Physics
Scientific paper
Jan 1970
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1970rspsa.314..499d&link_type=abstract
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 314, Issue 1519, pp. 499-527
Physics
152
Scientific paper
Definitions are proposed for the total momentum vector p^α 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 p_βSαβ = 0 for the centre of mass. The total rest energy M is 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 + 1/2S^kappaΩ_kappa + Φ, where Ω_kappa is the angular velocity of the body and S^kappa its spin vector.
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