Localizing Energy in Fierz-Lanczos theory

Abstract

We calculate energy carried by the massless spin-2 field using Fierz-Lanczos representation of the theory. For this purpose Hamiltonian formulation of the field dynamic is thoroughly analyzed. Final expression for the energy is very much analogous to the Maxwell energy in electrodynamics (spin-1 field) and displays the locality property. Known as a "super-energy" in gravity theory, this quantity differs considerably from the well understood gravitational field energy (represented in linear gravity by the quadratic term in Taylor expansion of the A.D.M. mass) which cannot be localized.