Asymptotically flat spacetimes in 3D bigravity

We report that a class of three-dimensional bimetric theories contain asymptotically flat solutions. These spacetimes can be cast in a set of asymptotic conditions at null infinity which are preserved under the infinite dimensional BMS group. Moreover, the algebra of the canonical generators exhibits a central extension. The possibility that these solutions describe regular black holes is also discussed.Comment: 6 page

Boundary dynamics of asymptotically flat 3D gravity coupled to higher spin fields

We construct a two-dimensional action principle invariant under a spin-three extension of BMS$_3$ group. Such a theory is obtained through a reduction of Chern-Simons action with a boundary. This procedure is carried out by imposing a set of boundary conditions obtained from asymptotically flat spacetimes in three dimensions. When implementing part of this set, we obtain an analog of chiral WZW model based on a contraction of $sl(3,\mathbb{R}) \times sl(3,\mathbb{R})$. The remaining part of the boundary conditions imposes constraints on the conserved currents of the model, which allows to further reduce the action principle. It is shown that a sector of this latter theory is related to a flat limit of Toda theory.Comment: 16 pages, no figure

Quasi-Exactly Solvable Potentials on the Line and Orthogonal Polynomials

In this paper we show that a quasi-exactly solvable (normalizable or periodic) one-dimensional Hamiltonian satisfying very mild conditions defines a family of weakly orthogonal polynomials which obey a three-term recursion relation. In particular, we prove that (normalizable) exactly-solvable one-dimensional systems are characterized by the fact that their associated polynomials satisfy a two-term recursion relation. We study the properties of the family of weakly orthogonal polynomials defined by an arbitrary one-dimensional quasi-exactly solvable Hamiltonian, showing in particular that its associated Stieltjes measure is supported on a finite set. From this we deduce that the corresponding moment problem is determined, and that the $k$-th moment grows like the $k$-th power of a constant as $k$ tends to infinity. We also show that the moments satisfy a constant coefficient linear difference equation, and that this property actually characterizes weakly orthogonal polynomial systems.Comment: 22 pages, plain TeX. Please typeset only the file orth.te

Supertranslations and Superrotations at the Black Hole Horizon

We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.Comment: 6 pages, references added, published versio

Trade and Morality: Preserving Public Morals Without Sacrificing the Global Economy

The World Trade Organization (WTO) exists for the purpose of promoting and facilitating trade amongst its member nations. When those member nations acceded to the WTO\u27s agreements, however, they acknowledged that sometimes trade barriers are useful tools in protecting themselves from certain evils. This Note addresses one of those useful tools--the public morals exception--which allows a member nation to maintain trade barriers with respect to certain goods or services. Since the WTO agreements have been in effect, the public morals has lacked two critical things.: a definition and boundaries. This Note will attempt to define the public morals exception in a way that preserves the spirit of the WTO agreements. Furthermore, this Note will propose a test that will allow future WTO panels to decide whether a country\u27s law or regulation, justified under the public morals exception, can legitimately fall within the ambit of the WTO agreements