K-causality and degenerate spacetimes

The causal relation $K^+$ was introduced by Sorkin and Woolgar to extend the standard causal analysis of $C^2$ spacetimes to those that are only $C^0$. Most of their results also hold true in the case of spacetimes with degeneracies. In this paper we seek to examine $K^+$ explicitly in the case of Lorentzian topology changing Morse spacetimes containing isolated degeneracies. We first demonstrate some interesting features of this relation in globally Lorentzian spacetimes. In particular, we show that $K^+$ is robust and that it coincides with the Seifert relation when the spacetime is stably causal. Moreover, the Hawking and Sachs characterisation of causal continuity translates into a natural expression in terms of $K^+$ for general spacetimes. We then examine $K^+$ in topology changing Morse spacetimes both with and without the degeneracies and find further characterisations of causal continuity.Comment: Latex, 23 pages, 4 figure

Boundary contributions in the causal set action

Evidence is provided for a conjecture that, in the continuum limit, the mean of the causal set action of a causal set sprinkled into a globally hyperbolic Lorentzian spacetime, M, of finite volume equals the Einstein Hilbert action of M plus the volume of the co-dimension 2 intersection of the future boundary with the past boundary. We give the heuristic argument for this conjecture and analyse some examples in 2 dimensions and one example in 4 dimensions

Zero modes, entropy bounds and partition functions

Some recent finite temperature calculations arising in the investigation of the Verlinde-Cardy relation are re-analysed. Some remarks are also made about temperature inversion symmetry.Comment: 12 pages, JyTe

Causality in Time-Neutral Cosmologies

Gell-Mann and Hartle (GMH) have recently considered time-neutral cosmological models in which the initial and final conditions are independently specified, and several authors have investigated experimental tests of such models. We point out here that GMH time-neutral models can allow superluminal signalling, in the sense that it can be possible for observers in those cosmologies, by detecting and exploiting regularities in the final state, to construct devices which send and receive signals between space-like separated points. In suitable cosmologies, any single superluminal message can be transmitted with probability arbitrarily close to one by the use of redundant signals. However, the outcome probabilities of quantum measurements generally depend on precisely which past {\it and future} measurements take place. As the transmission of any signal relies on quantum measurements, its transmission probability is similarly context-dependent. As a result, the standard superluminal signalling paradoxes do not apply. Despite their unusual features, the models are internally consistent. These results illustrate an interesting conceptual point. The standard view of Minkowski causality is not an absolutely indispensable part of the mathematical formalism of relativistic quantum theory. It is contingent on the empirical observation that naturally occurring ensembles can be naturally pre-selected but not post-selected.Comment: 5 pages, RevTeX. Published version -- minor typos correcte

Determinants on lens spaces and cyclotomic units

The Laplacian functional determinants for conformal scalars and coexact one-forms are evaluated in closed form on inhomogeneous lens spaces of certain orders, including all odd primes when the essential part of the expression is given, formally as a cyclotomic unitComment: 18 pages, 1 figur

Symmetry-breaking and zero-one laws

We offer further evidence that discreteness of the sort inherent in a causal set cannot, in and of itself, serve to break Poincaré invariance. In particular we prove that a Poisson sprinkling of Minkowski spacetime cannot endow spacetime with a distinguished spatial or temporal orientation, or with a distinguished lattice of spacetime points, or with a distinguished lattice of timelike directions (corresponding respectively to breakings of reflection-invariance, translation-invariance, and Lorentz invariance). Along the way we provide a proof from first principles of the zero-one law on which our new arguments are based

Gravitating Fluxbranes

We consider the effect that gravity has when one tries to set up a constant background form field. We find that in analogy with the Melvin solution, where magnetic field lines self-gravitate to form a flux-tube, the self-gravity of the form field creates fluxbranes. Several exact solutions are found corresponding to different transverse spaces and world-volumes, a dilaton coupling is also considered.Comment: 14 pages, 5 figure

Morse index and causal continuity. A criterion for topology change in quantum gravity

Studies in 1+1 dimensions suggest that causally discontinuous topology changing spacetimes are suppressed in quantum gravity. Borde and Sorkin have conjectured that causal discontinuities are associated precisely with index 1 or n-1 Morse points in topology changing spacetimes built from Morse functions. We establish a weaker form of this conjecture. Namely, if a Morse function f on a compact cobordism has critical points of index 1 or n-1, then all the Morse geometries associated with f are causally discontinuous, while if f has no critical points of index 1 or n-1, then there exist associated Morse geometries which are causally continuous.Comment: Latex, 20 pages, 3 figure

Decay Modes of Intersecting Fluxbranes

Just as the single fluxbrane is quantum mechanically unstable to the nucleation of a locally charged spherical brane, so intersecting fluxbranes are unstable to various decay modes. Each individual element of the intersection can decay via the nucleation of a spherical brane, but uncharged spheres can also be nucleated in the region of intersection. For special values of the fluxes, however, intersecting fluxbranes are supersymmetric, and so are expected to be stable. We explicitly consider the instanton describing the decay modes of the two--element intersection (an F5-brane in the string theory context), and show that in dimensions greater than four the action for the decay mode of the supersymmetric intersection diverges. This observation allows us to show that stable intersecting fluxbranes should also exist in type 0A string theory.Comment: 19 pages, 6 figures. References adde