A New Formulation of General Relativity - Part III: GR as Scalar Field Theory

TL;DR

This paper proposes a novel formulation of general relativity as a scalar field theory using generating functions, generalized density, and temperature, providing new perspectives on fundamental concepts and outlining open problems for future research.

Contribution

It introduces a scalar field formulation of GR with a generalized Einstein equation and expresses core concepts through generating functions, offering a new theoretical framework.

Findings

Formulation of GR as a scalar field theory

Expression of orientation and isometry via generating functions

Presentation of six open problems for future research

Abstract

The aim of this paper (Part III) is formulating GR as a scalar field theory. The basic structural elements of it are a generating function, a generalized density and a generalized temperature. One of the axioms of this theory is a generalized Einstein equation which determines the generating function directly. It is shown that basic concepts like orientation, time orientation and isometry are expressible in terms of generating functions. At the end of the paper six problems are formulated which are still unsolved and can act as a stimulant for further research.