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Analogue Models For General Relativity

Analogue Models For General Relativity. Tim Lamberton and Dr Katrina Hibberd. Centre for Mathematical Physics. Talk Outline. Motivation Analogies provide new ways of looking at a problem . home.tiscali.nl. Talk Outline. An analogue model The “acoustic metric”. Motivation

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Analogue Models For General Relativity

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  1. Analogue Models For General Relativity Tim Lamberton and Dr Katrina Hibberd Centre for Mathematical Physics

  2. Talk Outline • Motivation • Analogies provide new ways of looking at a problem home.tiscali.nl

  3. Talk Outline • An analogue model • The “acoustic metric” • Motivation • Analogies provide new ways of looking at a problem home.tiscali.nl

  4. Talk Outline • An analogue model • The “acoustic metric” • General relativity • Metrics, black hole horizon, Hawking radiation • Motivation • Analogies provide new ways of looking at a problem home.tiscali.nl

  5. Talk Outline • An analogue model • The “acoustic metric” • General relativity • Metrics, black hole horizon, Hawking radiation • Bose-Einstein condensates (BECs) • Future directions – quantum gravity • Motivation • Analogies provide new ways of looking at a problem home.tiscali.nl

  6. An analogue model of gravity • Sound waves in a fluid are used as an analogy for light waves under the effect of gravity Analogue gravity [1] http://www.iihr.uiowa.edu/products/dhrm.html

  7. An analogue model of gravity • Sound waves in a fluid are used as an analogy for light waves under the effect of gravity • “Dumb hole”Video of Supersonic flow Analogue gravity [1] http://www.iihr.uiowa.edu/products/dhrm.html

  8. An analogue model of gravity • Sound waves in a fluid are used as an analogy for light waves under the effect of gravity • “Dumb hole”Video of Supersonic flow • Unruh predicts Hawking radiationfrom a dumb hole (Experimental black hole evaporation, W. G. Unruh 1981) Analogue gravity [1] http://www.iihr.uiowa.edu/products/dhrm.html

  9. Advances in analogue gravity • Condensed matter-based models – Superfluids, BECs Analogue gravity [1]

  10. Advances in analogue gravity • Condensed matter-based models – Superfluids, BECs • Wormholes • Slow light • Faster-than-light travel Analogue gravity [1]

  11. Advances in analogue gravity • Condensed matter-based models – Superfluids, BECs • Wormholes • Slow light • Faster-than-light travel • Rotating black holes • Back-reaction • Cosmological particle creation Analogue gravity [1]

  12. Advances in analogue gravity • Condensed matter-based models – Superfluids, BECs • Wormholes • Slow light • Faster-than-light travel • Rotating black holes • Back-reaction • Cosmological particle creation • Quantum gravity Analogue gravity [1]

  13. Advances in analogue gravity • Condensed matter-based models – Superfluids, BECs • Wormholes • Slow light • Faster-than-light travel • Rotating black holes • Back-reaction • Cosmological particle creation • Quantum gravity Impact: workshops, conference sessions, books, articles Analogue gravity [1]

  14. Model – The Acoustic Metric • First, the black hole and event horizon www.aip.org

  15. Model – The Acoustic Metric • First, the black hole and event horizon • Our model – sound waves propagating in a perfect fluid www.aip.org

  16. Model – The Acoustic Metric • First, the black hole and event horizon • Our model – sound waves propagating in a perfect fluid • Equation of continuity www.aip.org • Euler's equation for adiabatic, irrotational fluid • This is describes a 'steady flow'

  17. Model – The Acoustic Metric • Separate fluid components into that of the background fluid motion and sound waves moving in the fluid

  18. Model – The Acoustic Metric • Separate fluid components into that of the background fluid motion and sound waves moving in the fluid • Wave equation for sound waves in the fluid

  19. Model – The Acoustic Metric • Separate fluid components into that of the background fluid motion and sound waves moving in the fluid • Wave equation for sound waves in the fluid • We can deduce the acoustic metric ‘felt' by sound waves

