Does a relativistic metric generalization of Newtonian gravity exist in 2+1 dimensions?

TL;DR

This paper demonstrates that a scalar tensor theory of Brans-Dicke type can serve as a relativistic extension of Newtonian gravity in 2+1 dimensions, with solutions matching Newtonian behavior in the weak field limit.

Contribution

It shows that a metric scalar tensor theory provides a consistent relativistic generalization of Newtonian gravity in 2+1 dimensions, contrary to previous claims.

Findings

Scalar tensor theory is metric and geodesic test particles follow space-time geodesics.

Static isotropic solutions can be matched at matter-vacuum interfaces.

Newtonian behavior is recovered in the weak field regime.

Abstract

It is shown that, contrary to previous claims, a scalar tensor theory of Brans-Dicke type provides a relativistic generalization of Newtonian gravity in 2+1 dimensions. The theory is metric and test particles follow the space-time geodesics. The static isotropic solution is studied in vacuum and in regions filled with an incompressible perfect fluid. It is shown that the solutions can be consistently matched at the matter vacuum interface, and that the Newtonian behavior is recovered in the weak field regime.