9,583 research outputs found
Compactifications of Deformed Conifolds, Branes and the Geometry of Qubits
We present three families of exact, cohomogeneity-one Einstein metrics in
dimensions, which are generalizations of the Stenzel construction of
Ricci-flat metrics to those with a positive cosmological constant. The first
family of solutions are Fubini-Study metrics on the complex projective spaces
, written in a Stenzel form, whose principal orbits are the Stiefel
manifolds divided by . The second family are
also Einstein-K\"ahler metrics, now on the Grassmannian manifolds
, whose principal orbits are the
Stiefel manifolds (with no factoring in this case). The
third family are Einstein metrics on the product manifolds , and are K\"ahler only for . Some of these metrics are believed
to play a role in studies of consistent string theory compactifications and in
the context of the AdS/CFT correspondence. We also elaborate on the geometric
approach to quantum mechanics based on the K\"ahler geometry of Fubini-Study
metrics on , and we apply the formalism to study the quantum
entanglement of qubits.Comment: 31 page
Bulk/Boundary Thermodynamic Equivalence, and the Bekenstein and Cosmic-Censorship Bounds for Rotating Charged AdS Black Holes
We show that one may pass from bulk to boundary thermodynamic quantities for
rotating AdS black holes in arbitrary dimensions so that if the bulk quantities
satisfy the first law of thermodynamics then so do the boundary CFT quantities.
This corrects recent claims that boundary CFT quantities satisfying the first
law may only be obtained using bulk quantities measured with respect to a
certain frame rotating at infinity, and which therefore do not satisfy the
first law. We show that the bulk black hole thermodynamic variables, or
equivalently therefore the boundary CFT variables, do not always satisfy a
Cardy-Verlinde type formula, but they do always satisfy an AdS-Bekenstein
bound. The universal validity of the Bekenstein bound is a consequence of the
more fundamental cosmic censorship bound, which we find to hold in all cases
examined. We also find that at fixed entropy, the temperature of a rotating
black hole is bounded above by that of a non-rotating black hole, in four and
five dimensions, but not in six or more dimensions. We find evidence for
universal upper bounds for the area of cosmological event horizons and
black-hole horizons in rotating black-hole spacetimes with a positive
cosmological constant.Comment: Latex, 42 page
A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge
In this paper, we study the recently discovered family of higher dimensional
Kerr-AdS black holes with an extra NUT-like parameter. We show that the inverse
metric is additively separable after multiplication by a simple function. This
allows us to separate the Hamilton-Jacobi equation, showing that geodesic
motion is integrable on this background. The separation of the Hamilton-Jacobi
equation is intimately linked to the existence of an irreducible Killing
tensor, which provides an extra constant of motion. We also demonstrate that
the Klein-Gordon equation for this background is separable.Comment: LaTeX, 14 pages. v2: Typo corrected and equation added. v3: Reference
added, introduction expanded, published versio
Sea surface velocities from visible and infrared multispectral atmospheric mapping sensor imagery
High resolution (100 m), sequential Multispectral Atmospheric Mapping Sensor (MAMS) images were used in a study to calculate advective surface velocities using the Maximum Cross Correlation (MCC) technique. Radiance and brightness temperature gradient magnitude images were formed from visible (0.48 microns) and infrared (11.12 microns) image pairs, respectively, of Chandeleur Sound, which is a shallow body of water northeast of the Mississippi delta, at 145546 GMT and 170701 GMT on 30 Mar. 1989. The gradient magnitude images enhanced the surface water feature boundaries, and a lower cutoff on the gradient magnitudes calculated allowed the undesirable sunglare and backscatter gradients in the visible images, and the water vapor absorption gradients in the infrared images, to be reduced in strength. Requiring high (greater than 0.4) maximum cross correlation coefficients and spatial coherence of the vector field aided in the selection of an optimal template size of 10 x 10 pixels (first image) and search limit of 20 pixels (second image) to use in the MCC technique. Use of these optimum input parameters to the MCC algorithm, and high correlation and spatial coherence filtering of the resulting velocity field from the MCC calculation yielded a clustered velocity distribution over the visible and infrared gradient images. The velocity field calculated from the visible gradient image pair agreed well with a subjective analysis of the motion, but the velocity field from the infrared gradient image pair did not. This was attributed to the changing shapes of the gradient features, their nonuniqueness, and large displacements relative to the mean distance between them. These problems implied a lower repeat time for the imagery was needed in order to improve the velocity field derived from gradient imagery. Suggestions are given for optimizing the repeat time of sequential imagery when using the MCC method for motion studies. Applying the MCC method to the infrared brightness temperature imagery yielded a velocity field which did agree with the subjective analysis of the motion and that derived from the visible gradient imagery. Differences between the visible and infrared derived velocities were 14.9 cm/s in speed and 56.7 degrees in direction. Both of these velocity fields also agreed well with the motion expected from considerations of the ocean bottom topography and wind and tidal forcing in the study area during the 2.175 hour time interval
Almost Special Holonomy in Type IIA&M Theory
We consider spaces M_7 and M_8 of G_2 holonomy and Spin(7) holonomy in seven
and eight dimensions, with a U(1) isometry. For metrics where the length of the
associated circle is everywhere finite and non-zero, one can perform a
Kaluza-Klein reduction of supersymmetric M-theory solutions (Minkowksi)_4\times
M_7 or (Minkowksi)_3\times M_8, to give supersymmetric solutions
(Minkowksi)_4\times Y_6 or (Minkowksi)_3\times Y_7 in type IIA string theory
with a non-singular dilaton. We study the associated six-dimensional and
seven-dimensional spaces Y_6 and Y_7 perturbatively in the regime where the
string coupling is weak but still non-zero, for which the metrics remain
Ricci-flat but that they no longer have special holonomy, at the linearised
level. In fact they have ``almost special holonomy,'' which for the case of Y_6
means almost Kahler, together with a further condition. For Y_7 we are led to
introduce the notion of an ``almost G_2 manifold,'' for which the associative
3-form is closed but not co-closed. We obtain explicit classes of non-singular
metrics of almost special holonomy, associated with the near Gromov-Hausdorff
limits of families of complete non-singular G_2 and Spin(7) metrics.Comment: Latex, 26 page
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