Floyd L. Williams

Using a resonance nonlinear Schrödinger equation as a bridge, we explore a direct connection of cold plasma physics to two-dimensional black holes. Namely, we compute and diagonalize a metric attached to the propagation of magnetoacoustic waves in a cold plasma subject to a transverse magnetic field, and we construct an explicit change of variables by which this metric is transformed exactly to a Jackiw-Teitelboim black hole metric.

We present a new family of solutions for the Jackiw-Teitelboim model of two-dimensional gravity with a negative cosmological constant. Here, a metric of constant Ricci scalar curvature is constructed, and explicit linearly independent solutions of the corresponding dilaton field equations are determined. The metric is transformed to a black hole metric, and the dilaton solutions are expressed in terms of Jacobi elliptic functions. Using these solutions we compute, for example, Killing vectors for the metric.

We find a Selberg zeta function expression of certain one-loop spin partition functions on three-dimensional thermal anti-de Sitter space. Of particular interest is the partition function of higher spin fermionic particles. We also set up, in the presence of spin, a Patterson-type formula involving the logarithmic derivative of zeta.

A new, seemingly useful presentation of zeta functions on complex tori is derived by using contour integration. It is shown to agree with the one obtained by using the Chowla-Selberg series formula, for which an alternative proof is thereby given. In addition, a new proof of the functional determinant on the torus results, which does not use the Kronecker first limit formula nor the functional equation of the non-holomorphic Eisenstein series. As a bonus, several identities involving the Dedekind eta function are obtained as well.

This paper continues earlier work where an explicit parametrized solution of a particular nonlinear ordinary differential equation was obtained in terms of the Weierstrass elliptic phi-function, sigma, function, and zeta function-work which therefore generalized that of G.Lemaitre. Further study of this solution and applications to cosmology are presented.

We obtain in terms of the Weierstrass elliptic $\wp-$function, sigma function, and zeta function an explicit parametrized solution of a particular nonlinear, ordinary differential equation. This equation includes, in special cases, equations that occur in the study of both homogeneous and inhomogeneous cosmological models, and also in the dynamic Bose-Einstein condensates - cosmology correspondence, for example.