Research in General Relativity and Gravitation

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There are important questions which refer to gravity on very tiny scales--scales where quantum gravity reigns--and therefore they implicitly raise the prior question whether spacetime is ultimately continuous or discrete. No matter what the answer here, discrete models of spacetime are needed for practical reasons: for the computer simulations which will tell us how to interpret the data coming from gravitational wave telescopes like LIGO. This research would address the following specific topics within this broad framework. The methods would be both analytic (paper and pencil computations and derivations) and numerical (computer simulations). properties of black holes: does the surface of the black hole (its `horizon`) possess a `fractal` structure, as Newtonian analysis indicates? discrete spacetime: further development of Regge Calculus as a practical tool for solving the Einstein equations numerically; further development of causal set theory, focusing on the issues of locality and the cosmological constant. spacetime topology and topology-change: what are the properties of topological geons and what happens when they are created and destroyed? quantum cosmology: what are the observational effects of the time varying cosmological constant indicated by causal set theory? sum-over-histories approach to quantum mechanics: how can we continue to make predictions with quantum mechanics in the presence of gravity?