Field-theoretical formulation of Regge–Teitelboim gravity

Abstract

Theory of gravity is considered in the Regge–Teitelboim approach in which the pseudo-Rimannian space is treated as a surface isometrically embedded in an ambient Minkowski space of higher dimension. This approach is formulated in terms of a field theory in which the original pseudo-Rimannian space is defined by the field constant-value surfaces. The symmetry properties of the proposed theory are investigated, and possible structure of the field-theoretical Lagrangian is discussed.