8,031 research outputs found
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
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 , and the ellipticity maximum at around . The result has been compared with that of Chandrasekhar and
Miller which was obtained in the full 4-spacetime formalism
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
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
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
Selection of the lamprey VLRC antigen receptor repertoire
The alternative adaptive immune system of jawless vertebrates is based on different isotypes of variable lymphocyte receptors (VLRs) that are composed of leucine-rich repeats (LRRs) and expressed by distinct B- and T-like lymphocyte lineages. VLRB is expressed by B-like cells, whereas VLRA and VLRC are expressed by two T-like lineages that develop in the thymoid, a thymus-like structure in lamprey larvae. In each case, stepwise combinatorial insertions of different types of short donor LRR cassettes into incomplete germ-line genes are required to generate functional VLR gene assemblies. It is unknown, however, whether the diverse repertoires of VLRs that are expressed by peripheral blood lymphocytes are shaped by selection after their assembly. Here, we identify signatures of selection in the peripheral repertoire of VLRC antigen receptors that are clonally expressed by one of the T-like cell types in lampreys. Selection strongly favors VLRC molecules containing four internal variable leucine-rich repeat (LRRV) modules, although VLRC assemblies encoding five internal modules are initially equally frequent. In addition to the length selection, VLRC molecules in VLRC+ peripheral lymphocytes exhibit a distinct pattern of high entropy sites in the N-terminal LRR1 module, which is inserted next to the germ-line–encoded LRRNT module. This is evident in comparisons to VLRC gene assemblies found in the thymoid and to VLRC gene assemblies found in some VLRA+ cells. Our findings are the first indication to our knowledge that selection operates on a VLR repertoire and provide a framework to establish the mechanism by which this selection occurs during development of the VLRC+ lymphocyte lineage
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