562 research outputs found
Nonexistence of conformally flat slices of the Kerr spacetime
Initial data for black hole collisions are commonly generated using the
Bowen-York approach based on conformally flat 3-geometries. The standard
(constant Boyer-Lindquist time) spatial slices of the Kerr spacetime are not
conformally flat, so that use of the Bowen-York approach is limited in dealing
with rotating holes. We investigate here whether there exist foliations of the
Kerr spacetime that are conformally flat. We limit our considerations to
foliations that are axisymmetric and that smoothly reduce in the Schwarzschild
limit to slices of constant Schwarzschild time. With these restrictions, we
show that no conformally flat slices can exist.Comment: 5 LaTeX pages; no figures; to be submitted to Phys. Rev.
Symmetries and Motions in Manifolds
In these lectures the relations between symmetries, Lie algebras, Killing
vectors and Noether's theorem are reviewed. A generalisation of the basic ideas
to include velocity-dependend co-ordinate transformations naturally leads to
the concept of Killing tensors. Via their Poisson brackets these tensors
generate an {\em a priori} infinite-dimensional Lie algebra. The nature of such
infinite algebras is clarified using the example of flat space-time. Next the
formalism is extended to spinning space, which in addition to the standard real
co-ordinates is parametrized also by Grassmann-valued vector variables. The
equations for extremal trajectories (`geodesics') of these spaces describe the
pseudo-classical mechanics of a Dirac fermion. We apply the formalism to solve
for the motion of a pseudo-classical electron in Schwarzschild space-time.Comment: 19 pages. Lectures at 28th Winter School of Theoretical Physics,
Karpacz (Poland, 1992) by J.W. van Holte
Thermally assisted magnetization reversal in the presence of a spin-transfer torque
We propose a generalized stochastic Landau-Lifshitz equation and its
corresponding Fokker-Planck equation for the magnetization dynamics in the
presence of spin transfer torques. Since the spin transfer torque can pump a
magnetic energy into the magnetic system, the equilibrium temperature of the
magnetic system is ill-defined. We introduce an effective temperature based on
a stationary solution of the Fokker-Planck equation. In the limit of high
energy barriers, the law of thermal agitation is derived. We find that the
N\'{e}el-Brown relaxation formula remains valid as long as we replace the
temperature by an effective one that is linearly dependent of the spin torque.
We carry out the numerical integration of the stochastic Landau-Lifshitz
equation to support our theory. Our results agree with existing experimental
data.Comment: 5 figure
On static spherically symmetric solutions of the vacuum Brans-Dicke theory
It is shown that among the four classes of the static spherically symmetric
solution of the vacuum Brans-Dicke theory of gravity only two are really
independent. Further by matching exterior and interior (due to physically
reasonable spherically symmetric matter source) scalar fields it is found that
only Brans class I solution with certain restriction on solution parameters may
represent exterior metric for a nonsingular massive object. The physical
viability of the black hole nature of the solution is investigated. It is
concluded that no physical black hole solution different from the Schwarzschild
black hole is available in the Brans-Dicke theory.Comment: 15 pages, To be published in Gen. Rel. and Grav, typos in references
correcte
Decay rate and renormalized frequency shift of a quantum wire Wannier exciton in a planar microcavity
The superradiant decay rate and frequency shift of a Wannier exciton in a
one-dimensional quantum wire are studied. It is shown that the dark mode
exciton can be examined experimentally when the quantum wire is embedded in a
planar microcavity. It is also found that the decay rate is greatly enhanced as
the cavity length is equal to the multiple wavelength of the emitted
photon. Similar to its decay rate counterpart, the frequency shift also shows
discontinuities at resonant modes.Comment: 12 pages, 2 figures. To appear in P. R. B. September 200
Tiling groupoids and Bratteli diagrams
Let T be an aperiodic and repetitive tiling of R^d with finite local
complexity. Let O be its tiling space with canonical transversal X. The tiling
equivalence relation R_X is the set of pairs of tilings in X which are
translates of each others, with a certain (etale) topology. In this paper R_X
is reconstructed as a generalized "tail equivalence" on a Bratteli diagram,
with its standard AF-relation as a subequivalence relation.
Using a generalization of the Anderson-Putnam complex, O is identified with
the inverse limit of a sequence of finite CW-complexes. A Bratteli diagram B is
built from this sequence, and its set of infinite paths dB is homeomorphic to
X. The diagram B is endowed with a horizontal structure: additional edges that
encode the adjacencies of patches in T. This allows to define an etale
equivalence relation R_B on dB which is homeomorphic to R_X, and contains the
AF-relation of "tail equivalence".Comment: 34 pages, 4 figure
Charge Transport Through Open, Driven Two-Level Systems with Dissipation
We derive a Floquet-like formalism to calculate the stationary average
current through an AC driven double quantum dot in presence of dissipation. The
method allows us to take into account arbitrary coupling strengths both of a
time-dependent field and a bosonic environment. We numerical evaluate a
truncation scheme and compare with analytical, perturbative results such as the
Tien-Gordon formula.Comment: 14 pages, 6 figures. To appear in Phys. Rev.
Pulsar Timing and its Application for Navigation and Gravitational Wave Detection
Pulsars are natural cosmic clocks. On long timescales they rival the
precision of terrestrial atomic clocks. Using a technique called pulsar timing,
the exact measurement of pulse arrival times allows a number of applications,
ranging from testing theories of gravity to detecting gravitational waves. Also
an external reference system suitable for autonomous space navigation can be
defined by pulsars, using them as natural navigation beacons, not unlike the
use of GPS satellites for navigation on Earth. By comparing pulse arrival times
measured on-board a spacecraft with predicted pulse arrivals at a reference
location (e.g. the solar system barycenter), the spacecraft position can be
determined autonomously and with high accuracy everywhere in the solar system
and beyond. We describe the unique properties of pulsars that suggest that such
a navigation system will certainly have its application in future astronautics.
We also describe the on-going experiments to use the clock-like nature of
pulsars to "construct" a galactic-sized gravitational wave detector for
low-frequency (f_GW ~1E-9 - 1E-7 Hz) gravitational waves. We present the
current status and provide an outlook for the future.Comment: 30 pages, 9 figures. To appear in Vol 63: High Performance Clocks,
Springer Space Science Review
Domain Wall Spacetimes: Instability of Cosmological Event and Cauchy Horizons
The stability of cosmological event and Cauchy horizons of spacetimes
associated with plane symmetric domain walls are studied. It is found that both
horizons are not stable against perturbations of null fluids and massless
scalar fields; they are turned into curvature singularities. These
singularities are light-like and strong in the sense that both the tidal forces
and distortions acting on test particles become unbounded when theses
singularities are approached.Comment: Latex, 3 figures not included in the text but available upon reques
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