Involution products in Coxeter groups

For W a Coxeter group, let = {w ∈ W | w = xy where x, y ∈ W and x 2 = 1 = y 2}. It is well known that if W is finite then W = . Suppose that w ∈ . Then the minimum value of ℓ(x) + ℓ(y) – ℓ(w), where x, y ∈ W with w = xy and x 2 = 1 = y 2, is called the excess of w (ℓ is the length function of W). The main result established here is that w is always W-conjugate to an element with excess equal to zero

Thermodynamics and Stability of Higher Dimensional Rotating (Kerr) AdS Black Holes

We study the thermodynamic and gravitational stability of Kerr anti-de Sitter black holes in five and higher dimensions. We show, in the case of equal rotation parameters, $a_i=a$, that the Kerr-AdS background metrics become stable, both thermodynamically and gravitationally, when the rotation parameters $a_i$ take values comparable to the AdS curvature radius. In turn, a Kerr-AdS black hole can be in thermal equilibrium with the thermal radiation around it only when the rotation parameters become not significantly smaller than the AdS curvature radius. We also find with equal rotation parameters that a Kerr-AdS black hole is thermodynamically favored against the existence of a thermal AdS space, while the opposite behavior is observed in the case of a single non-zero rotation parameter. The five dimensional case is however different and also special in that there is no high temperature thermal AdS phase regardless of the choice of rotation parameters. We also verify that at fixed entropy, the temperature of a rotating black hole is always bounded above by that of a non-rotating black hole, in four and five dimensions, but not in six and more dimensions (especially, when the entropy approaches zero or the minimum of entropy does not correspond to the minimum of temperature). In this last context, the six dimensional case is marginal.Comment: 15 pages, 23 eps figures, RevTex

Recurrence relation for the 6j-symbol of su_q(2) as a symmetric eigenvalue problem

A well known recurrence relation for the 6j-symbol of the quantum group su_q(2) is realized as a tridiagonal, symmetric eigenvalue problem. This formulation can be used to implement an efficient numerical evaluation algorithm, taking advantage of existing specialized numerical packages. For convenience, all formulas relevant for such an implementation are collected in the appendix. This realization is a byproduct of an alternative proof of the recurrence relation, which generalizes a classical (q=1) result of Schulten and Gordon and uses the diagrammatic spin network formalism of Temperley-Lieb recoupling theory to simplify intermediate calculations.Comment: v3: 13 pages, ws-ijgmmp; minor corrections, slight update to presentation; close to published versio

Transonic Elastic Model for Wiggly Goto-Nambu String

The hitherto controversial proposition that a ``wiggly" Goto-Nambu cosmic string can be effectively represented by an elastic string model of exactly transonic type (with energy density $U$ inversely proportional to its tension $T$) is shown to have a firm mathematical basis.Comment: 8 pages, plain TeX, no figure

Skylab-EREP investigations of wetlands ecology

There are no author-identified significant results in this report

Skylab - EREP investigations of wetlands ecology

There are no author-identified significant results in this report

Staticity Theorem for Higher Dimensional Generalized Einstein-Maxwell System

We derive formulas for variations of mass, angular momentum and canonical energy in Einstein (n-2)-gauge form field theory by means of the ADM formalism. Considering the initial data for the manifold with an interior boundary which has the topology of (n-2)-sphere we obtained the generalized first law of black hole thermodynamics. Supposing that a black hole evevt horizon comprisesw a bifurcation Killing horizon with a bifurcate surface we find that the solution is static in the exterior world, when the Killing timelike vector field is normal to the horizon and has vanishing electric or magnetic fields on static slices.Comment: 10 pages, REVTEX, to published in Phys.Rev. D1