Some aspects of the three dimensional gravity theories with temporal scalar field

TL;DR

This paper introduces a new 3D gravity theory with a temporal scalar field, derived from a reduction of a timelike extra dimension, aiming to resolve contradictions in existing models and align with 4D physics.

Contribution

It proposes a consistent 3D gravity model with a temporal scalar field, extending Jordan-Brans-Dicke theory to lower dimensions with a novel approach to space and time.

Findings

The new theory is free of contradictions.

It aligns with conventional 4D physics.

It offers a lower-dimensional analog of scalar-tensor theories.

Abstract

The present paper proposes a new explanation for the 3-dimensional Einstein general theory of relativity which is free of contradictions and consistent with usual 4-dimensional physics. We discuss the property of the new gravity theory with temporal scalar field arise in lower-dimensional theories as the reduction of timelike extra dimension. These ideas we continued by using the 3-dimensional analog of Jordan, Brans-Dicke theory with temporal scalar field where space and time are treated in different ways.