Exact solutions and critical chaos in dilaton gravity with a boundary

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.

Comments on 2D dilaton gravity system with a hyperbolic dilaton potential

“…Finally, it is interesting to consider a similar deformation of the asymptotically flat case [50] by following [51]. It is also nice to study how the holographic relation should be modified in the case with a reflecting dynamical boundary by generalizing [52]. The integrability techniques discussed there would still be useful even after performing Yang-Baxter deformations.…”

Asymptotic fragility, near AdS2 holography and T T ¯ $$ T\overline{T} $$

“…It appears that the required deformation is likely to introduce a direct coupling between the JT dilaton and matter fields. Indeed, the most straightforward way to introduce black holes into the JT gravity is to perform the dilaton dependent Weyl rescaling of the JT metric (see, e.g., [51] for a recent study of the resulting black holes).…”

Failure of mean-field approximation in weakly coupled dilaton gravity

“…The gravitational coupling parameter e φ < e φ 0 , it makes the model weakly coupled. Note that black holes in the model (1) have masses larger than M cr = 2λe −2φ 0 [4]. As a matter content we add the massless scalar field f ,…”