New 2D dilaton gravity for nonsingular black holes

Abstract

We construct a two-dimensional action that is an extension of spherically symmetric Einstein–Lanczos–Lovelock (ELL) gravity. The action contains arbitrary functions of the areal radius and the norm squared of its gradient, but the field equations are second order and obey Birkhoff’s theorem. In complete analogy with spherically symmetric ELL gravity, the field equations admit the generalized Misner–Sharp mass as the first integral that determines the form of the vacuum solution. The arbitrary functions in the action allow for vacuum solutions that describe a larger class of interesting nonsingular black hole spacetimes than previously available.