Statistical Entropy of BTZ Black Hole in Higher Curvature Gravity

For the BTZ black hole in the Einstein gravity, a statistical entropy has been calculated to be equal to the Bekenstein-Hawking entropy. In this paper, the statistical entropy of the BTZ black hole in the higher curvature gravity is calculated and shown to be equal to the one derived by using the Noether charge method. This suggests that the equivalence of the geometrical and statistical entropies of the black hole is retained in the general diffeomorphism invariant theories of gravity. A relation between the cosmic censorship conjecture and the unitarity of the conformal field theory on the boundary of AdS is also discussed.Comment: 9 pages, no figure, submitted to Physics Letters

Linear maps on k^I, and homomorphic images of infinite direct product algebras

Let k be an infinite field, I an infinite set, V a k-vector-space, and g:k^I\to V a k-linear map. It is shown that if dim_k(V) is not too large (under various hypotheses on card(k) and card(I), if it is finite, respectively countable, respectively < card(k)), then ker(g) must contain elements (u_i)_{i\in I} with all but finitely many components u_i nonzero. These results are used to prove that any homomorphism from a direct product \prod_I A_i of not-necessarily-associative algebras A_i onto an algebra B, where dim_k(B) is not too large (in the same senses) must factor through the projection of \prod_I A_i onto the product of finitely many of the A_i, modulo a map into the subalgebra \{b\in B | bB=Bb=\{0\}\}\subseteq B. Detailed consequences are noted in the case where the A_i are Lie algebras.Comment: 14 pages. Lemma 6 has been strengthened, with resulting strengthening of other results. Some typos etc. have been correcte

Mill’s Moral Standard

A book chapter (about 7,000 words, plus references) on the interpretation of Mill’s criterion of right and wrong, with particular attention to act utilitarianism, rule utilitarianism, and sanction utilitarianism. Along the way, major topics include Mill’s thoughts on liberalism, supererogation, the connection between wrongness and punishment, and breaking rules when doing so will produce more happiness than complying with them will

A Simulation Study on Multicomponent Lipid Bilayer

Simulation of a multicomponent lipid bilayer having a fixed percentage of cholesterol is done to study phase transition leading to domain formation. The concept of random lattice has been used in simulation to account for the coupling between the internal and translational degrees of freedom of lipid molecules. Considering a canonical ensemble, dissimilar lipid molecules are allowed to exchange their positions in the lattice subject to standard metropolis algorithm. The steps involved in the process effectively takes into account for the movement of sphingolipids and cholesterol molecules helping formation of cholesterol rich domains of saturated lipids as found in natural membranes

Catastrophe and Environmental Restoration: Analyzing the Frames and Sources of Oyster Restoration News Stories

Restoration of oyster habitats is a critical solution to halt the decline of one of the world’s most threatened resources. News coverage about environmental topics, like oyster restoration, is important to local communities that are directly impacted. However, little research has assessed how restoration topics are framed by journalists, nor how environmental disasters may affect framing of news stories for the public. This study employed a longitudinal framing analysis, using the quantity of coverage and social responsibility theories, to examine how coverage of the restoration of oyster ecosystems shifted before, during, and after the BP Deepwater Horizon oil spill. The frames and sources of 763 newspaper articles were assessed, including 18 local newspapers from five U.S. Gulf Coast states and three high-circulation national newspapers. Logistic regression analyses revealed that the occurrence of an environmental catastrophe shifted media focus from environmental frames before the spill to community and economic frames during and after the spill. Stories were dominated by environmental frames (49%) and primarily relied on quotes from resource managers (50%) over all other groups. Local resource users were quoted less than 5% of the time in local articles. Findings provide a foundation for natural resource managers and communication specialists to understand how information about natural resources changes during disasters and reveals the perspectives that are most and least commonly used to frame and define stories about coastal resources and important gaps in coverage

Orbits, masses, and evolution of main belt triple (87) Sylvia

Sylvia is a triple asteroid system located in the main belt. We report new adaptive optics observations of this system that extend the baseline of existing astrometric observations to a decade. We present the first fully dynamical 3-body model for this system by fitting to all available astrometric measurements. This model simultaneously fits for individual masses, orbits, and primary oblateness. We find that Sylvia is composed of a dominant central mass surrounded by two satellites orbiting at 706.5 +/- 2.5 km and 1357 +/- 4.0 km, i.e., about 5 and nearly 10 primary radii. We derive individual masses of 1.484 -0.014/+0.016 x 10^19 kg for the primary (corresponding to a density of 1.29 +/- 0.39 g cm^-3), 7.33 -2.3/+4.7 x 10^14 kg for the inner satellite, and 9.32 -8.3/+20.7 x 10^14 kg for the outer satellite. The oblateness of the primary induces substantial precession and the J_2 value can be constrained to the range of 0.0985-0.1. The orbits of the satellites are relatively circular with eccentricities less than 0.04. The spin axis of the primary body and the orbital poles of both satellites are all aligned within about two degrees of each other, indicating a nearly coplanar configuration and suggestive of satellite formation in or near the equatorial plane of the primary. We also investigate the past orbital evolution of the system by simulating the effects of a recent passage through 3:1 mean-motion eccentricity-type resonances. In some scenarios this allow us to place constraints on interior structure and past eccentricities.Comment: 14 pages, 8 figures, accepted to A

Anatomic Fat Depots and Coronary Plaque Among Human Immunodeficiency Virus-Infected and Uninfected Men in the Multicenter AIDS Cohort Study.

