Abstract:
Following the recent recognition of a positive value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit the classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models: Kantowski-Sachs, Bianchi type-I and Bianchi type-III universes, with dust and a cosmological constant, in order to find out which are physically permitted. We find that these models undergo isotropization up to the point that the observations will not be able to distinguish between them and the standard model, except for the Kantowski-Sachs model $(\Omega_{k_{0}}<0)$ and for the Bianchi type-III $(\Omega_{k_{0}}>0)$ with $\Omega_{\Lambda_{0}}$ smaller than some critical value $\Omega_{\Lambda_{M}}$. Even if one imposes that the Universe should be nearly isotropic since the last scattering epoch ($z\approx 1000$), meaning that the Universe should have approximately the same Hubble parameter in all directions (considering the COBE 4-Year data), there is still a large range for the matter density parameter compatible with Kantowsky-Sachs and Bianchi type-III if $|\Omega_0+\Omega_{\Lambda_0}-1|\leq \delta$, for a very small $\delta$ . The Bianchi type-I model becomes exactly isotropic owing to our restrictions and we have $\Omega_0+\Omega_{\Lambda_0}=1$ in this case. Of course, all these models approach locally an exponential expanding state provided the cosmological constant $\Omega_\Lambda>\Omega_{\Lambda_{M}}$.

Abstract:
In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogeneities in the distribution of matter on the surface of the last scattering produce anisotropies in large angular scales (larger than $\vartheta \gtrsim 2^\circ$) which do not differ from the ones produced in Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometries. That is, for these anisotropic models, the imprint left on the cosmic microwave background radiation (CMBR) by the primordial density fluctuations, in the form of a fractional variation of the temperature of this radiation, is governed by the same expression as the one given for FLRW models. More precisely, under adiabatic initial conditions, the classical Sachs-Wolfe effect is recovered, provided the anisotropy of the overall expansion is small. This conclusion is in agreement with previous work on the same anisotropic models where we found that they may go through an `isotropization' process up to the point that the observations are unable to distinguish them from the standard FLRW model, if the Hubble parameters along the orthogonal directions are assumed to be approximately equal at the present epoch. Here we assumed upper bounds on the present values of anisotropic parameters imposed by COBE observations.

Abstract:
Following recent considerations of a non-zero value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit the classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models: Kantowski-Sachs, Bianchi I and Bianchi III universes, with dust and cosmological constant, in order to find out which are physically permitted. In fact, these models undergo isotropisation, except for the Kantowski-Sachs model (Omega_{k_{0}}>0) with Omega_{Lambda_{0}}< Omega_{Lambda_{M}} and for the Bianchi III (Omega_{k_{0}}<0) with Omega_{Lambda_{0}}

Abstract:
General Relativity is contaminated with non-trivial geometries which generate closed timelike curves. These apparently violate causality, producing time-travel paradoxes. We shall briefly discuss these geometries and analyze some of their physical aspects.

Abstract:
Recent solutions to the Einstein Field Equations involving negative energy densities, i.e., matter violating the weak-energy-condition, have been obtained, namely traversable wormholes, the Alcubierre warp drive and the Krasnikov tube. These solutions are related to superluminal travel, although locally the speed of light is not surpassed. It is difficult to define faster-than-light travel in generic space-times, and one can construct metrics which apparently allow superluminal travel, but are in fact flat Minkowski space-times. Therefore, to avoid these difficulties it is important to provide an appropriate definition of superluminal travel.

Abstract:
We analyze the stability of generic spherically symmetric thin shells to linearized perturbations around static solutions. We include the momentum flux term in the conservation identity, deduced from the ''ADM'' constraint and the Lanczos equations. Following the Ishak-Lake analysis, we deduce a master equation which dictates the stable equilibrium configurations. Considering the transparency condition, we study the stability of thin shells around black holes, showing that our analysis is in agreement with previous results. Applying the analysis to traversable wormhole geometries, by considering specific choices for the form function, we deduce stability regions, and find that the latter may be significantly increased by considering appropriate choices for the redshift function.

