arXiv subjects

David Rideout

Publications and source records attributed to David Rideout.

21 records · Page 2Linked to original sources

arXiv2006

Spatial Hypersurfaces in Causal Set Cosmology

Within the causal set approach to quantum gravity, a discrete analog of a spacelike region is a set of unrelated elements, or an antichain. In the continuum approximation of the theory, a moment-of-time hypersurface is well represented by an inextendible antichain. We construct a richer structure corresponding to a thickening of this antichain containing non-trivial geometric and topological information. We find that covariant observables can be associated with such thickened antichains and transitions between them, in classical stochastic growth models of causal sets. This construction highlights the difference between the covariant measure on causal set cosmology and the standard sum-over-histories approach: the measure is assigned to completed histories rather than to histories on a restricted spacetime region. The resulting re-phrasing of the sum-over-histories may be fruitful in other approaches to quantum gravity.

gr-qc↗

arXiv2003

Toward standard testbeds for numerical relativity

In recent years, many different numerical evolution schemes for Einstein's equations have been proposed to address stability and accuracy problems that have plagued the numerical relativity community for decades. Some of these approaches have been tested on different spacetimes, and conclusions have been drawn based on these tests. However, differences in results originate from many sources, including not only formulations of the equations, but also gauges, boundary conditions, numerical methods, and so on. We propose to build up a suite of standardized testbeds for comparing approaches to the numerical evolution of Einstein's equations that are designed to both probe their strengths and weaknesses and to separate out different effects, and their causes, seen in the results. We discuss general design principles of suitable testbeds, and we present an initial round of simple tests with periodic boundary conditions. This is a pivotal first step toward building a suite of testbeds to serve the numerical relativists and researchers from related fields who wish to assess the capabilities of numerical relativity codes. We present some examples of how these tests can be quite effective in revealing various limitations of different approaches, and illustrating their differences. The tests are presently limited to vacuum spacetimes, can be run on modest computational resources, and can be used with many different approaches used in the relativity community.

gr-qc↗

arXiv2002

Dynamics of Causal Sets

The Causal Set approach to quantum gravity asserts that spacetime, at its smallest length scale, has a discrete structure. This discrete structure takes the form of a locally finite order relation, where the order, corresponding with the macroscopic notion of spacetime causality, is taken to be a fundamental aspect of nature. After an introduction to the Causal Set approach, this thesis considers a simple toy dynamics for causal sets. Numerical simulations of the model provide evidence for the existence of a continuum limit. While studying this toy dynamics, a picture arises of how the dynamics can be generalized in such a way that the theory could hope to produce more physically realistic causal sets. By thinking in terms of a stochastic growth process, and positing some fundamental principles, we are led almost uniquely to a family of dynamical laws (stochastic processes) parameterized by a countable sequence of coupling constants. This result is quite promising in that we now know how to speak of dynamics for a theory with discrete time. In addition, these dynamics can be expressed in terms of state models of Ising spins living on the relations of the causal set, which indicates how non-gravitational matter may arise from the theory without having to be built in at the fundamental level. These results are encouraging in that there exists a natural way to transform this classical theory, which is expressed in terms of a probability measure, to a quantum theory, expressed in terms of a quantum measure. A sketch as to how one might proceed in doing this is provided. Thus there is good reason to expect that Causal Sets are close to providing a background independent theory of quantum gravity.

gr-qc↗