Static Einstein-Maxwell Solutions in 2+1 dimensions

We obtain the Einstein-Maxwell equations for (2+1)-dimensional static space-time, which are invariant under the transformation $q_0=i\,q_2,q_2=i\,q_0,\alpha \rightleftharpoons \gamma$. It is shown that the magnetic solution obtained with the help of the procedure used in Ref.~\cite{Cataldo}, can be obtained from the static BTZ solution using an appropriate transformation. Superpositions of a perfect fluid and an electric or a magnetic field are separately studied and their corresponding solutions found.Comment: 8 pages, LaTeX, no figures, to appear in Physical Review

Self-Gravitating Strings In 2+1 Dimensions

We present a family of classical spacetimes in 2+1 dimensions. Such a spacetime is produced by a Nambu-Goto self-gravitating string. Due to the special properties of three-dimensional gravity, the metric is completely described as a Minkowski space with two identified worldsheets. In the flat limit, the standard string is recovered. The formalism is developed for an open string with massive endpoints, but applies to other boundary conditions as well. We consider another limit, where the string tension vanishes in geometrical units but the end-masses produce finite deficit angles. In this limit, our open string reduces to the free-masses solution of Gott, which possesses closed timelike curves when the relative motion of the two masses is sufficiently rapid. We discuss the possible causal structures of our spacetimes in other regimes. It is shown that the induced worldsheet Liouville mode obeys ({\it classically}) a differential equation, similar to the Liouville equation and reducing to it in the flat limit. A quadratic action formulation of this system is presented. The possibility and significance of quantizing the self-gravitating string, is discussed.Comment: 55 page

Quantum Stability of (2+1)-Spacetimes with Non-Trivial Topology

Quantum fields are investigated in the (2+1)-open-universes with non-trivial topologies by the method of images. The universes are locally de Sitter spacetime and anti-de Sitter spacetime. In the present article we study spacetimes whose spatial topologies are a torus with a cusp and a sphere with three cusps as a step toward the more general case. A quantum energy momentum tensor is obtained by the point stripping method. Though the cusps are no singularities, the latter cusps cause the divergence of the quantum field. This suggests that only the latter cusps are quantum mechanically unstable. Of course at the singularity of the background spacetime the quantum field diverges. Also the possibility of the divergence of topological effect by a negative spatial curvature is discussed. Since the volume of the negatively curved space is larger than that of the flat space, one see so many images of a single source by the non-trivial topology. It is confirmed that this divergence does not appear in our models of topologies. The results will be applicable to the case of three dimensional multi black hole\cite{BR}.Comment: 17 pages, revtex, 3 uuencoded figures containe

Genus Topology of the Cosmic Microwave Background from the WMAP 3-Year Data

We have independently measured the genus topology of the temperature fluctuations in the cosmic microwave background seen in the Wilkinson Microwave Anisotropy Probe (WMAP) 3-year data. A genus analysis of the WMAP data indicates consistency with Gaussian random-phase initial conditions, as predicted by standard inflation. We set 95% confidence limits on non-linearities of -101 < f_{nl} < 107. We also find that the observed low l (l <= 8) modes show a slight anti-correlation with the Galactic foreground, but not exceeding 95% confidence, and that the topology defined by these modes is consistent with that of a Gaussian random-phase distribution (within 95% confidence).Comment: MNRAS LaTeX style (mn2e.cls), EPS and JPEG figure

The Evolution of the Cosmic Microwave Background

We discuss the time dependence and future of the Cosmic Microwave Background (CMB) in the context of the standard cosmological model, in which we are now entering a state of endless accelerated expansion. The mean temperature will simply decrease until it reaches the effective temperature of the de Sitter vacuum, while the dipole will oscillate as the Sun orbits the Galaxy. However, the higher CMB multipoles have a richer phenomenology. The CMB anisotropy power spectrum will for the most part simply project to smaller scales, as the comoving distance to last scattering increases, and we derive a scaling relation that describes this behaviour. However, there will also be a dramatic increase in the integrated Sachs-Wolfe contribution at low multipoles. We also discuss the effects of tensor modes and optical depth due to Thomson scattering. We introduce a correlation function relating the sky maps at two times and the closely related power spectrum of the difference map. We compute the evolution both analytically and numerically, and present simulated future sky maps.Comment: 23 pages, 11 figures; references added; one figure dropped and minor changes to match published version. For high-resolution versions of figures and animations, see http://www.astro.ubc.ca/people/scott/future.htm