Extrinsic Curvature Embedding Diagrams

Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an extrinsic curvature embedding diagram, when used together with the usual kind of intrinsic curvature embedding diagram, carries the information of how a surface is {\it embedded} in the higher dimensional curved space. Simple examples are given to illustrate the idea.Comment: 22 pages, 4 figure

Thick atomic layers of maximum density as bulk terminations of quasicrystals

The clean surfaces of quasicrystals, orthogonal to the directions of the main symmetry axes, have a terrace-like appearance. We extend the Bravais' rule for crystals to quasicrystals, allowing that instead of a single atomic plane a layer of atomic planes may form a bulk termination.Comment: 4 pages, 4 figure

Global embedding of D-dimensional black holes with a cosmological constant in Minkowskian spacetimes: Matching between Hawking temperature and Unruh temperature

We study the matching between the Hawking temperature of a large class of static D-dimensional black holes and the Unruh temperature of the corresponding higher dimensional Rindler spacetime. In order to accomplish this task we find the global embedding of the D-dimensional black holes into a higher dimensional Minkowskian spacetime, called the global embedding Minkowskian spacetime procedure (GEMS procedure). These global embedding transformations are important on their own, since they provide a powerful tool that simplifies the study of black hole physics by working instead, but equivalently, in an accelerated Rindler frame in a flat background geometry. We discuss neutral and charged Tangherlini black holes with and without cosmological constant, and in the negative cosmological constant case, we consider the three allowed topologies for the horizons (spherical, cylindrical/toroidal and hyperbolic).Comment: 7 pages; ReVTeX

Stability of six-dimensional hyperstring braneworlds

We study a six-dimensional braneworld model with infinite warped extra dimensions in the case where the four-dimensional brane is described by a topological vortex of a U(1) symmetry-breaking Abelian Higgs model in presence of a negative cosmological constant. A detailed analysis of the microscopic parameters leading to a finite volume space-time in the extra dimensions is numerically performed. As previously shown, we find that a fine-tuning is required to avoid any kind of singularity on the brane. We then discuss the stability of the vortex by investigating the scalar part of the gauge-invariant perturbations around this fine-tuned configuration. It is found that the hyperstring forming Higgs and gauge fields, as well as the background metric warp factors, cannot be perturbed at all, whereas transverse modes can be considered stable. The warped space-time structure that is imposed around the vortex thus appears severely constrained and cannot generically support nonempty universe models. The genericness of our conclusions is discussed; this will shed some light on the possibility of describing our space-time as a general six-dimensional warped braneworld.Comment: 26 pages, 13 figures, uses RevTex, fine-tuning and stability analysis discussed in greater details. Matches published versio

Analytic Coulomb matrix elements in the lowest Landau level in disk geometry

Using Darling's theorem on products of generalized hypergeometric series an analytic expression is obtained for the Coulomb matrix elements in the lowest Landau level in the representation of angular momentum. The result is important in the studies of Fractional Quantum Hall effect (FQHE) in disk geometry. Matrix elements are expressed as simple finite sums of positive terms, eliminating the need to approximate these quantities with slowly-convergent series. As a by-product, an analytic representation for certain integals of products of Laguerre polynomials is obtained.Comment: Accepted to J. Math. Phys.; 3 pages revtex, no figure

Thermodynamics of Quantum Hall Ferromagnets

The two-dimensional interacting electron gas at Landau level filling factor $\nu =1$ and temperature $T=0$ is a strong ferromagnet; all spins are completely aligned by arbitrarily weak Zeeman coupling. We report on a theoretical study of its thermodynamic properties using a many-body perturbation theory approach and concentrating on the recently measured temperature dependence of the spin magnetization. We discuss the interplay of collective and single-particle aspects of the physics and the opportunities for progress in our understanding of itinerant electron ferromagnetism presented by quantum Hall ferromagnets.Comment: REVTex, 10 pages, 3 uuencoded, compressed and tarred PostScript figures appende

Gaussian coordinate systems for the Kerr metric

We present the whole class of Gaussian coordinate systems for the Kerr metric. This is achieved through the uses of the relationship between Gaussian observers and the relativistic Hamilton-Jacobi equation. We analyze the completeness of this coordinate system. In the appendix we present the equivalent JEK formulation of General Relativity -- the so-called quasi-Maxwellian equations -- which acquires a simpler form in the Gaussian coordinate system. We show how this set of equations can be used to obtain the internal metric of the Schwazschild solution, as a simple example. We suggest that this path can be followed to the search of the internal Kerr metric

Vacuum solutions which cannot be written in diagonal form

A vacuum solution of the Einstein gravitational field equation is given that follows from a general ansatz but fails to follow from it if a certain symmetric matrix is assumed to be in diagonal form from the beginning.Comment: 18 pages, latex, no figures. An Acknowledgement, 4 references, and the section "Note added" are adde

On Applications of Campbell's Embedding Theorem

A little known theorem due to Campbell is employed to establish the local embedding of a wide class of 4-dimensional spacetimes in 5-dimensional Ricci-flat spaces. An embedding for the class of n-dimensional Einstein spaces is also found. The local nature of Campbell's theorem is highlighted by studying the embedding of some lower-dimensional spaces.Comment: 17 pages, standard Latex sourc

Anisotropic domain walls

We find an anisotropic, non-supersymmetric generalization of the extreme supersymmetric domain walls of simple non-dilatonic supergravity theory. As opposed to the isotropic non- and ultra-extreme domain walls, the anisotropic non-extreme wall has the \emph{same} spatial topology as the extreme wall. The solution has naked singularities which vanish in the extreme limit. Since the Hawking temperature on the two sides is different, the generic solution is unstable to Hawking decay.Comment: 11 pages, LaTeX, 3 PostScript figures, uses amstex and epsfi