Investigation of Faddeev variant of embedding theory

TL;DR

This paper explores the Faddeev variant of embedding theory for gravity, analyzing its solutions and differences from General Relativity, especially regarding extra solutions and matter contributions.

Contribution

It introduces a formulation of the Faddeev variant as GR with additional action terms and constructs an exact solution with matter and torsion.

Findings

Existence of extra solutions in Faddeev variant that differ from GR.

Formulation of the theory as GR with extra action contributions.

Construction of an exact solution with matter and torsion.

Abstract

Faddeev variant of embedding theory is an example of using the embedding approach for the description of gravity. In the original form of the embedding approach, the gravity is described by an embedding function of a four-dimensional surface representing our spacetime. In Faddeev variant, the independent variable is a non-square vielbein, which is a derivative of embedding function in embedding theory. We study the possibility of the existence of extra solutions in Faddeev variant, which makes this theory non-equivalent to GR. To separate the degrees of freedom corresponding to extra matter, we propose a formulation of this theory as GR with an additional contribution to the action. We analyze the equations of motion for a specific class of solutions corresponding to a weak gravitational field. We construct a simple exact solution corresponding to arbitrary matter and nontrivial torsion, which is an extra solution in Faddeev variant in the absence of real matter.