Anisotropic fluid with SU(2) type structure in general relativity: A model of localized matter

A model of anisotropic fluid with three perfect fluid components in interaction is studied. Each fluid component obeys the stiff matter equation of state and is irrotational. The interaction is chosen to reproduce an integrable system of equations similar to the one associated to self-dual SU(2) gauge fields. An extension of the BelinskyZakharov version of the inverse scattering transform is presented and used to find soliton solutions to the coupled Einstein equations. A particular class of solutions that can be interpreted as lumps of matter propagating in empty space-time is examined.

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

Los conceptos de espacio y tiempo en la teoría de la relatividad

Algunos filósofos no han vacilado en afirmar que la teoria de la relatividad era el relativismo aplicado a la Física. Para probar su apreciación han aducido algunas expresiones de EINSTEIN -de otros físicosno nos ocuparemos aquí-, que pueden inducir a confusión: así, por ejemplo, la afirmación de que no se puede hablar de la trayectoria deun móvil, de que en la realidad no es válida la ley de composición de ve locidades, etc. Con su acostumbrada brillantez ha dicho ORTEGA YGASSET frases como la siguiente: "Para la física de EINSTEIN, nuestro conocimiento es absoluto, la realidad es la relativa".Para ver si aquellas aprensiones son justificadas y, sobre todo, para ver si se puede admitir lo filosófico que hay en la teoría de la relatividad,vamos a someter a ésta a una dura prueba: a ser examinada por la filosofía que mejor ha sabido armonizar, a nuestro parecer, lo sensible y loideal: la filosofía escolástica, que al no apoyarse en teorías científicas, sino en la observación cierta de las cosas, podemos considerarla comoadecuado instrumento de trabajo. Entre los filósofos escolásticos nos ha parecido muy digno de tenerse en cuenta SUAREZ. El llega, efectivamente,al campo escolástico en una época de intenso renacimiento. Las grandes aportaciones medievales son sometidas por él a una aguda críticay sin integrarse en ninguna escuela, tiene la suficiente libertad de espíritu para seguir sus propios derroteros. Además, en este problema, nose aparta SUAREZ en lo esencial del sentir común de los filósofos escolásticos.

Dynamics of F=1 87Rb condensates at finite temperatures

We investigate the dynamics of a F=1 spinor Bose-Einstein condensate of 87Rb atoms confined in a quasi-one-dimensional trap both at zero and at finite temperature. At zero temperature, we observe coherent oscillations between populations of the various spin components and the formation of multiple domains in the condensate. We study also finite temperature effects in the spin dynamics taking into account the phase fluctuations in the Bogoliubov-de Gennes framework. At finite T, despite complex multidomain formation in the condensate, population equipartition occurs. The length scale of these spin domains seems to be determined intrinsically by nonlinear interactions.

Higher-dimensional rotating charged black holes

Using the blackfold approach, we study new classes of higher-dimensional rotating black holes with electric charges and string dipoles, in theories of gravity coupled to a 2-form or 3-form field strength and to a dilaton with arbitrary coupling. The method allows to describe not only black holes with large angular momenta, but also other regimes that include charged black holes near extremality with slow rotation. We construct explicit examples of electric rotating black holes of dilatonic and non-dilatonic Einstein-Maxwell theory, with horizons of spherical and non-spherical topology. We also find new families of solutions with string dipoles, including a new class of prolate black rings. Whenever there are exact solutions that we can compare to, their properties in the appropriate regime are reproduced precisely by our solutions. The analysis of blackfolds with string charges requires the formulation of the dynamics of anisotropic fluids with conserved string-number currents, which is new, and is carried out in detail for perfect fluids. Finally, our results indicate new instabilities of near-extremal, slowly rotating charged black holes, and motivate conjectures about topological constraints on dipole hair.

Nonperturbative semiclassical stability of de Sitter spacetime for small metric deviations

We consider the linearized semiclassical Einstein equations for small deviations around de Sitter spacetime including the vacuum polarization effects of conformal fields. Employing the method of order reduction, we find the exact solutions for general metric perturbations (of scalar, vector and tensor type). Our exact (nonperturbative) solutions show clearly that in this case de Sitter is stable with respect to small metric deviations and a late-time attractor. Furthermore, they also reveal a breakdown of perturbative solutions for a sufficiently long evolution inside the horizon. Our results are valid for any conformal theory, even self-interacting ones with arbitrarily strong coupling.

A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

Holographic isotropization linearized

The holographic isotropization of a highly anisotropic, homogeneous, strongly coupled, non-Abelian plasma was simplified in ref. [1] by linearizing Einstein"s equations around the final, equilibrium state. This approximation reproduces the expectation value of the boundary stress tensor with a 20% accuracy. Here we elaborate on these results and extend them to observables that are directly sensitive to the bulk interior, focusing for simplicity on the entropy production on the event horizon. We also consider next-to-leading-order corrections and show that the leading terms alone provide a better description of the isotropization process for the states that are furthest from equilibrium.

The differentiable chain functor is not homotopy equivalent to the continuous chain functor

Let $S_*$ and $S_*^\{infty}$ be the functors of continuous and differentiable singular chains on the category of differentiable manifolds. We prove that the natural transformation $i: S_*^\infty \rightarrow S_*$, which induces homology equivalences over each manifold, is not a natural homotopy equivalence.

Bose-Fermi mixtures in optical lattices

Using mean field theory, we have studied Bose-Fermi mixtures in a one-dimensional optical lattice in the case of an attractive boson-fermion interaction. We consider that the fermions are in the degenerate regime and that the laser intensities are such that quantum coherence across the condensate is ensured. We discuss the effect of the optical lattice on the critical rotational frequency for vortex line creation in the Bose-Einstein condensate, as well as how it affects the stability of the boson-fermion mixture. A reduction of the critical frequency for nucleating a vortex is observed as the strength of the applied laser is increased. The onset of instability of the mixture occurs for a sizably lower number of fermions in the presence of a deep optical lattice.

E=mc2

Quan hom ha d'escriure un text de divulgació científica ha de posar a l'abast de tothom conceptes i idees que inicialment poden semblar difícils. Pera ixò mai s'hi inclouen fórmules matemàtiques. L'única que és permesa en aquests escrits és la famosa equació d'Einstein, que encapçala aquest article. Molt poca gent entén totes les seves implicacions, però és tan senzilla i elegant, i l'hem vista tantes vegades, que ningú la troba estranya [...].