The equation of motion and gravitational radiation of an ideal fluid sphere moving in a gravitational background.
Abstract
On the basis of an approximation method developed in a previous paper the motion of an ideal fluid sphere in a weak gravitational backgroundbegin{array}{*{20}c} {(in)} & {(in)} \ {g_{μ v} = η _{μ v} + γ _{μ v} } & {} \ is investigated. The sphere is assumed to be small in the sense that its radius is small compared with the change of the backgroundbegin{array}{*{20}c} {(in)} \ {γ _{μ v} } \ . Furthermore the deformations of the sphere when accelerated by the background are assumed to be small compared with the extension of the sphere in the absence of acceleration. In the lowest mixed order (mixed of the backgroundbegin{array}{*{20}c} {(in)} \ {γ _{μ v} } \ and the retarded potentials of the sphere in lowest order) the equation of motion is yielded by integrating Einstein's conservation law of energy and momentum over the worldtube of the sphere. One obtains an equation of motion for the center of the sphere that is identical with the geodesic line linearized inbegin{array}{*{20}c} {(in)} \ {γ _{μ v} } \ . In the case of a static background of a localized matter distribution it is shown that Einstein's energymomentum complex formed with the retarded potentials from the accelerated motion of the sphere in lowest order (lowest mixed order) leads to an outgoing radiation of gravitational energy. All radiation terms can be expressed in terms of the background and the worldline of the center of the sphere.
 Publication:

General Relativity and Gravitation
 Pub Date:
 April 1979
 DOI:
 10.1007/BF00760223
 Bibcode:
 1979GReGr..10..401L
 Keywords:

 Center Of Gravity;
 Equations Of Motion;
 Gravitational Waves;
 Ideal Fluids;
 Mass Distribution;
 Conservation Laws;
 Einstein Equations;
 Energy Conservation;
 Field Theory (Physics);
 Kinetic Energy;
 Particle Size Distribution;
 Spheres;
 Astrophysics;
 Gravitational Radiation