Abstract:
Using the improved quantization technique to the mini-superspace approximation of loop quantum gravity, we study the evolution of black holes supported by a cosmological constant. The addition of a cosmological constant allows for classical solutions with planar, cylindrical, toroidal and higher genus black holes. Here we study the quantum analog of these space-times. In all scenarios studied, the singularity present in the classical counter-part is avoided in the quantized version and is replaced by a bounce, and in the late evolution, a series of less severe bounces. Interestingly, although there are differences during the evolution between the various symmetries and topologies, the evolution on the other side of the bounce asymptotes to space-times of Nariai-type, with the exception of the planar black hole analyzed here, whose $T$-$R$=constant subspaces seem to continue expanding in the long term evolution. For the other cases, Nariai-type universes are attractors in the quantum evolution, albeit with different parameters. We study here the quantum evolution of each symmetry in detail.

Abstract:
In the context of loop quantum gravity, we construct the phase-space of isolated horizons with genus greater than 0. Within the loop quantum gravity framework, these horizons are described by genus g surfaces with N punctures and the dimension of the corresponding phase-space is calculated including the genus cycles as degrees of freedom. From this, the black hole entropy can be calculated by counting the microstates which correspond to a black hole of fixed area. We find that the leading term agrees with the A/4 law and that the sub-leading contribution is modified by the genus cycles.

Abstract:
Supersymmetric solutions of supergravity theories, and consequently metrics with special holonomy, have played an important role in the development of string theory. We describe how a Lorentzian manifold is either completely reducible, and thus essentially known, or not completely reducible so that there exists a degenerate holonomy invariant lightlike subspace and consequently admits a covariantly constant or a recurrent null vector and belongs to the higher-dimensional Kundt class of spacetimes. These Kundt spacetimes (which contain the vanishing and constant curvature invariant spacetimes as special cases) are genuinely Lorentzian and have a number of interesting and unusual properties, which may lead to novel and fundamental physics.

Abstract:
Studying spacetimes with continuous symmetries by dimensional reduction to a lower dimensional spacetime is a well known technique in field theory and gravity. Recently, its use has been advocated in numerical relativity as an efficient computational technique for the numerical study of axisymmetric asymptotically flat 4-dimensional spacetimes. We prove here that if the dimensionally reduced spacetime is a physically reasonable 3-dimensional asymptotically flat or asymptotically anti-de Sitter spacetime, then, surprisingly, the topology of the higher dimensional spacetime must be one of two product topologies. Reductions of other topologies result in physically pathological spacetimes. In particular, reduction of asymptotically flat 4-dimensional spacetimes must lead to pathologies. These results use only the topological censorship theorem and topological methods and consequently are independent of the field equations and reduction method.

Abstract:
The question of the averaging of inhomogeneous spacetimes in cosmology is important for the correct interpretation of cosmological data. In this paper a conceptually simpler approach to averaging in cosmology is suggested, based on the averaging of scalars within unimodular gravity. As an illustration, the example of an exact spherically symmetric dust model is considered, and it is shown that within this approach averaging introduces correlations (corrections) to the effective dynamical evolution equation in the form of a spatial curvature term.

Abstract:
It is known that the SU(2) degrees of freedom manifest in the description of the gravitational field in loop quantum gravity are generally reduced to U(1) degrees of freedom on an $S^2$ isolated horizon. General relativity also allows black holes with planar, toroidal, or higher genus topology for their horizons. These solutions also meet the criteria for an isolated horizon, save for the topological criterion, which is not crucial. We discuss the relevant corresponding symmetry reduction for black holes of various topologies (genus 0 and $\geq 2$) here and discuss its ramifications to black hole entropy within the loop quantum gravity paradigm. Quantities relevant to the horizon theory are calculated explicitly using a generalized ansatz for the connection and densitized triad, as well as utilizing a general metric admitting hyperbolic sub-spaces. In all scenarios, the internal symmetry may be reduced to combinations of U(1).

Abstract:
We construct a framework within which a mathematically precise, fully covariant, and exact averaging procedure for tensor fields on a manifold can be formulated. In particular, we introduce the Weitzenb\"ock connection for parallel transport and argue that, within the context of averaging, frames and connections are the natural geometrical objects on the manifold.

Abstract:
The velocity of perihelion rotation of Mercury's orbit relatively motionless space is computed. It is prove that it coincides with that calculated by the Newtonian interaction of the planets and of the compound model of the Sun’s rotation.

Abstract:
Ion beam deceleration properties of a newly developed low-energy ion beam implantation system were studied. The objective of this system was to produce general purpose low-energy (5 to 15 keV) implantations with high current beam of hundreds of μA level, providing the most wide implantation area possible and allowing continuously magnetic scanning of the beam over the sample(s). This paper describes the developed system installed in the high-current ion implanter at the Laboratory of Accelerators and Radiation Technologies of the Nuclear and Technological Cam-pus, Sacavém, Portugal (CTN).

Abstract:
If the augmented density of a spherical anisotropic system is assumed to be multiplicatively separable to functions of the potential and the radius, the radial function, which can be completely specified by the behavior of the anisotropy parameter alone, also fixes the anisotropic ratios of every higher-order velocity moment. It is inferred from this that the non-negativity of the distribution function necessarily limits the allowed behaviors of the radial function. This restriction is translated into the constraints on the behavior of the anisotropy parameter. We find that not all radial variations of the anisotropy parameter satisfy these constraints and thus that there exist anisotropy profiles that cannot be consistent with any separable augmented density.