3,752 research outputs found
Universality of the Future Chronological Boundary
The purpose of this note is to establish, in a categorical manner, the
universality of the Geroch-Kronheimer-Penrose causal boundary when considering
the types of causal structures that may profitably be put on any sort of
boundary for a spacetime. Actually, this can only be done for the future causal
boundary (or the past causal boundary) separately; furthermore, only the
chronology relation, not the causality relation, is considered, and the GKP
topology is eschewed. The final result is that there is a unique map, with the
proper causal properties, from the future causal boundary of a spacetime onto
any ``reasonable" boundary which supports some sort of chronological structure
and which purports to consist of a future completion of the spacetime.
Furthermore, the future causal boundary construction is categorically unique in
this regard.Comment: 25 pages, AMS-TeX; 2 figures, PostScript (separate); captions
(separate); submitted to Class. Quantum Grav, slight revision: bottom lines
legible, figures added, expanded discussion and example
Discrete Group Actions on Spacetimes: Causality Conditions and the Causal Boundary
Suppose a spacetime is a quotient of a spacetime by a discrete group
of isometries. It is shown how causality conditions in the two spacetimes are
related, and how can one learn about the future causal boundary on by
studying structures in . The relations between the two are particularly
simple (the boundary of the quotient is the quotient of the boundary) if both
and have spacelike future boundaries and if it is known that the
quotient of the future completion of is past-distinguishing. (That last
assumption is automatic in the case of being multi-warped.)Comment: 32 page
Topological Sector Fluctuations and Curie Law Crossover in Spin Ice
At low temperatures, a spin ice enters a Coulomb phase - a state with
algebraic correlations and topologically constrained spin configurations. In
Ho2Ti2O7, we have observed experimentally that this process is accompanied by a
non-standard temperature evolution of the wave vector dependent magnetic
susceptibility, as measured by neutron scattering. Analytical and numerical
approaches reveal signatures of a crossover between two Curie laws, one
characterizing the high temperature paramagnetic regime, and the other the low
temperature topologically constrained regime, which we call the spin liquid
Curie law. The theory is shown to be in excellent agreement with neutron
scattering experiments. On a more general footing, i) the existence of two
Curie laws appears to be a general property of the emergent gauge field for a
classical spin liquid, and ii) sheds light on the experimental difficulty of
measuring a precise Curie-Weiss temperature in frustrated materials; iii) the
mapping between gauge and spin degrees of freedom means that the susceptibility
at finite wave vector can be used as a local probe of fluctuations among
topological sectors.Comment: 10 pages, 5 figure
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