The Monopole Equations in Topological Yang-Mills

We twist the monopole equations of Seiberg and Witten and show how these equations are realized in topological Yang-Mills theory. A Floer derivative and a Morse functional are found and are used to construct a unitary transformation between the usual Floer cohomologies and those of the monopole equations. Furthermore, these equations are seen to reside in the vanishing self-dual curvature condition of an $OSp(1|2)$-bundle. Alternatively, they may be seen arising directly from a vanishing self-dual curvature condition on an $SU(2)$-bundle in which the fermions are realized as spanning the tangent space for a specific background.Comment: 7 pgs., LaTeX (fullpage

Monopoles and the Emergence of Black Hole Entropy

One of the remarkable features of black holes is that they possess a thermodynamic description, even though they do not appear to be statistical systems. We use self-gravitating magnetic monopole solutions as tools for understanding the emergence of this description as one goes from an ordinary spacetime to one containing a black hole. We describe how causally distinct regions emerge as a monopole solution develops a horizon. We define an entropy that is naturally associated with these regions and that has a clear connection with the Hawking-Bekenstein entropy in the critical black hole limit.Comment: 6 pages, one figure RevTe

Quasi-Black Holes from Extremal Charged Dust

One can construct families of static solutions that can be viewed as interpolating between nonsingular spacetimes and those containing black holes. Although everywhere nonsingular, these solutions come arbitrarily close to having a horizon. To an observer in the exterior region, it becomes increasingly difficulty to distinguish these from a true black hole as the critical limiting solution is approached. In this paper we use the Majumdar-Papapetrou formalism to construct such quasi-black hole solutions from extremal charged dust. We study the gravitational properties of these solutions, comparing them with the the quasi-black hole solutions based on magnetic monopoles. As in the latter case, we find that solutions can be constructed with or without hair.Comment: 18 page

How the orbital period of a test particle is modified by the Dvali-Gabadadze-Porrati gravity?

In addition to the pericentre \omega, the mean anomaly M and, thus, the mean longitude \lambda, also the orbital period Pb and the mean motion $n$ of a test particle are modified by the Dvali-Gabadadze-Porrati gravity. While the correction to Pb depends on the mass of the central body and on the geometrical features of the orbital motion around it, the correction to $n$ is independent of them, up to terms of second order in the eccentricity $e$. The latter one amounts to about 2\times 10^-3 arcseconds per century. The present-day accuracy in determining the mean motions of the inner planets of the Solar System from radar ranging and differential Very Long Baseline Interferometry is 10^-2-5\times 10^-3 arcseconds per century, but it should be improved in the near future when the data from the spacecraft to Mercury and Venus will be available.Comment: LaTex, 7 pages, 13 references, no tables, no figures. Section 2.3 added. To appear in JCA

Gravitational Properties of Monopole Spacetimes Near the Black Hole Threshold

Although nonsingular spacetimes and those containing black holes are qualitatively quite different, there are continuous families of configurations that connect the two. In this paper we use self-gravitating monopole solutions as tools for investigating the transition between these two types of spacetimes. We show how causally distinct regions emerge as the black hole limit is achieved, even though the measurements made by an external observer vary continuously. We find that near-critical solutions have a naturally defined entropy, despite the absence of a true horizon, and that this has a clear connection with the Hawking-Bekenstein entropy. We find that certain classes of near-critical solutions display naked black hole behavior, although they are not truly black holes at all. Finally, we present a numerical simulation illustrating how an incident pulse of matter can induce the dynamical collapse of a monopole into an extremal black hole. We discuss the implications of this process for the third law of black hole thermodynamics.Comment: 23 pages, 4 figures RevTe