Entropy of gravitating systems: scaling laws versus radial profiles

Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which it is no longer an extensive quantity (it does not scale with system's size). To accomplish this, the methods introduced by Oppenheim [1] to characterize non-extensivity are used, suitably generalized to the case of gravitating systems subject to an external pressure. In particular when, far from the system's Schwarzschild limit, both area scaling for conventional entropy and inverse radius law for the temperature set in (i.e. the same properties of the corresponding black hole thermodynamical quantities), the entropy profile is found to behave like 1/r, being r the area radius inside the system. In such circumstances thus entropy heavily resides in internal layers, in opposition to what happens when area scaling is gained while approaching the Schwarzschild mass, in which case conventional entropy lies at the surface of the system. The information content of these systems, even if it globally scales like the area, is then stored in the whole volume, instead of packed on the boundary.Comment: 16 pages, 11 figures. v2: addition of some references; the stability of equilibrium configurations is readdresse

Fractal Holography: a geometric re-interpretation of cosmological large scale structure

The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit representation of information content, and also the value itself is a geometric signature of area. It is proposed that the fractal distribution of galaxies may thus be interpreted as a signature of holography (``fractal holography''), providing more support for current theories of holographic cosmologies. Implications for entropy bounds are addressed. In particular, because of spatial scale invariance in the matter distribution, it is shown that violations of the spherical entropy bound can be removed. This holographic condition instead becomes a rigid constraint on the nature of the matter density and distribution in the Universe. Inclusion of a dark matter distribution is also discussed, based on theoretical considerations of possible universal CDM density profiles.Comment: 13 pp, LaTeX. Revised version; to appear in JCA

Heavy Mineral Variability And Provenance Of The Virginia Inner Shelf And Lower Chesapeake Bay

The mineral composition of the 3- to 4-phi (0.125 to 0.063 mm) size fraction of 49 surficial grab samples,located north and south of the entrance to Chesapeake Bay and of 38 surficial samples, located in the bay mouth, was determined during this study. Although up to 17 minerals were identified, principal components analysis indicated that seven minerals accounted for 96 percent of the composition variance in the bay samples. By using Q-mode factor analysis, three mineral composition end-members (factors) were selected from the sample data and provided an adequate description of the spatial variation in heavy-mineral composition. The end members suggest possible mineral sources.https://scholarworks.wm.edu/vimsbooks/1105/thumbnail.jp

A Procedure for Assessing Heavy Mineral Resources Potential

Supplies of placer heavy minerals, such as ilmenite, rutile, zircon, and monazite, are anticipated to be in short supply by early in the next century. The depletion of conventional onshore deposits coupled with the declaration of the Exclusive Economic Zone in 1983 have provided the impetus to assess the resource potential of heavy-mineral concentrations in U.S. Continental Shelf sediments as future sources for these mineral commodities. Mineralogically imprecise assessments of placer resources result from analyses of concentrates derived from small volume samples because of the particle-sparsity effect. The overall low grade of heavy minerals in Atlantic Continental Shelf sediments require the analysis of mineral concentrates from large volumes of bulk sample. A set of procedures to extract and analyze heavy minerals from large-volume samples is presented.https://scholarworks.wm.edu/vimsbooks/1103/thumbnail.jp

Heavy Mineral Concentrations In Sediments Of The Virginia Inner Continental Shelf

The Virginia Division of Mineral Resources and the Virginia Institute of Marine Science investigated the occurrence of heavy minerals in the offshore sediments of Virginia. We began the project because earlier reconnaissance studies reported high heavy-mineral concentrations from several samples collected off the Eastern Shore of Virginia. Our work confirms the previously reported mineral values and locates additional high concentrations up to 20 nautical miles offshore. Furthermore, we show that potentially economic mineral values are not restricted no surficial sediments, but also are found in the upper 15 to 20 feet of inner continental shelf sediments. Several core samples indicate that potential economic values of heavy minerals are clustered offshore of Hog Island, Smith Island, Virginia Beach, and False Cape. These areas are likely targets for resource assessment studies of heavy minerals and construction or beach nourishment sand. The high heavy-mineral concentrations suggest that further investigations are warranted.https://scholarworks.wm.edu/vimsbooks/1104/thumbnail.jp

Hologrphy and holographic dark energy model

The holographic principle is used to discuss the holographic dark energy model. We find that the Bekenstein-Hawking entropy bound is far from saturation under certain conditions. A more general constraint on the parameter of the holographic dark energy model is also derived.Comment: no figures, use revtex, v2: use iop style, some typos corrected and references updated, will appear in CQ

Leptogenesis from Pseudo-Scalar Driven Inflation

We examine recent claims for a considerable amount of leptogenesis, in some inflationary scenarios, through the gravitational anomaly in the lepton number current. We find that when the short distances contributions are properly included the amount of lepton number generated is actually much smaller.Comment: JHEP style, 11 pages. Corrected typ

Vacuum Bubble in an Inhomogeneous Cosmology

We study the propagation of bubbles of new vacuum in a radially inhomogeneous Lemaitre-Tolman-Bondi background that includes a cosmological constant. This exemplifies the classical evolution of a tunneling bubble through a metastable state with curvature inhomogeneities, and will be relevant in the context of the Landscape. We demand that the matter profile in the LTB background satisfy the weak energy condition. For sample profiles that satisfy this restriction, we find that the evolution of the bubble (in terms of the physically relevant coordinates intrinsic to the shell) is largely unaffected by the prsence of local inhomogeneities. Our setup should also be a useful toy model for capturing the effects of ambient inhomogeneities on an inflating region.Comment: 31 pages, 21(!) figures, v2: minor changes, figures re-sized (might require zoom on some systems), references adde

Finite Number of States, de Sitter Space and Quantum Groups at Roots of Unity

This paper explores the use of a deformation by a root of unity as a tool to build models with a finite number of states for applications to quantum gravity. The initial motivation for this work was cosmological breaking of supersymmetry. We explain why the project was unsuccessful. What is left are some observations on supersymmetry for q-bosons, an analogy between black holes in de Sitter and properties of quantum groups, and an observation on a noncommutative quantum mechanics model with two degrees of freedom, depending on one parameter. When this parameter is positive, the spectrum has a finite number of states; when it is negative or zero, the spectrum has an infinite number of states. This exhibits a desirable feature of quantum physics in de Sitter space, albeit in a very simple, non-gravitational context.Comment: 25 pages, 5 figure

A finite cutoff on the string worldsheet?

D-brane backgrounds are specified in closed string theories by holes with appropriate mixed Dirichlet and Neumann boundary conditions on the string worldsheet. As presently stated, the prescription defining D-brane backgrounds is such that the Einstein equation is not equivalent to the condition for scale invariance on the string worldsheet. A modified D-brane prescription is found, that leads to the desired equivalence, while preserving all known D-brane lore. A possible interpretation is that the worldsheet cutoff is finite. Possible connections to recent work of Maldacena and Strominger, and Gopakumar and Vafa are suggested.Comment: 7 pages, RevTex; v2: typos corrected, superstring calculation included, discussion expanded - to be published in Phys.Rev.