blackholic energy and the canonical Gamma-Ray Burst

We outline the main results of our GRB model, based on the three interpretation paradigms we proposed in July 2001, comparing and contrasting them with the ones in the current literature. Thanks to the observations by Swift and by VLT, this analysis points to a "canonical GRB" originating from markedly different astrophysical scenarios. The communality is that they are all emitted in the formation of a black hole with small or null angular momentum. The following sequence appears to be canonical: the vacuum polarization process creating an optically thick self accelerating electron-positron plasma; the engulfment of baryonic mass during the plasma expansion; the adiabatic expansion of the optically thick "fireshell" up to the transparency; the interaction of the remaining accelerated baryons with the interstellar medium (ISM). This leads to the canonical GRB composed of a proper GRB (P-GRB), emitted at the moment of transparency, followed by an extended afterglow. The parameters are the plasma total energy, the fireshell baryon loading and the ISM filamentary distribution around the source. In the limit of no baryon loading the total energy is radiated in the P-GRB. In this limit, the canonical GRBs explain as well the short GRBs.Comment: 163 pages, 89 figures, to appear on the "Proceedings of the XIIth Brazilian School of Cosmology and Gravitation", M. Novello, S.E. Perez-Bergliaffa (editors), AIP, in pres