Las didácticas específicas: consideraciones sobre principios y actividades.

Las didácticas específicas son parte significativa de la didáctica general, formas de su concreción. Su objeto es hacer educativo el conocimiento que les concierne en cada caso. La dificultad estriba en la forma de su comunicación. En este sentido se busca concretarlas, con finalidad aclaradora, para las matemáticas y las ciencias de la naturaleza

Relativistic dynamics of cylindrical shells of counter-rotating particles

Although infinite cylinders are not astrophysical entities, it is possible to learn a great deal about the basic qualitative features of generation of gravitational waves and the behavior of the matter conforming such shells in the limits of very small radius. We describe the analytical model using kinetic theory for the matter and the junction conditions through the shell to obtain its equation of motion. The nature of the static solutions are analyzed, both for a single shell as well as for two concentric shells. In this second case, for a time dependent external shell, we integrate numerically the equation of motion for several values of the constants of the system. Also, a brief description in terms of the Komar mass is given to account for the gravitational wave energy emitted by the system.Comment: 19 pages, 8 figure

Las didácticas específicas: consideraciones sobre principios y actividades.

Las didácticas específicas son parte significativa de la didáctica general, formas de su concreción. Su objeto es hacer educativo el conocimiento que les concierne en cada caso. La dificultad estriba en la forma de su comunicación. En este sentido se busca concretarlas, con finalidad aclaradora, para las matemáticas y las ciencias de la naturaleza

Gravitational Collapse of Cylindrical Shells Made of Counter-Rotating Dust Particles

The general formulas of a non-rotating dynamic thin shell that connects two arbitrary cylindrical regions are given using Israel's method. As an application of them, the dynamics of a thin shell made of counter-rotating dust particles, which emits both gravitational waves and massless particles when it is expanding or collapsing, is studied. It is found that when the models represent a collapsing shell, in some cases the angular momentum of the dust particles is strong enough to halt the collapse, so that a spacetime singularity is prevented from forming, while in other cases it is not, and a line-like spacetime singularity is finally formed on the symmetry axis.Comment: To appear in Phys. Rev.

Evolution of thin-wall configurations of texture matter

We consider the free matter of global textures within the framework of the perfect fluid approximation in general relativity. We examine thermodynamical properties of texture matter in comparison with radiation fluid and bubble matter. Then we study dynamics of thin-wall selfgravitating texture objects, and show that classical motion can be elliptical (finite), parabolical or hyperbolical. It is shown that total gravitational mass of neutral textures in equilibrium equals to zero as was expected. Finally, we perform the Wheeler-DeWitt's minisuperspace quantization of the theory, obtain exact wave functions and discrete spectra of bound states with provision for spatial topology.Comment: intermediate research on nature of dual-radiation matter; LaTeX, 12 pages, 1 figure and epsfig style file included; slightly shortened version was published in December issue of GR

Black hole mimickers: regular versus singular behavior

Black hole mimickers are possible alternatives to black holes, they would look observationally almost like black holes but would have no horizon. The properties in the near-horizon region where gravity is strong can be quite different for both type of objects, but at infinity it could be difficult to discern black holes from their mimickers. To disentangle this possible confusion, we examine the near-horizon properties, and their connection with far away properties, of some candidates to black mimickers. We study spherically symmetric uncharged or charged but non-extremal objects, as well as spherically symmetric charged extremal objects. Within the uncharged or charged but non-extremal black hole mimickers, we study non-extremal $\epsilon$-wormholes on the threshold of the formation of an event horizon, of which a subclass are called black foils, and gravastars. Within the charged extremal black hole mimickers we study extremal $\epsilon$-wormholes on the threshold of the formation of an event horizon, quasi-black holes, and wormholes on the basis of quasi-black holes from Bonnor stars. We elucidate, whether or not the objects belonging to these two classes remain regular in the near-horizon limit. The requirement of full regularity, i.e., finite curvature and absence of naked behavior, up to an arbitrary neighborhood of the gravitational radius of the object enables one to rule out potential mimickers in most of the cases. A list ranking the best mimickers up to the worse is given. Since, in observational astrophysics it is difficult to find extremal configurations (the best mimickers in the ranking), whereas non-extremal configurations are really bad mimickers, the task of distinguishing black holes from their mimickers seems to be less difficult than one could think of.Comment: 30 pages, 1 figure, references added, minor changes in the revised versio

Generalized Vaidya Solutions

A large family of solutions, representing, in general, spherically symmetric Type II fluid, is presented, which includes most of the known solutions to the Einstein field equations, such as, the monopole-de Sitter-charged Vaidya ones.Comment: Gen. Relativ. Grav. 31 (1), 107-114 (1999

Pseudo-heteroclinic connections between bicircular restricted four-body problems

In this paper, we show a mechanism to explain transport from the outer to the inner Solar system. Such a mechanism is based on dynamical systems theory. More concretely, we consider a sequence of uncoupled bicircular restricted four-body problems -BR4BP -(involving the Sun, Jupiter, a planet and an infinitesimal mass), being the planet Neptune, Uranus and Saturn. For each BR4BP, we compute the dynamical substitutes of the collinear equilibrium points of the corresponding restricted three-body problem (Sun, planet and infinitesimal mass), which become periodic orbits. These periodic orbits are unstable, and the role that their invariant manifolds play in relation with transport from exterior planets to the inner ones is discussed

Critical phenomena of collapsing massless scalar wave packets

An analytical model that represents the collapse of a massless scalar wave packet with continuous self-similarity is constructed, and critical phenomena are found. In the supercritical case, the mass of black holes is finite and has the form $M \propto (p - p^{*})^{\gamma}$, with $\gamma = 1/2$.Comment: Latex file, including 2 figures, avalaible upon reques

On Charged Black Holes in Anti-de Sitter Space

We study the region inside the event horizon of charged black holes in five dimensional asymptotically anti-de Sitter space, using as a probe two-sided correlators which are dominated by spacelike geodesics penetrating the horizon. The spacetimes we investigate include the Reissner-Nordstrom black hole and perturbations thereof. The perturbed spacetimes can be found exactly, enabling us to perform a local scan of the region between the inner and outer horizons. Surprisingly, the two-sided correlators we calculate seem to be geometrically protected from the instability of the inner horizon.Comment: 1+37 pages, 20 ps and eps figures, LaTeX. References added and changes made to section