# Exact solutions and critical chaos in dilaton gravity with a boundary

## TL;DR

This paper presents an exactly solvable (1+1)-dimensional dilaton gravity model with a boundary, revealing classical solutions, soliton dynamics, and critical chaos phenomena relevant to black hole physics.

## Contribution

It introduces a new exactly solvable dilaton gravity model with a boundary, analyzes its classical solutions, soliton reflections, and links to integrable systems, highlighting critical chaos near black hole formation.

## Key findings

- Model is exactly solvable at the classical level.
- Soliton solutions describe matter reflection and black hole formation.
- Critical regime exhibits dynamical instabilities akin to chaos.

## Abstract

We consider (1+1)-dimensional dilaton gravity with a reflecting dynamical boundary. The boundary cuts off the region of strong coupling and makes our model causally similar to the spherically-symmetric sector of multidimensional gravity. We demonstrate that this model is exactly solvable at the classical level and possesses an on-shell SL(2,R) symmetry. After introducing general classical solution of the model, we study a large subset of soliton solutions. The latter describe reflection of matter waves off the boundary at low energies and formation of black holes at energies above critical. They can be related to the eigenstates of the auxiliary integrable system, the Gaudin spin chain. We argue that despite being exactly solvable, the model in the critical regime, i.e. at the verge of black hole formation, displays dynamical instabilities specific to chaotic systems. We believe that this model will be useful for studying black holes and gravitational scattering.