Boundary Dynamics in Dilaton Gravity

TL;DR

This paper investigates the boundary dynamics in dilaton gravity with matter, revealing conditions for stability and the onset of runaway behavior leading to singularities and horizons.

Contribution

It rederives boundary conditions emphasizing reparametrization invariance and analyzes semiclassical boundary behavior with matter flux in dilaton gravity.

Findings

Stable boundary for matter energy below a critical threshold

Runaway boundary behavior with singularities at high energy flux

Critical energy levels determine boundary stability and spacetime structure

Abstract

We study the dynamics of the boundary dilaton gravity coupled to N massles scalars. We rederive the boundary conditions of [1] and [3] in a way which makes the requirement of reparametrization invariance and role of conformal anomaly explicit. We then study the semiclassical behaviour of the boundary in the N = 24 theory in the presence of an incoming matter wave with a constant energy flux spreaded over a finite interval. There is a critical value of the matter energy density below which the boundary is stable and all the matter is reflected back. For energy densities greater than this critical value there is a similar behaviour for small values of total energy thrown in. However, when the total energy exceeds another critical value, the boundary exibits a runaway behaviour and the spacetime devolopes singularities and horizons.