  20. Model – The Acoustic Metric • Separate fluid components into that of the background fluid motion and sound waves moving in the fluid • Wave equation for sound waves in the fluid • We can deduce the acoustic metric ‘felt' by sound waves • and rewrite the wave equation

  21. General relativity • Gravity is curved space-time www.zarm.uni-bremen.de www.math.sk jilawww.colorado.edu/bec/

  22. General relativity • Gravity is curved space-time • The metric – distance between objects in curved space-time www.zarm.uni-bremen.de www.math.sk jilawww.colorado.edu/bec/

  23. General relativity • Gravity is curved space-time • The metric – distance between objects in curved space-time www.zarm.uni-bremen.de www.math.sk jilawww.colorado.edu/bec/ • Einstein's equations • Geometry of space determined by matter

  24. General relativity • Black holes are described by Schwarzschild metric www.ifa.hawaii.edu www.scielo.br www.dailytech.com

  25. General relativity • Black holes are described by Schwarzschild metric www.ifa.hawaii.edu www.scielo.br www.dailytech.com • Hawking radiation • thermal radiation from black hole horizon due to quantum fluctuations (Black hole explosions S. W. Hawking 1974)

  26. General relativity • Black holes are described by Schwarzschild metric www.ifa.hawaii.edu www.scielo.br www.dailytech.com • Hawking radiation • thermal radiation from black hole horizon due to quantum fluctuations (Black hole explosions S. W. Hawking 1974) • Also found produced by dumb holes

  27. The Bose-Einstein Condensate • Predicted in 1920, created in 1995

  28. The Bose-Einstein Condensate • Predicted in 1920, created in 1995 • A Bose-Einstein condensate is a gas of particles in the lowest quantum energy state • Quantum effects become visible on a macroscopic level www.colorado.edu/physics/2000/bec/

  29. The Bose-Einstein Condensate • Predicted in 1920, created in 1995 • A Bose-Einstein condensate is a gas of particles in the lowest quantum energy state • Quantum effects become visible on a macroscopic level Importantly, BEC based models predict measurable sonic radiation from horizon and are relatively easy to conduct experiments with. www.colorado.edu/physics/2000/bec/

  30. Future directions – quantum gravity • Quantum gravity – the idea that general relativity is a low-energy approximation of a more fundamental theory www.liftport.com

  31. Future directions – quantum gravity • Quantum gravity – the idea that general relativity is a low-energy approximation of a more fundamental theory • Analogue models provide good hints to how such a fundamental theory might work www.liftport.com

  32. Future directions – quantum gravity • Quantum gravity – the idea that general relativity is a low-energy approximation of a more fundamental theory • Analogue models provide good hints to how such a fundamental theory might work • That's all guys www.liftport.com

  33. "Analogue Gravity" Carlos Barceló and Stefano Liberati and Matt Visser, Living Rev. Relativity 8, (2005), 12 and references therein “Sonic analogue of gravitational black holes in Bose-Einstein condensates” L. G. Garay, J. R. Anglin, J. I. Cirac, P. Zoller, Phys. Rev. Lett. 85, (2000), 4643 “Hydrodynamics” Sir Horace Lamb, “Fluid Mechanics” Landau and Lifshitz, (1959) “Statistical Mechanics” K. Huang, (1987) “General relativity primer” Richard H. Price, Am. J. Phys. 50, (1982), 300, “Gravitation” Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, (1973) “Critical Behaviour in the Gravitational Collapse of a Scalar Field with Angular Momentum in Spherical Symmetry” W. G. Unruh, Ignacio Olaberrieta, Jason F. Ventrella, Matthew W. Choptuik – gr-qc/0708.0513 “Quantum toy model for black-hole back-reaction” Clovis Maria, Ralf Schützhold – gr-qc/0706.4010 “Trans-Planckian physics and signature change events in Bose gas hydrodynamics” Silke Weinfurtner, Angela White, Matt Visser – gr-qc/0703117 References

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