Existence of CMC Cauchy surfaces and spacetime splitting

In this paper, we review results on the existence (and nonexistence) of constant mean curvature spacelike hypersurfaces in the cosmological setting, and discuss the connection to the spacetime splittng problem. It is a pleasure to dedicate this paper to Robert Bartnik, who has made fundamental contributions to this area.Comment: 16 page

Nomenclatural notes on Pseudocyphellaria V : some Brazilian taxa

A new, phyllidiate, white-medulla species with yellow pseudocyphellae and a green photobiont, Pseudocyphellaria kalbii D.J.Galloway, is described from Brazilian collections, and typification and notes on P. aurora (De Not.) Vainio are presented

Studies on the lichen genus Sticta (Schreber) Ach. : 5., Australian species

Twenty five species of Sticta occur in Australia. These are: Sticta baileyi, S. brevipes, S. camarae, S. caperata, S. cyphellulata, S. diversa, S. duplolimbata, S. filix, S. flavocyphellata, S. fuliginosa, S. howei, S. hypopsiloides, S. latifrons, S. limbata, S. marginifera, S. myrioclada, S. pedunculata, S. rutilans, S. sayeri, S. stipitata, S. sublimbata, S. subtomentella, S. variabilis and S. weigelii. A key and descriptions of each taxon are given together with details of biogeography, distribution, ecology and nomenclature. Sticta baileyi, S. flavocyphellata and S. howei are newly described, and Sticta myrioloba (Müll.Arg.) D.J.Galloway comb. & stat. nov., is proposed

Rigidity of outermost MOTS - the initial data version

In [5], a rigidity result was obtained for outermost marginally outer trapped surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This allowed one to treat the "borderline case" in the author's work with R. Schoen concerning the topology of higher dimensional black holes [8]. The proof of this rigidity result involved bending the initial data manifold in the vicinity of the MOTS within the ambient spacetime. In this note we show how to circumvent this step, and thereby obtain a pure initial data version of this rigidity result and its consequence concerning the topology of black holes.Comment: 8 pages; v2: minor changes; version to appear in GR

Maximum Principles for Null Hypersurfaces and Null Splitting Theorems

A maximum principle for C^0 null hypersurfaces is obtained and used to derive a splitting theorem for spacetimes which contain null lines. As a consequence of this null splitting theorem, it is proved that an asymptotically simple vacuum (Ricci flat) spacetime which contains a null line is isometric to Minkowski space.Comment: 26 pages, latex2

Historical development of noise exposure metrics

Some of the historical events that led to the introduction of night penalties are reported with emphasis on what happens with different kinds of day/night operations when night pentalties are employed. These effects are considered in terms of the difference between a nighttime weighting cumulative measure of noise exposure verses simply not using any night weighting at all, in decibles

dS/CFT and spacetime topology

Motivated by recent proposals for a de Sitter version of the AdS/CFT correspondence, we give some topological restrictions on spacetimes of de Sitter type, i.e., spacetimes with $\Lambda>0$, which admit a regular past and/or future conformal boundary. For example we show that if $M^{n+1}$, $n \ge 2$, is a globally hyperbolic spacetime obeying suitable energy conditions, which is of de Sitter type, with a conformal boundary to both the past and future, then if one of these boundaries is compact, it must have finite fundamental group and its conformal class must contain a metric of positive scalar curvature. Our results are closely related to theorems of Witten and Yau hep-th/9910245 pertaining to the Euclidean formulation of the AdS/CFT correspondence.Comment: 16 pages, Latex2e, v2: reference corrected, v3: reference added, material added to the introductio

Some uniqueness results for dynamical horizons

We first show that the intrinsic, geometrical structure of a dynamical horizon is unique. A number of physically interesting constraints are then established on the location of trapped and marginally trapped surfaces in the vicinity of any dynamical horizon. These restrictions are used to prove several uniqueness theorems for dynamical horizons. Ramifications of some of these results to numerical simulations of black hole spacetimes are discussed. Finally several expectations on the interplay between isometries and dynamical horizons are shown to be borne out.Comment: 26 pages, 4 figures, v4: references updated, minor corrections, to appear in Advances in Theoretical and Mathematical Physic