Gravity as a field theory in flat space-time

TL;DR

This paper presents a novel formulation of gravity as a field theory in higher-dimensional flat space-time, where four-dimensional surfaces represent our universe, potentially aiding in quantum gravity research.

Contribution

It introduces a new approach to gravity as a field theory in higher-dimensional flat space, linking solutions to Einstein's equations with surface configurations.

Findings

Surfaces satisfy Regge-Teitelboim equations when equations of motion hold.

Matter fields propagate only along the four-dimensional surfaces.

The formulation may facilitate quantization of gravity.

Abstract

We propose a formulation of gravity theory in the form of a field theory in a flat space-time with a number of dimensions greater than four. Configurations of the field under consideration describe the splitting of this space-time into a system of mutually noninteracting four-dimensional surfaces. Each of these surfaces can be considered our four-dimensional space-time. If the theory equations of motion are satisfied, then each surface satisfies the Regge-Teitelboim equations, whose solutions, in particular, are solutions of the Einstein equations. Matter fields then satisfy the standard equations, and their excitations propagate only along the surfaces. The formulation of the gravity theory under consideration could be useful in attempts to quantize it.