Polar foliations and isoparametric maps

A singular Riemannian foliation $F$ on a complete Riemannian manifold $M$ is called a polar foliation if, for each regular point $p$, there is an immersed submanifold $\Sigma$, called section, that passes through $p$ and that meets all the leaves and always perpendicularly. A typical example of a polar foliation is the partition of $M$ into the orbits of a polar action, i.e., an isometric action with sections. In this work we prove that the leaves of $F$ coincide with the level sets of a smooth map $H: M\to \Sigma$ if $M$ is simply connected. In particular, we have that the orbits of a polar action on a simply connected space are level sets of an isoparametric map. This result extends previous results due to the author and Gorodski, Heintze, Liu and Olmos, Carter and West, and Terng.Comment: 9 pages; The final publication is available at springerlink.com http://www.springerlink.com/content/c72g4q5350g513n1

Singular riemannian foliations with sections, transnormal maps and basic forms

A singular riemannian foliation F on a complete riemannian manifold M is said to admit sections if each regular point of M is contained in a complete totally geodesic immersed submanifold (a section) that meets every leaf of F orthogonally and whose dimension is the codimension of the regular leaves of F. We prove that the algebra of basic forms of M relative to F is isomorphic to the algebra of those differential forms on a section that are invariant under the generalized Weyl pseudogroup of this section. This extends a result of Michor for polar actions. It follows from this result that the algebra of basic function is finitely generated if the sections are compact. We also prove that the leaves of F coincide with the level sets of a transnormal map (generalization of isoparametric map) if M is simply connected, the sections are flat and the leaves of F are compact. This result extends previous results due to Carter and West, Terng, and Heintze, Liu and Olmos.Comment: Preprint IME-USP; The final publication is available at springerlink.com http://www.springerlink.com/content/q48682633730t831

Classical Boundary-value Problem in Riemannian Quantum Gravity and Taub-Bolt-anti-de Sitter Geometries

For an $SU(2)\times U(1)$-invariant $S^3$ boundary the classical Dirichlet problem of Riemannian quantum gravity is studied for positive-definite regular solutions of the Einstein equations with a negative cosmological constant within biaxial Bianchi-IX metrics containing bolts, i.e., within the family of Taub-Bolt-anti-de Sitter (Taub-Bolt-AdS) metrics. Such metrics are obtained from the two-parameter Taub-NUT-anti-de Sitter family. The condition of regularity requires them to have only one free parameter ($L$) and constrains $L$ to take values within a narrow range; the other parameter is determined as a double-valued function of $L$ and hence there is a bifurcation within the family. We found that {\it{any}} axially symmetric $S^3$-boundary can be filled in with at least one solution coming from each of these two branches despite the severe limit on the permissible values of $L$. The number of infilling solutions can be one, three or five and they appear or disappear catastrophically in pairs as the values of the two radii of $S^3$ are varied. The solutions occur simultaneously in both branches and hence the total number of independent infillings is two, six or ten. We further showed that when the two radii are of the same order and large the number of solutions is two. In the isotropic limit this holds for small radii as well. These results are to be contrasted with the one-parameter self-dual Taub-NUT-AdS infilling solutions of the same boundary-value problem studied previously.Comment: Minor changes and references added: Version in the Journa

Current-carrying cosmic string loops 3D simulation: towards a reduction of the vorton excess problem

The dynamical evolution of superconducting cosmic string loops with specific equations of state describing timelike and spacelike currents is studied numerically. This analysis extends previous work in two directions: first it shows results coming from a fully three dimensional simulation (as opposed to the two dimensional case already studied), and it now includes fermionic as well as bosonic currents. We confirm that in the case of bosonic currents, shocks are formed in the magnetic regime and kinks in the electric regime. For a loop endowed with a fermionic current with zero-mode carriers, we show that only kinks form along the string worldsheet, therefore making these loops slightly more stable against charge carrier radiation, the likely outcome of either shocks or kinks. All these combined effects tend to reduce the number density of stable loops and contribute to ease the vorton excess problem. As a bonus, these effects also may provide new ways of producing high energy cosmic rays.Comment: 11 pages, RevTeX 4 format, 8 figures, submitted to PR

