Irreversible Time Flow in a Two-Dimensional Dilaton Black Hole with Matter

TL;DR

This paper demonstrates that in a two-dimensional dilaton gravity model with matter, the system exhibits an irreversible flow towards flat space with zero cosmological constant, driven by matter back reaction and described via renormalization-group flow.

Contribution

It provides an exact solution showing the irreversible time evolution towards a stable flat space in a two-dimensional dilaton gravity model with matter.

Findings

System flows towards flat space with zero cosmological constant.

Non-zero cosmological constant leads to non-equilibrium dynamics.

Flow is derived from the renormalization-group flow of the Zamolodchikov function.

Abstract

We show that an exact solution of two-dimensional dilaton gravity with matter discovered previously exhibits an irreversible temporal flow towards flat space with a vanishing cosmological constant. This time flow is induced by the back reaction of matter on the space-time geometry. We demonstrate that the system is not in equilibrium if the cosmological constant is non-zero, whereas the solution with zero cosmological constant is stable. The flow of the system towards this stable end-point is derived from the renormalization-group flow of the Zamolodchikov function. This behaviour is interpreted in terms of non-critical Liouville string, with the Liouville field identified as the target time.