Black hole entropy is studied for an exactly solvable model of two-dimensional gravity, using recently developed Noether charge techniques. This latter approach is extended to accommodate the nonlocal 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.

• Received 26 May 1994

DOI:https://doi.org/10.1103/PhysRevD.50.6412