Computer Science
Scientific paper
Oct 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976gregr...7..781l&link_type=abstract
General Relativity and Gravitation, Volume 7, Issue 10, pp.781-803
Computer Science
1
Scientific paper
On the basis of an approximation method developed in a previous paper the motion of an extended small mass on a gravitational backgroundbegin{array}{*{20}c} {(in)} \ {g_{μ ν } } \ = η _{μ ν } + begin{array}{*{20}c} {(in)} \ {γ _{μ ν } } \ is investigated. The mass is described by a spherically symmetric rest mass distribution with some form of “rigidity;” the smallness of the mass is defined by the assumption that the radius of the mass is small compared with the change of the backgroundbegin{array}{*{20}c} {(in)} \ {γ _{μ ν } } \ . The equation of motion is yielded by integrating Einstein's conservation law of energy and momentum over the world tube of the mass. In the lowest mixed order (mixed of the backgroundbegin{array}{*{20}c} {(in)} \ {γ _{μ ν } } \ and the retarded potentials of the mass in lowest order) this equation is identical with the geodesic line linearized inbegin{array}{*{20}c} {(in)} \ {γ _{μ ν } } \ . In the case when the motion on a static background generated by a localized matter distribution is finite, the gravitational radiation of the mass in lowest order is given.
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