Black Hole Entropy in Two Dimensions

TL;DR

The paper uses Wald's Noether-charge framework to derive black hole entropy for a solvable two-dimensional dilaton gravity model with semiclassical corrections. By reformulating the nonlocal Polyakov action with an auxiliary field, it obtains a total horizon entropy S_RST that remains nondecreasing on both global and apparent horizons for eternal black holes, and shows how proper vacuum choices extend the second law to evaporating black holes. In conformal gauge, the entropy reduces to a local horizon expression, linking entropy to the horizon geometry and the dilaton/auxiliary fields. The results illuminate how nonlocal quantum corrections contribute to black hole entropy and suggest that Wald-type entropy definitions can extend to higher dimensions, underpinning intrinsic and generalized second-law statements. The work also connects entropy to entanglement contributions and discusses boundary effects and potential long-range corrections.

Abstract

Black hole entropy is studied for an exactly solvable model of two-dimensional gravity\cite{rst1}, using recently developed Noether charge techniques\cite{wald1}. This latter approach is extended to accomodate the non-local form of the semiclassical effective action. In the two-dimensional model, the final black hole entropy can be expressed as a local quantity evaluated on the horizon. This entropy is shown to satisfy an increase theorem on either the global or apparent horizon of a two-dimensional black hole.