arXiv subjects
Publications and source records attributed to Jim Isenberg.
GGR News: - Remembering Wheeler, by Jim Isenberg; Research Briefs: - A Brief Summary of the WMAP5 Results, by Lyman Page; - Science with LIGO, by Maria Alessandra Papa; Conference Reports: - 7th LISA Symposium, by Edward K. Porter; - The Fourth Gulf Coast Gravity Conference, by Lior Burko
We determine sufficient and necessary conditions for a spherically symmetric initial data set to satisfy the dynamical horizon conditions in the spacetime development. The constraint equations reduce to a single second order linear master equation, which leads to a systematic construction of all spherically symmetric dynamical horizons (SSDH) satisfying certain boundedness conditions. We also find necessary and sufficient conditions for a given spherically symmetric spacetime to contain a SSDH.
We review the properties of the constraint equations, from their geometric origin in hypersurface geometry through to their roles in the Cauchy problem and the Hamiltonian formulation of the Einstein equations. We then review properties of the space of solutions and construction techniques, including the conformal and conformal thin sandwich methods, the thin sandwich method, quasi-spherical and generalized QS methods, gluing techniques and the Corvino-Schoen projection.