A Causal Set Black Hole

We explicitly compute the causal structure of the Schwarzschild black hole spacetime, by providing an algorithm to decide if any pair of events is causally related. The primary motivation for this study comes from discrete quantum gravity, in particular the causal set approach, in which the fundamental variables can be thought of as the causal ordering of randomly selected events in spacetime. This work opens the way to simulating non-conformally flat spacetimes within the causal set approach, which may allow one to study important questions such as black hole entropy and Hawking radiation on a full four dimensional causal set black hole.Comment: 22 pages, 9 figures, LaTeX; response to referee comment

On the "renormalization" transformations induced by cycles of expansion and contraction in causal set cosmology

We study the ``renormalization group action'' induced by cycles of cosmic expansion and contraction, within the context of a family of stochastic dynamical laws for causal sets derived earlier. We find a line of fixed points corresponding to the dynamics of transitive percolation, and we prove that there exist no other fixed points and no cycles of length two or more. We also identify an extensive ``basin of attraction'' of the fixed points but find that it does not exhaust the full parameter space. Nevertheless, we conjecture that every trajectory is drawn toward the fixed point set in a suitably weakened sense.Comment: 22 pages, 1 firgure, submitted to Phys. Rev.

Manifold dimension of a causal set: Tests in conformally flat spacetimes

This paper describes an approach that uses flat-spacetime dimension estimators to estimate the manifold dimension of causal sets that can be faithfully embedded into curved spacetimes. The approach is invariant under coarse graining and can be implemented independently of any specific curved spacetime. Results are given based on causal sets generated by random sprinklings into conformally flat spacetimes in 2, 3, and 4 dimensions, as well as one generated by a percolation dynamics.Comment: 8 pages, 8 figure

The Currituck Sound Drainage Basin: Perceived Issues and Prospective Management Alternatives

This paper will summarize the results of a project designed to gather and analyze background information necessary for development of a comprehensive management plan for the Currituck Sound drainage basin, a small portion of the greater Albemarle-Pamlico watershed. In addition to the waters of Currituck Sound, the study area included 26,000 acres of open water in Back Bay, Virginia and the land draining into Currituck Sound, Back Bay, Northwest River, North Landing River, and other tributaries to Currituck Sound (Figure I). Based on North Carolina Center for Geographic Information and Analysis calculations, the Currituck Sound watershed covers approximately 733 square miles