# Elliptic function solutions in Jackiw-Teitelboim dilaton gravity

## TL;DR

This paper introduces a new family of solutions in Jackiw-Teitelboim gravity, utilizing elliptic functions to describe black hole metrics and dilaton fields, advancing understanding of 2D quantum gravity models.

## Contribution

It provides explicit elliptic function solutions for the dilaton and metric in Jackiw-Teitelboim gravity, including black hole configurations, which were not previously characterized in this form.

## Key findings

- Derived explicit elliptic function solutions for the dilaton field.
- Constructed a black hole metric with constant Ricci scalar.
- Computed Killing vectors for the new solutions.

## Abstract

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.