Lower-dimensional Regge-Teitelboim gravity

TL;DR

This paper explores a modified gravity theory called Regge-Teitelboim, showing that in 2+1 dimensions, vacuum solutions can have non-flat geometries without matter, unlike in general relativity.

Contribution

It provides specific solutions in Regge-Teitelboim gravity demonstrating non-flat vacuum spacetimes in 2+1 dimensions, highlighting differences from GR.

Findings

Vacuum solutions are non-flat in 2+1D Regge-Teitelboim gravity.

Gravity can exist without matter or cosmological constant in this framework.

The solutions differ fundamentally from those in standard GR.

Abstract

We study modified gravity theory known as Regge-Teitelboim approach, in which the gravity is represented by dynamics of a surface isometrically embedded in a flat bulk. We obtain some particular solutions of Regge-Teitelboim equations corresponding to a central symmetric vacuum 2+1-dimensional spacetime. In contrast with GR, this vacuum spacetime is not flat, so it is possible for the gravitational field to exist even without matter or cosmological constant.