Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes

We construct and analyze a large class of exact five- and six-dimensional regular and static solutions of the vacuum Einstein equations. These solutions describe sequences of Kaluza-Klein bubbles and black holes, placed alternately so that the black holes are held apart by the bubbles. Asymptotically the solutions are Minkowski-space times a circle, i.e. Kaluza-Klein space, so they are part of the (\mu,n) phase diagram introduced in hep-th/0309116. In particular, they occupy a hitherto unexplored region of the phase diagram, since their relative tension exceeds that of the uniform black string. The solutions contain bubbles and black holes of various topologies, including six-dimensional black holes with ring topology S^3 x S^1 and tuboid topology S^2 x S^1 x S^1. The bubbles support the S^1's of the horizons against gravitational collapse. We find two maps between solutions, one that relates five- and six-dimensional solutions, and another that relates solutions in the same dimension by interchanging bubbles and black holes. To illustrate the richness of the phase structure and the non-uniqueness in the (\mu,n) phase diagram, we consider in detail particular examples of the general class of solutions.Comment: 71 pages, 22 figures, v2: Typos fixed, comment added in sec. 5.

Introduction to Loop Quantum Gravity

This article is based on the opening lecture at the third quantum geometry and quantum gravity school sponsored by the European Science Foundation and held at Zakopane, Poland in March 2011. The goal of the lecture was to present a broad perspective on loop quantum gravity for young researchers. The first part is addressed to beginning students and the second to young researchers who are already working in quantum gravity.Comment: 30 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:gr-qc/041005

Generalized Quantum Theory of Recollapsing Homogeneous Cosmologies

A sum-over-histories generalized quantum theory is developed for homogeneous minisuperspace type A Bianchi cosmological models, focussing on the particular example of the classically recollapsing Bianchi IX universe. The decoherence functional for such universes is exhibited. We show how the probabilities of decoherent sets of alternative, coarse-grained histories of these model universes can be calculated. We consider in particular the probabilities for classical evolution defined by a suitable coarse-graining. For a restricted class of initial conditions and coarse grainings we exhibit the approximate decoherence of alternative histories in which the universe behaves classically and those in which it does not. For these situations we show that the probability is near unity for the universe to recontract classically if it expands classically. We also determine the relative probabilities of quasi-classical trajectories for initial states of WKB form, recovering for such states a precise form of the familiar heuristic "J d\Sigma" rule of quantum cosmology, as well as a generalization of this rule to generic initial states.Comment: 41 pages, 4 eps figures, revtex 4. Modest revisions throughout. Physics unchanged. To appear in Phys. Rev.

Being, Becoming and the Undivided Universe: A Dialogue between Relational Blockworld and the Implicate Order Concerning the Unification of Relativity and Quantum Theory

In this paper two different approaches to unification will be compared, Relational Blockworld (RBW) and Hiley's implicate order. Both approaches are monistic in that they attempt to derive matter and spacetime geometry 'at once' in an interdependent and background independent fashion from something underneath both quantum theory and relativity. Hiley's monism resides in the implicate order via Clifford algebras and is based on process as fundamental while RBW's monism resides in spacetimematter via path integrals over graphs whereby space, time and matter are co-constructed per a global constraint equation. RBW's monism therefore resides in being (relational blockworld) while that of Hiley's resides in becoming (elementary processes). Regarding the derivation of quantum theory and relativity, the promises and pitfalls of both approaches will be elaborated. Finally, special attention will be paid as to how Hiley's process account might avoid the blockworld implications of relativity and the frozen time problem of canonical quantum gravity.Comment: 33 pages, 7 figures. Revised to include modified Regge calculus results. Accepted for publication in Foundations of Physics. arXiv admin note: substantial text overlap with arXiv:1106.333