A New 2D Formulation of Modified General Relativity

Abstract

It is well known that the Einstein–Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. The authors present a new, intrinsically two-dimensional, approach to this problem based on the Einstein action. This yields a well defined variational approach which results in new field equations that break diffeomorphism invariance. This proposed approach does not require the introduction of additional scalar fields, nor the use of conformal transformations. However, how including conformal counter terms leads to equivalent results is shown. In doing so, an explanation for why previous approaches worked can be provided. Solutions to the field equations are briefly discussed.