Dynamics of extended bodies in general relativity. I. Momentum and angular momentum

Source abstract

Abstract Definitions are proposed for the total momentum vector pα and spin tensor Sαβ of an extended body in arbitrary gravitational and electromagnetic fields. These are based on the requirement that a symmetry of the external fields should imply conservation of a corresponding component of momentum and spin. The particular case of a test body in a de Sitter universe is considered in detail, and used to support the definition pβSαβ = 0 for the centre of mass. The total rest energy Mis defined as the length of the momentum vector. Using equations of motion to be derived in subsequent papers on the basis of these definitions, the time dependence of M is studied, and shown to be expressible as the sum of two contributions, the change in a potential energy function ϕ and a term representing energy inductively absorbed, as in Bondi’s illustration of Tweedledum and Tweedledee. For a body satisfying certain conditions described as ‘dynamical rigidity’, there exists, for motion in arbitrary external fields, a mass constant m such that M = m + ½SκΩκ+ ϕ, where Ωk is the angular velocity of the body and Sκ its spin vector.