Vorticity in the Acoustic Analogue of Gravity. Part 1 [PDF]

School of Mathematical and Computing Sciences Te Kura Pangarau, Rorohiko Vorticity in the acoustic analogue of gravity Matt Visser Text School of Mathematical and Computing Sciences Te Kura Pangarau, Rorohiko And I cherish more than anything else the Analogies, my most trustworthy masters. They know all the secrets of Nature, and they ought least to be neglected in Geometry. --- Johannes Kepler Text Abstract: Sound waves propagating in a flowing fluid can be described by a wave equation on an “acoustic geometry”. This geometry is described by an “effective metric” that leads to a “curved spacetime” qualitatively similar to that of general relativity. In particular, it is relatively easy to set up “dumb holes” which trap sound in the same way that the black holes of general relativity trap light. rTelativext ely easy to set up "dum b holes" which trap sound in the same way that the black holes of gener al relativ ity trap light. Vorte x flow create s an "acou stic geom etry" that is qualit atively simila r to the equat orial plane of a rotati ng Kerr black hole. There is an acous tic analog y to the gneral relativ ity notio n of an "ergo spher e" as well as to the gener al relativ ity notio n of "horiz on". I will first qualit atively explai n these ideas, and descri be why they are useful, and then make a quanti tative comp arison betwe en the analog acous tic and gener al relativ istic sytem s. Abstract: Vortex flow creates an “acoustic geometry” that is qualitatively similar to the equatorial plane of a rotating Kerr black hole. There is an acoustic analogy to the general relativity notion of an “ergosphere” as well as to the general relativity notion of “horizon”. I will first qualitatively explain these ideas, and describe why they are useful, and then make a quantitative comparison between the analog acoustic and general relativistic sytems. Key idea: Consider sound waves in a flowing fluid. If the fluid is moving faster than sound, then the sound waves are swept along with the flow, and cannot escape from that region. This sounds awfully similar to a black hole in general relativity --- is there any connection? Yes! (Of course the devil is in the details...) Key results: Acoustic propagation in fluids can be described in terms of Lorentzian differential geometry. The acoustic metric depends algebraically on the fluid flow. Acoustic geometry shares kinematic aspects of general relativity, but not the dynamics. Einstein equations versus Euler equation. In particular: Acoustic black holes divorce kinematic aspects of black hole physics from the specific dynamics due to the Einstein equations. Advanced features: There are also other “analogue models” of general relativity, apart from the acoustic models. Acoustic black holes have Hawking radiation without black hole entropy. Hawking radiation is a purely kinematic effect that exists independent of whether or not the Lorentzian geometry obeys any particular geometrodynamics. You do not need the Einstein equations to get Hawking radiation. April 2000 Sponsored by: Photonics Technology News Send News to: [email protected] Water down the Drain Leads to Black Holes in the Lab Archimedes, the famous story goes, cried, "Eureka!" and leapt from his overflowing bathtub, having discovered the principle of buoyancy. But the drain has much to offer, too. Physicists Ulf Leonhardt and Paul Piwnicki of the Royal Institute of Technology suggest in the Jan. 31 issue of Physical Review Letters that vortices or other rapid flows analogous to the swirl of water down the drain may enable researchers to model the relativistic effects Sponsoredof black holes.by: April 2000 AprilSponsored 2000 by: Leonhardt explained that, as early as 1818, Augustin-Jean Fresnel predicted from theories of the luminiferous ether that a flowing medium will drag light with it. "For quite a long time we Photonics Technology Photonics Technology were rather puzzled and could not understand what is happening in moving media if one takes them seriously," said Leonhardt. "Then, News News suddenly, the picture emerged, and we realized the connection to Send News to: Send News to: gravity and curved space-time. This has come as a surprise." 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