Abstract:
Spherically symmetric thin-shell wormholes in the presence of a cosmological constant are constructed applying the cut-and-paste technique implemented by Visser. Using the Darmois-Israel formalism the surface stresses, which are concentrated at the wormhole throat, are determined. This construction allows one to apply a dynamical analysis to the throat, considering linearized radial perturbations around static solutions. For a large positive cosmological constant, i.e., for the Schwarzschild-de Sitter solution, the region of stability is significantly increased, relatively to the null cosmological constant case, analyzed by Poisson and Visser. With a negative cosmological constant, i.e., the Schwarzschild-anti de Sitter solution, the region of stability is decreased. In particular, considering static solutions with a generic cosmological constant, the weak and dominant energy conditions are violated, while for $a_0 \leq 3M$ the null and strong energy conditions are satisfied. The surface pressure of the static solution is strictly positive for the Schwarzschild and Schwarzschild-anti de Sitter spacetimes, but takes negative values, assuming a surface tension in the Schwarzschild-de Sitter solution, for high values of the cosmological constant and the wormhole throat radius.

Abstract:
New exact solutions of Einstein's gravity coupled to a self-interacting conformal scalar field are derived in this work. Our approach extends a solution-generating technique originally introduced by Bekenstein for massless conformal scalar fields. Solutions are obtained for a Friedmann-Robertson-Walker geometry both for the cases of zero and non-zero curvatures, and a variety of interesting features are found. It is shown that one class of solutions tends asymptotically to a power-law inflationary behaviour $S(t)\sim t^p$ with $p>1$, while another class exhibits a late time approach to the $S(t)\sim t$ behaviour of the coasting models. Bouncing models which avoid an initial singularity are also obtained. A general discussion of the asymptotic behaviour and of the possibility of occurrence of inflation is provided.

Abstract:
The Schwarzschild solution has played a fundamental conceptual role in general relativity, and beyond, for instance, regarding event horizons, spacetime singularities and aspects of quantum field theory in curved spacetimes. However, one still encounters the existence of misconceptions and a certain ambiguity inherent in the Schwarzschild solution in the literature. By taking into account the point of view of an observer in the interior of the event horizon, one verifies that new conceptual difficulties arise. In this work, besides providing a very brief pedagogical review, we further analyze the interior Schwarzschild black hole solution. Firstly, by deducing the interior metric by considering time-dependent metric coefficients, the interior region is analyzed without the prejudices inherited from the exterior geometry. We also pay close attention to several respective cosmological interpretations, and briefly address some of the difficulties associated to spacetime singularities. Secondly, we deduce the conserved quantities of null and timelike geodesics, and discuss several particular cases in some detail. Thirdly, we examine the Eddington-Finkelstein and Kruskal coordinates directly from the interior solution. In concluding, it is important to emphasize that the interior structure of realistic black holes has not been satisfactorily determined, and is still open to considerable debate.

Abstract:
A reduced scale model of the coupled carbon cycle, population dynamics, energy system and land use characteristics is used to assess the sensitivity of atmospheric carbon to a variety of policies. Policies simulated include reduction of the rate of growth of the population; reduction of the rate of conversion of forested land to cropland; reduction in per capita energy demand in developed nations; reduction in per capita energy demand in developing nations; reduction in the carbon intensity of energy production in developed nations; and reduction in the carbon intensity of energy production in developing nations. For each policy, both the time to onset of the policy and the fractional annual rate of change in the associated model variable are established. Using as a measure of sensitivity the extension in years required for atmospheric carbon to reach the policy ceiling of 1160 BMT, achieved at a policy that introduces a rate of change in each affected model variable of 0.05 per year (a 5% change per year), then the policies in decreasing order of sensitivity are: Developing nations per capita growth (17 years), Developing nations carbon intensity (17 years), Population control (11 years), Developed nations carbon intensity (2.9 years), Developed nations per capita growth (2.8 years) and Land use (1.3 years). These values are all approximately doubled when population is stabilised first. An analysis of the model results also shows a convergence of the developed and developing nations per capita carbon emissions by 2100 when a portfolio of policies is selected to prevent a doubling of the pre-industrial revolution level of atmospheric carbon at any point in the future, consistent with a principle of “contract and converge”.