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.
Highlights
(b) with the principles of quantum theory
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
Summary
Where the integrand in the first line is the CGHS Lagrangian [4] describing interaction of the metric gμν and dilaton φ with massless scalar f ; the dimensionful parameter λ sets the energy scale of the model. The GibbonsHawking term with extrinsic curvature ensures consistency of the gravitational action. Without this term the boundary conditions following from eq (2.1) would be incompatible with the Dirichlet condition φ = φ0, see [51] and cf appendix A.1. The only natural generalization of our model would include an arbitrary constant in the last term of eq (2.1). This parameter needs to be fine-tuned in order to retain Minkowski solution (see below). The action (2.1) describing interaction of the boundary with the gravitational sector of the CGHS model is fixed [33]. Note that the Minkowski vacuum (2.3) is a solution in our model due to exact matching between the bulk and boundary terms with λ in the action (2.1)
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