Geodesics of Sound Waves and Their Wave Fronts in Curved Space-Time

Physics

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Scientific paper

In order to clarify the focusing effects of the energy and momentum by wave motion, the wave propagations of a photon and sound wave are investigated in Kerr space-time. By using a canonical-type formulation for the propagations of electromagnetic disturbances in vacuum and hydrodynamical disturbances in accretion disk, the basic properties of sound wave propagation and the numerical calculations of motion of the locus of simultaneous fronts of wave packets are presented. The propagation of sound wave is described by a ``sound metric.'' In the accreting matter of rotating disk, the ``sound horizon'' and ``sound ergoregion'' exists. The effective potential governing sound wave motions show that there is a potential hill near a rotating black hole for the retrograde motion of sound wave. The sound waves inside the potential's hill converge into the rotation axis of the black hole. The light rays emitted into the direction perpendicular to the equatorial plane also converge into the rotation axis. The collimation mechanism of the jet by radiation which is emitted from the accretion disk is discussed.

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