General Relativity \`a la string: a progress report

TL;DR

This paper explores a novel canonical formulation of general relativity inspired by string theory, focusing on embedding functions instead of metric components, and discusses current limitations and comparisons with traditional approaches.

Contribution

It introduces a string-inspired canonical formalism for general relativity using embedding functions, highlighting its differences from standard metric-based methods.

Findings

Preliminary results on a new formalism based on spacetime embeddings.

Identification of the main challenge: the 'fourth constraint' cannot be expressed in closed form.

Comparison with traditional canonical approaches and string theory.

Abstract

Preliminary results on a canonical formulation of general relativity based on an analogy with the string model of elementary particles are presented. Rather than the metric components, the basic fields of the formalism are taken to be the functions describing the embedding of four dimensional spacetime in a ten or possibly higher dimensional manifold. So far, the main drawback of the formalism is that the generator of normal deformations ("fourth constraint") cannot be written down in closed form. The present approach is compared and contrasted with the usual one and with the canonical description of the relativistic string.