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James Isenberg Rafe Mazzeo Daniel Pollack 《Communications in Mathematical Physics》2002,231(3):529-568
We establish a general gluing theorem for constant mean curvature solutions of the vacuum Einstein constraint equations.
This allows one to take connected sums of solutions or to glue a handle (wormhole) onto any given solution. Away from this
handle region, the initial data sets we produce can be made as close as desired to the original initial data sets. These constructions
can be made either when the initial manifold is compact or asymptotically Euclidean or asymptotically hyperbolic, with suitable
corresponding conditions on the extrinsic curvature. In the compact setting a mild nondegeneracy condition is required. In
the final section of the paper, we list a number ways this construction may be used to produce new types of vacuum spacetimes.
Received: 4 October 2001 / Accepted: 26 July 2002 Published online: 29 October 2002
RID="*"
ID="*" Supported by the NSF under Grant PHY-0099373
RID="**"
ID="**" Supported by the NSF under Grant DMS-9971975 and at MSRI by NSF grant DMS-9701755
RID="***"
ID="***" Supported by the NSF under Grant DMS-9704515 相似文献
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Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualitative properties of the nearest-neighbor "spin ice" model. We discuss the dipolar energy scale present in both these materials and discuss how spin-ice behavior can occur despite the presence of long-range dipolar interactions. We present results of numerical simulations and a mean field analysis of Ising pyrochlore systems. Based on our quantitative theory, we suggest that the spin-ice behavior in these systems is due to long-range dipolar interactions, and that the nearest-neighbor exchange in Dy2Ti2O7 is antiferromagnetic. 相似文献
5.
D. Eardley J. Isenberg J. Marsden V. Moncrief 《Communications in Mathematical Physics》1986,106(1):137-158
We present several results about the nonexistence of solutions of Einstein's equations with homothetic or conformal symmetry. We show that the only spatially compact, globally hyperbolic spacetimes admitting a hypersurface of constant mean extrinsic curvature, and also admitting an infinitesimal proper homothetic symmetry, are everywhere locally flat; this assumes that the matter fields either obey certain energy conditions, or are the Yang-Mills or massless Klein-Gordon fields. We find that the only vacuum solutions admitting an infinitesimal proper conformal symmetry are everywhere locally flat spacetimes and certain plane wave solutions. We show that if the dominant energy condition is assumed, then Minkowski spacetime is the only asymptotically flat solution which has an infinitesimal conformal symmetry that is asymptotic to a dilation. In other words, with the exceptions cited, homothetic or conformal Killing fields are in fact Killing in spatially compact or asymptotically flat spactimes. In the conformal procedure for solving the initial value problem, we show that data with infinitesimal conformal symmetry evolves to a spacetime with full isometry. 相似文献
6.
James Isenberg 《Foundations of Physics》1986,16(7):651-665
We discuss the present status of the Cauchy problem for Einstein's classical field theory of gravity. 相似文献
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James A Isenberg 《Annals of Physics》1980,129(2):223-248
We show how to use the 3 + 1 construction program to build globally heperbolic spacetimes with topologically nontrivial Cauchy surfaces. Spacetimes in which the classical fields are sections of a nontrivial bundle are handled as well. In evolving the initial data in these spacetimes, one must work with an atlas of overlapping patches. Data must be transfered from patch to patch during the evolution, so the transition functions on patch intersections must be evolved as well. We describe how to do this. Often the evolution of the Cauchy data is considerably simplified by choosing the coordinate-shift field and the gaugeshift field A↓ to be patch dependent. We give examples of this phenomenon and show how to incorporate the patch dependence of and A↓ into a consistent evolution program for the spacetime. 相似文献