Methods.  In a cross-sectional substudy of the Multicenter AIDS Cohort Study, noncontrast cardiac computed tomography (CT) scanning for coronary artery calcium (CAC) scoring was performed on all men, and, for men with normal renal function, coronary CT angiography (CTA) was performed. Associations between fat depots (visceral adipose tissue [VAT], abdominal subcutaneous adipose tissue [aSAT], and thigh subcutaneous adipose tissue [tSAT]) with coronary plaque presence and extent were assessed with logistic and linear regression adjusted for age, race, cardiovascular disease (CVD) risk factors, body mass index (BMI), and human immunodeficiency virus (HIV) parameters. Results.  Among HIV-infected men (n = 597) but not HIV-uninfected men (n = 343), having greater VAT was positively associated with noncalcified plaque presence (odds ratio [OR] = 1.04, P &lt; .05), with a significant interaction (P &lt; .05) by HIV serostatus. Human immunodeficiency virus-infected men had lower median aSAT and tSAT and greater median VAT among men with BMI &lt;25 and 25-29.9 kg/m(2). Among HIV-infected men, VAT was positively associated with presence of coronary plaque on CTA after adjustment for CVD risk factors (OR = 1.04, P &lt; .05), but not after additional adjustment for BMI. There was an inverse association between aSAT and extent of total plaque among HIV-infected men, but not among HIV-uninfected men. Lower tSAT was associated with greater CAC and total plaque score extent regardless of HIV serostatus. Conclusions.  The presence of greater amounts of VAT and lower SAT may contribute to increased risk for coronary artery disease among HIV-infected persons

Noncommutative knot theory

The classical abelian invariants of a knot are the Alexander module, which is the first homology group of the the unique infinite cyclic covering space of S^3-K, considered as a module over the (commutative) Laurent polynomial ring, and the Blanchfield linking pairing defined on this module. From the perspective of the knot group, G, these invariants reflect the structure of G^(1)/G^(2) as a module over G/G^(1) (here G^(n) is the n-th term of the derived series of G). Hence any phenomenon associated to G^(2) is invisible to abelian invariants. This paper begins the systematic study of invariants associated to solvable covering spaces of knot exteriors, in particular the study of what we call the n-th higher-order Alexander module, G^(n+1)/G^(n+2), considered as a Z[G/G^(n+1)$-module. We show that these modules share almost all of the properties of the classical Alexander module. They are torsion modules with higher-order Alexander polynomials whose degrees give lower bounds for the knot genus. The modules have presentation matrices derived either from a group presentation or from a Seifert surface. They admit higher-order linking forms exhibiting self-duality. There are applications to estimating knot genus and to detecting fibered, prime and alternating knots. There are also surprising applications to detecting symplectic structures on 4-manifolds. These modules are similar to but different from those considered by the author, Kent Orr and Peter Teichner and are special cases of the modules considered subsequently by Shelly Harvey for arbitrary 3-manifolds.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-19.abs.htm

Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy

We consider a general, classical theory of gravity with arbitrary matter fields in $n$ dimensions, arising from a diffeomorphism invariant Lagrangian, \bL. We first show that \bL always can be written in a ``manifestly covariant" form. We then show that the symplectic potential current $(n-1)$-form, $\th$, and the symplectic current $(n-1)$-form, \om, for the theory always can be globally defined in a covariant manner. Associated with any infinitesimal diffeomorphism is a Noether current $(n-1)$-form, \bJ, and corresponding Noether charge $(n-2)$-form, \bQ. We derive a general ``decomposition formula" for \bQ. Using this formula for the Noether charge, we prove that the first law of black hole mechanics holds for arbitrary perturbations of a stationary black hole. (For higher derivative theories, previous arguments had established this law only for stationary perturbations.) Finally, we propose a local, geometrical prescription for the entropy, $S_{dyn}$, of a dynamical black hole. This prescription agrees with the Noether charge formula for stationary black holes and their perturbations, and is independent of all ambiguities associated with the choices of \bL, $\th$, and \bQ. However, the issue of whether this dynamical entropy in general obeys a ``second law" of black hole mechanics remains open. In an appendix, we apply some of our results to theories with a nondynamical metric and also briefly develop the theory of stress-energy pseudotensors.Comment: 30 pages, LaTe

Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem

The Euclidean black hole has topology $\Re^2 \times {\cal S}^{d-2}$. It is shown that -in Einstein's theory- the deficit angle of a cusp at any point in $\Re^2$ and the area of the ${\cal S}^{d-2}$ are canonical conjugates. The black hole entropy emerges as the Euler class of a small disk centered at the horizon multiplied by the area of the ${\cal S}^{d-2}$ there.These results are obtained through dimensional continuation of the Gauss-Bonnet theorem. The extension to the most general action yielding second order field equations for the metric in any spacetime dimension is given.Comment: 7 pages, RevTe