Specific Surface

Surface area largely determines many physical and chemical properties of materials. Physical adsorption of molecules, heat loss or gain resulting from that adsorption, swelling and shrinking, and many other physical and chemical processes are closely related to surface area. Surface or exposed area is also closely related to and often the controlling factor in many biological processes. Soils vary widely in their reactive surface because of differences in mineralogical and organic composition and in their particle-size distribution. Water retention and movement, cation exchange capacity, and pesticide adsorption are closely related to the specific surface (defined as the surface area per unit mass of soil). Specific surface is usually expressed in square meters per gram (m2/g)

Classical Boundary-value Problem in Riemannian Quantum Gravity and Self-dual Taub-NUT-(anti)de Sitter Geometries

The classical boundary-value problem of the Einstein field equations is studied with an arbitrary cosmological constant, in the case of a compact ($S^{3}$) boundary given a biaxial Bianchi-IX positive-definite three-metric, specified by two radii $(a,b).$ For the simplest, four-ball, topology of the manifold with this boundary, the regular classical solutions are found within the family of Taub-NUT-(anti)de Sitter metrics with self-dual Weyl curvature. For arbitrary choice of positive radii $(a,b),$ we find that there are three solutions for the infilling geometry of this type. We obtain exact solutions for them and for their Euclidean actions. The case of negative cosmological constant is investigated further. For reasonable squashing of the three-sphere, all three infilling solutions have real-valued actions which possess a ``cusp catastrophe'' structure with a non-self-intersecting ``catastrophe manifold'' implying that the dominant contribution comes from the unique real positive-definite solution on the ball. The positive-definite solution exists even for larger deformations of the three-sphere, as long as a certain inequality between $a$ and $b$ holds. The action of this solution is proportional to $-a^{3}$ for large $a (\sim b)$ and hence larger radii are favoured. The same boundary-value problem with more complicated interior topology containing a ``bolt'' is investigated in a forthcoming paper.Comment: 20 pages, 11 figures; Latex; Revised version with important new results on real infilling solutions and corrections. To appear in Nuclear Physics B, issue 648 (1,2), pp. 397-41

Supersymmetric AdS5 black holes

The first examples of supersymmetric, asymptotically AdS5, black hole solutions are presented. They form a 1-parameter family of solutions of minimal five-dimensional gauged supergravity. Their angular momentum can never vanish. The solutions are obtained by a systematic analysis of supersymmetric solutions with Killing horizons. Other new examples of such solutions are obtained. These include solutions for which the horizon is a homogeneous Nil or SL(2,R) manifold.Comment: 31 pages. v2: References and calculation of holographic stress tensor added. v3: Solutions preserve 2 supersymmetries. Our original claim that they preserve 4 supersymmetries was based on Ref. [30], which contains a mistake (the general timelike solution preserves 2, not 4, supersymmetries). Nothing else affecte

Mass, Angular Momentum and Thermodynamics in Four-Dimensional Kerr-AdS Black Holes

In this paper, the connection between the Lorentz-covariant counterterms that regularize the four-dimensional AdS gravity action and topological invariants is explored. It is shown that demanding the spacetime to have a negative constant curvature in the asymptotic region permits the explicit construction of such series of boundary terms. The orthonormal frame is adapted to appropriately describe the boundary geometry and, as a result, the boundary term can be expressed as a functional of the boundary metric, extrinsic curvature and intrinsic curvature. This choice also allows to write down the background-independent Noether charges associated to asymptotic symmetries in standard tensorial formalism. The absence of the Gibbons-Hawking term is a consequence of an action principle based on a boundary condition different than Dirichlet on the metric. This argument makes plausible the idea of regarding this approach as an alternative regularization scheme for AdS gravity in all even dimensions, different than the standard counterterms prescription. As an illustration of the finiteness of the charges and the Euclidean action in this framework, the conserved quantities and black hole entropy for four-dimensional Kerr-AdS are computed.Comment: 15 pages,no figures,few references added,JHEP forma

Study of 9Be+12C elastic scattering at energies near the Coulomb barrier

In this work, angular distribution measurements for the elastic channel were performed for the 9Be+12C reaction at the energies ELab=13.0, 14.5, 17.3, 19.0 and 21.0 MeV, near the Coulomb barrier. The data have been analyzed in the framework of the double folding S\~ao Paulo potential. The experimental elastic scattering angular distributions were well described by the optical potential at forward angles for all measured energies. However, for the three highest energies, an enhancement was observed for intermediate and backward angles. This can be explained by the elastic transfer mechanism. Keywords: 9Be+12C, Elastic Scattering, S\~aoo Paulo Potential