Coarse-grained entropy and causal holographic information in AdS/CFT

We propose bulk duals for certain coarse-grained entropies of boundary regions. The `one-point entropy' is defined in the conformal field theory by maximizing the entropy in a domain of dependence while fixing the one-point functions. We conjecture that this is dual to the area of the edge of the region causally accessible to the domain of dependence (i.e. the `causal holographic information' of Hubeny and Rangamani). The `future one-point entropy' is defined by generalizing this conjecture to future domains of dependence and their corresponding bulk regions. We show that the future one-point entropy obeys a nontrivial second law. If our conjecture is true, this answers the question "What is the field theory dual of Hawking's area theorem?"Comment: 43 pages, 9 figures. v3: minor changes suggested by referee v2: added a few additional reference

Spherical alterations of handles: embedding the manifold plus construction

A key tool in our earlier work on ends of manifolds high-dimensional manifolds was an ability to embed cobordisms provided by the Quillen Plus Construction into those ends. Here we develop a `spherical modification' trick which provides a constructive approach to obtaining such embeddings. More importantly, this approach allows for more general embedding results. In this paper we develop generalizations of the plus construction and show how the corresponding cobordisms can be embedded in manifolds satisfying appropriate fundamental group properties. Results obtained here play an important role in our ongoing study of noncompact manifolds.Comment: This final version will appear in Algebraic & Geometric Topology. Small corrections, including a fix to the statement of Theorem 5.3. 22 pages, 4 figure

The 30/20 GHz communications system functional requirements

The characteristics of 30/20 GHz usage in satellite systems to be used in support of projected communication requirements of the 1990's are defined. A requirements analysis which develops projected market demand for satellite services by general and specialized carriers and an analysis of the impact of propagation and system constraints on 30/20 GHz operation are included. A set of technical performance characteristics for the 30/20 GHz systems which can serve the resulting market demand and the experimental program necessary to verify technical and operational aspects of the proposed systems is also discussed

A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices

The generalized second law is proven for semiclassical quantum fields falling across a causal horizon, minimally coupled to general relativity. The proof is much more general than previous proofs in that it permits the quantum fields to be rapidly changing with time, and shows that entropy increases when comparing any slice of the horizon to any earlier slice. The proof requires the existence of an algebra of observables restricted to the horizon, satisfying certain axioms (Determinism, Ultralocality, Local Lorentz Invariance, and Stability). These axioms are explicitly verified in the case of free fields of various spins, as well as 1+1 conformal field theories. The validity of the axioms for other interacting theories is discussed.Comment: 44 pages, 1 fig. v3: clarified Sec. 2; signs, factors/notation corrected in Eq. 75-80, 105-107; reflects published version. v4: clearer axioms in Sec. 2.3, fixed compensating factor of 2 errors in Eq. 54,74 etc., and other errors. Results unaffected. v5: fixed typos. v6: replaced faulty 1+1 CFT argument, added note on recent progres

The Redshift Distribution of FIRST Radio Sources at 1 mJy

We present spectra for a sample of radio sources from the FIRST survey, and use them to define the form of the redshift distribution of radio sources at mJy levels.We targeted 365 sources and obtained 46 redshifts (13 per cent of the sample). We find that our sample is complete in redshift measurement to R $\sim 18.6$, corresponding to $z\sim 0.2$. Early-type galaxies represent the largest subset (45 per cent) of the sample and have redshifts 0.15\la z \la 0.5 ; late-type galaxies make up 15 per cent of the sample and have redshifts 0.05\la z \la 0.2; starbursting galaxies are a small fraction ($\sim 6$ per cent), and are very nearby (z\la 0.05). Some 9 per cent of the population have Seyfert1/quasar-type spectra, all at z\ga 0.8, and there are 4 per cent are Seyfert2 type galaxies at intermediate redshifts ($z\sim 0.2$). Using our measurements and data from the Phoenix survey, we obtain an estimate for $N(z)$ at $S_{1.4 \rm {GHz}}\ge 1$ mJy and compare this with model predictions. At variance with previous conclusions, we find that the population of starbursting objects makes up \la 5 per cent of the radio population at S $\sim 1$ mJy.Comment: 20 pages, sumbitted to MNRA

Planning assistance for the 30/20 GHz program, volume 3

The three basic experiment categories and consolidated experiments proposed by members of the Carrier Working Group are defined by category and by carrier. The three experiment categories are: (1) Possible Service (PS); (2) Possible Service and Technology (PSAT); and (3) Possible Technology (PT). Under Task 9 Western Union provided review, recommendations and critique of the NASA generated Statement of Work (SOW) defining the technical requirements governing design, launch and operation of the 30/20 GHz experimental systems

Planning assistance for the 30/20 GHz program, volume 1

Functional requirements for the 30/20 GHz communication system, planning assistance for the 30/20 GHz program, and a review of specified conceptual designs and recommendations are provided

Manifolds with non-stable fundamental groups at infinity, II

In this paper we continue an earlier study of ends non-compact manifolds. The over-arching goal is to investigate and obtain generalizations of Siebenmann's famous collaring theorem that may be applied to manifolds having non-stable fundamental group systems at infinity. In this paper we show that, for manifolds with compact boundary, the condition of inward tameness has substatial implications for the algebraic topology at infinity. In particular, every inward tame manifold with compact boundary has stable homology (in all dimensions) and semistable fundamental group at each of its ends. In contrast, we also construct examples of this sort which fail to have perfectly semistable fundamental group at infinity. In doing so, we exhibit the first known examples of open manifolds that are inward tame and have vanishing Wall finiteness obstruction at infinity, but are not pseudo-collarable.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper7.abs.htm

[OII] Emission, Eigenvector 1 and Orientation in Radio-quiet Quasars

We present supportive evidence that the Boroson and Green eigenvector 1 is not driven by source orientation. Until recently it was generally accepted that eigenvector 1 does not depend on orientation as it strongly correlates with [OIII]5007 emission, thought to be an isotropic property. However, recent studies of radio-loud AGN have questioned the isotropy of [OIII] emission and concluded that [OII]3727 emission is isotropic. In this paper we investigate the relation between eigenvector 1 and [OII] emission in radio-quiet BQS (Bright Quasar Survey) quasars, and readdress the issue of orientation as the driver of eigenvector 1. We find significant correlations between eigenvector 1 and orientation independent [OII] emission, which implies that orientation does not drive eigenvector 1. The luminosities and equivalent widths of [OIII] and [OII] correlate with one another, and the range in luminosities and equivalent widths is similar. This suggests that the radio-quiet BQS quasars are largely free of orientation dependent dust effects and ionization dependent effects in the narrow-line region. We also conclude that neither the [OIII] emission nor the [OII]/[OIII] ratio are dependent on orientation in our radio-quiet BQS quasar sample, contrary to recent results found for radio-loud quasars.Comment: 24 pages, 12 figures, accepted for publication in Ap