Centrifugal Force and Ellipticity behaviour of a slowly rotating ultra compact object

Using the optical reference geometry approach, we have derived in the following, a general expression for the ellipticity of a slowly rotating fluid configuration using Newtonian force balance equation in the conformally projected absolute 3-space, in the realm of general relativity. Further with the help of Hartle-Thorne (H-T) metric for a slowly rotating compact object, we have evaluated the centrifugal force acting on a fluid element and also evaluated the ellipticity and found that the centrifugal reversal occurs at around $R/R_s \approx 1.45$, and the ellipticity maximum at around $R/R_s \approx 2.75$. The result has been compared with that of Chandrasekhar and Miller which was obtained in the full 4-spacetime formalism

First law of black hole mechanics in Einstein-Maxwell and Einstein-Yang-Mills theories

The first law of black hole mechanics is derived from the Einstein-Maxwell (EM) Lagrangian by comparing two infinitesimally nearby stationary black holes. With similar arguments, the first law of black hole mechanics in Einstein-Yang-Mills (EYM) theory is also derived.Comment: Modified version, major changes made in the introduction. 14 pages, no figur

Pan-African alkali granites and syenites of Kerala as imprints of taphrogenic magmatism in the South Indian shield

Granite and syenite plutons with alkaline affinities ranging in age from 550 to 750 Ma sporadically puncture the Precambrian granulites of the Kerala region. All the bodies are small (20 to 60 sq km), E-W to NW-SE elongated elliptical intrusives with sharp contacts and lie on or close to major late Proterozoic lineaments. Geochemical plots of A-F-M and An-Ab-Or relations show an apparent alkali enrichment trend on the former, but the plutons define relatively distinct fields on the latter. Most of the plutons are adamellitic to granitic by chemistry. The variations of SiO2 with log sub 10 K2O/MgO (1) brings out the distinct alkaline nature of the plutons. Some of the granites are extremely potassic, like the Peralimala pluton, which shows up to 11.8 percent K2O. On a SiO2-Al2O3-Na2O+K2O (mol percent) plot, the plutons vary from peraluminous to peralkaline, but none are nepheline normative. Low MgO, low to moderate CaO and high Fe2O3/FeO values are other common characteristics. Among trace elements, depletion of Ba, Sr and Rb with high K/Ba and K/Rb values are typical. Overall, the plutons show a trend of decreasing K/Rb ratio with increasing K content. Individual plutons show more clearly defined trends similar to those from granitic masses characterized by plagioclase fractionation

Centrifugal force in Kerr geometry

We have obtained the correct expression for the centrifugal force acting on a particle at the equatorial circumference of a rotating body in the locally non-rotating frame of the Kerr geometry. Using this expression for the equilibrium of an element on the surface of a slowly rotating Maclaurin spheroid, we obtain the expression for the ellipticity (as discussed earlier by Abramowicz and Miller) and determine the radius at which the ellipticity is maximum.Comment: 6 pages, LateX macro

CO2 lidar system for atmospheric studies

A lidar facility using a TEA CO2 laser source is being developed at the ENEA Laboratories for Atmospheric Studies. The different subsystems and the proposed experimental activities are described

A fractional kinetic process describing the intermediate time behaviour of cellular flows

This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that start close enough to cell boundaries is a fractional kinetic process: A Brownian motion time changed by the local time of an independent Brownian motion. Our proof uses the Freidlin-Wentzell framework, and the key step is to establish an analogous averaging principle on shorter time scales. As a consequence of our main theorem, we obtain a homogenization result for the associated advection-diffusion equation. We show that on intermediate time scales the effective equation is a fractional time PDE that arises in modelling anomalous diffusion

Rights of passage: law and the biopolitics of dying

Deleuze and Law: Forensic Futures explores the relation between law and life and the advent of a politics of 'life'. How have recent events focused social, political and cultural attention on the living body and its maintenance and management? The central concept, through which the embodiment of the subject will be examined will be that of 'bio-power'. Articulated by Michel Foucault, but brought to attention more recently in the work of Giorgio Agamben, this concept recognises that the relation between life and law is both historical and necessary: the law must operate on bodies but can only do so by establishing a border between the body of the polity, and the mere life excepted from political concern. The contemporary advent of bio-politics occurs when the polity increasingly and invasively operates on this 'mere' life, and the body or organism – rather than the self – becomes the object of political management. The manner in which the body becomes the focus of contemporary power has led legal theory to explore new questions of the threshold between life and death and has led social theory to question the new extensions of the law and the polity into embodied life. The contributors explore the forensic shift in contemporary social theory and cultural sensibility from a number of perspectives. Description of book from publisher website at: http://www.palgrave.com

Efficient simulations with electronic open boundaries

We present a reformulation of the Hairy Probe method for introducing electronic open boundaries that is appropriate for steady state calculations involving non-orthogonal atomic basis sets. As a check on the correctness of the method we investigate a perfect atomic wire of Cu atoms, and a perfect non-orthogonal chain of H atoms. For both atom chains we find that the conductance has a value of exactly one quantum unit, and that this is rather insensitive to the strength of coupling of the probes to the system, provided values of the coupling are of the same order as the mean inter-level spacing of the system without probes. For the Cu atom chain we find in addition that away from the regions with probes attached, the potential in the wire is uniform, while within them it follows a predicted exponential variation with position. We then apply the method to an initial investigation of the suitability of graphene as a contact material for molecular electronics. We perform calculations on a carbon nanoribbon to determine the correct coupling strength of the probes to the graphene, and obtain a conductance of about two quantum units corresponding to two bands crossing the Fermi surface. We then compute the current through a benzene molecule attached to two graphene contacts and find only a very weak current because of the disruption of the π-conjugation by the covalent bond between the benzene and the graphene. In all cases we find that very strong or weak probe couplings suppress the current

Lagrangian perfect fluids and black hole mechanics

The first law of black hole mechanics (in the form derived by Wald), is expressed in terms of integrals over surfaces, at the horizon and spatial infinity, of a stationary, axisymmetric black hole, in a diffeomorphism invariant Lagrangian theory of gravity. The original statement of the first law given by Bardeen, Carter and Hawking for an Einstein-perfect fluid system contained, in addition, volume integrals of the fluid fields, over a spacelike slice stretching between these two surfaces. When applied to the Einstein-perfect fluid system, however, Wald's methods yield restricted results. The reason is that the fluid fields in the Lagrangian of a gravitating perfect fluid are typically nonstationary. We therefore first derive a first law-like relation for an arbitrary Lagrangian metric theory of gravity coupled to arbitrary Lagrangian matter fields, requiring only that the metric field be stationary. This relation includes a volume integral of matter fields over a spacelike slice between the black hole horizon and spatial infinity, and reduces to the first law originally derived by Bardeen, Carter and Hawking when the theory is general relativity coupled to a perfect fluid. We also consider a specific Lagrangian formulation for an isentropic perfect fluid given by Carter, and directly apply Wald's analysis. The resulting first law contains only surface integrals at the black hole horizon and spatial infinity, but this relation is much more restrictive in its allowed fluid configurations and perturbations than that given by Bardeen, Carter and Hawking. In the Appendix, we use the symplectic structure of the Einstein-perfect fluid system to derive a conserved current for perturbations of this system: this current reduces to one derived ab initio for this system by Chandrasekhar and Ferrari.Comment: 26 pages LaTeX-2