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

National identification, endorsement of acculturation ideologies and prejudice: The impact of perceived threat of immigration

This paper examines how the perceived threat of immigration affects the links between national identification, endorsement of assimilation or multiculturalism, and prejudice against immigrants in France. One hundred thirty-five French undergraduates completed a questionnaire measuring these factors. Path analysis showed that higher national identification increased perception of immigrants as a threat, which in turn predicted increased endorsement of assimilation for immigrants. The link between endorsement of assimilation and prejudice was not significant. In contrast, lower national identification decreased perception of immigrants as a threat and, in turn, increased endorsement of multiculturalism and reduced levels of prejudice. An alternative model specifying perception of threat as an outcome of preferences for multiculturalism or assimilation did not fit the data well. Results suggest that perceived threat from immigration is the key factor that guides the preferences of the majority group for acculturation ideologies and, through these preferences, shapes intergroup attitudes

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

Ferromagnetic feature from Mn near room temperature in the fine particles of GdMn2Ge2 and TbMn2Ge2

The magnetization behaviors of GdMn2Ge2 and TbMn2Ge2 in the bulk and in the fine particles obtained by high-energy ball-milling are compared. Pronounced modificayions in the spontaneous, remnent and high-field magnetization in the fine particle form, attributable to Mn are observed. The results indicate that the antiferromagnetism of Mn sub-lattice known for the bulk form in the range 100-300 K gets weakened in favor of ferromagnetism in the fine particles. On the basis of this observation, we infer that there are other factors like size (and possibly defects) also play a role to decide the exact nature of magnetic ordering of Mn in this ternary family of compounds, contrasting the traditionally held view that the basal plane Mn-Mn distance is the crucial controlling parameter.Comment: Communicated for publication on 2nd January 201

On the Noether charge form of the first law of black hole mechanics

The first law of black hole mechanics was derived by Wald in a general covariant theory of gravity for stationary variations around a stationary black hole. It is formulated in terms of Noether charges, and has many advantages. In this paper several issues are discussed to strengthen the validity of the Noether charge form of the first law. In particular, a gauge condition used in the derivation is justified. After that, we justify the generalization to non-stationary variations done by Iyer-Wald.Comment: Latex, 16 pages, arguments on gauge conditions and near-stationary entropy are added, accepted for publication in Physical Review

Stability of geometrically frustrated magnetic state of Ca3CoRhO6 to applications of positive and negative pressure

The influence of negative chemical pressure induced by gradual replacement of Ca by Sr as well as of external pressure (up to 10 kbar) on the magnetism of Ca3CoRhO6 has been investigated by magnetization studies. It is found that the solid solution, Ca(3-x)Sr(x)CoRhO6, exists at least till about x= 1.0 without any change in the crystal structure. Apart from insensitivity of the spin-chain feature to volume expansion, the characteristic features of geometrical frustration interestingly appear at the same temperatures for all compositions, in sharp contrast to the response to Y substitution for Ca (reported previously). Interestingly, huge frequency dependence of ac susceptibility known for the parent compound persists for all compositions. We do not find a change in the properties under external pressure. The stability of the magnetic anomalies of this compound to the volume change (about 4%) is puzzling

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

A stochastic-Lagrangian particle system for the Navier-Stokes equations

This paper is based on a formulation of the Navier-Stokes equations developed by P. Constantin and the first author (\texttt{arxiv:math.PR/0511067}, to appear), where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. In this paper, we take $N$ copies of the above process (each based on independent Wiener processes), and replace the expected value with $\frac{1}{N}$ times the sum over these $N$ copies. (We remark that our formulation requires one to keep track of $N$ stochastic flows of diffeomorphisms, and not just the motion of $N$ particles.) We prove that in two dimensions, this system of interacting diffeomorphisms has (time) global solutions with initial data in the space \holderspace{1}{\alpha} which consists of differentiable functions whose first derivative is $\alpha$ H\"older continuous (see Section \ref{sGexist} for the precise definition). Further, we show that as $N \to \infty$ the system converges to the solution of Navier-Stokes equations on any finite interval $[0,T]$. However for fixed $N$, we prove that this system retains roughly $O(\frac{1}{N})$ times its original energy as $t \to \infty$. Hence the limit $N \to \infty$ and $T\to \infty$ do not commute. For general flows, we only provide a lower bound to this effect. In the special case of shear flows, we compute the behaviour as $t \to \infty$ explicitly.Comment: v3: Typo fixes, and a few stylistic changes. 17 pages, 2 figure

Non-magnetic left-handed material

We develop a new approach to build a material with negative refraction index. In contrast to conventional designs which make use of a resonant behavior to achieve a non-zero magnetic response, our material is intrinsically non-magnetic and relies on an anisotropic dielectric constant to provide a left-handed response in waveguide geometry. We demonstrate that the proposed material can support surface (polariton) waves, and show the connection between polaritons and the enhancement of evanescent fields, also referred to as super-lensing