Analogue Models For General Relativity
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Transcript of Analogue Models For General Relativity
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Tim Lamberton and Dr Katrina Hibberd
Centre for Mathematical Physics
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Talk Outline
home.tiscali.nl
● Motivation Analogies provide
new ways of looking at a problem
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Talk Outline
● An analogue model The “acoustic metric”
home.tiscali.nl
● Motivation Analogies provide
new ways of looking at a problem
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Talk Outline
● An analogue model The “acoustic metric”
● General relativity Metrics, black hole horizon, Hawking radiation
home.tiscali.nl
● Motivation Analogies provide
new ways of looking at a problem
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Talk Outline
● An analogue model The “acoustic metric”
● General relativity Metrics, black hole horizon, Hawking radiation
● Bose-Einstein condensates (BECs)● Future directions – quantum gravity
home.tiscali.nl
● Motivation Analogies provide
new ways of looking at a problem
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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
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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
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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 radiation from a dumb hole (Experimental black hole evaporation, W. G. Unruh 1981)
Analogue gravity [1]
http://www.iihr.uiowa.edu/products/dhrm.html
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Advances in analogue gravity● Condensed matter-based models – Superfluids, BECs
Analogue gravity [1]
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Advances in analogue gravity● Condensed matter-based models – Superfluids, BECs ● Wormholes● Slow light● Faster-than-light travel
Analogue gravity [1]
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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]
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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]
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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]
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Model – The Acoustic Metric● First, the black hole and event horizon
www.aip.org
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● First, the black hole and event horizon
● Our model – sound waves propagating in a perfect fluid
www.aip.org
Model – The Acoustic Metric
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Euler's equation for adiabatic, irrotational fluid
This is describes a 'steady flow'
● First, the black hole and event horizon
● Our model – sound waves propagating in a perfect fluid Equation of continuity www.aip.org
Model – The Acoustic Metric
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● Separate fluid components into that of the background fluid motion and sound waves moving in the fluid
Model – The Acoustic Metric
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● 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
Model – The Acoustic Metric
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● 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
Model – The Acoustic Metric
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● 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
Model – The Acoustic Metric
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General relativity● Gravity is curved space-time
www.zarm.uni-bremen.dewww.math.skjilawww.colorado.edu/bec/
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General relativity● Gravity is curved space-time● The metric – distance between
objects in curved space-time
www.zarm.uni-bremen.dewww.math.skjilawww.colorado.edu/bec/
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General relativity● Gravity is curved space-time● The metric – distance between
objects in curved space-time
www.zarm.uni-bremen.dewww.math.skjilawww.colorado.edu/bec/
● Einstein's equations
Geometry of space determined by matter
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General relativity● Black holes are described by Schwarzschild metric
www.ifa.hawaii.eduwww.scielo.brwww.dailytech.com
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General relativity● Black holes are described by Schwarzschild metric
www.ifa.hawaii.eduwww.scielo.brwww.dailytech.com
● Hawking radiation thermal radiation from black hole horizon due to
quantum fluctuations (Black hole explosions S. W. Hawking 1974)
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General relativity● Black holes are described by Schwarzschild metric
www.ifa.hawaii.eduwww.scielo.brwww.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
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The Bose-Einstein Condensate● Predicted in 1920, created in 1995
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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/
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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/
Importantly, BEC based models predict measurable sonic radiation from horizon and are relatively easy to conduct experiments with.
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Future directions – quantum gravity
● Quantum gravity – the idea that general relativity is a low-energy approximation of a more fundamental theory
www.liftport.com
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Future directions – quantum gravity
● Quantum gravity – the idea that general relativity is a low-energy approximation of a more fundamental theory
www.liftport.com
● Analogue models provide good hints to how such a fundamental theory might work
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Future directions – quantum gravity
● Quantum gravity – the idea that general relativity is a low-energy approximation of a more fundamental theory
www.liftport.com
● Analogue models provide good hints to how such a fundamental theory might work
● That's all guys
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References
1. "Analogue Gravity" Carlos Barceló and Stefano Liberati and Matt Visser, Living Rev. Relativity 8, (2005), 12 and references therein
2. “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
3. “Hydrodynamics” Sir Horace Lamb, “Fluid Mechanics” Landau and Lifshitz, (1959)
4. “Statistical Mechanics” K. Huang, (1987)5. “General relativity primer” Richard H. Price, Am. J. Phys. 50,
(1982), 300, “Gravitation” Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, (1973)
6. “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
7. “Quantum toy model for black-hole back-reaction” Clovis Maria, Ralf Schützhold – gr-qc/0706.4010
8. “Trans-Planckian physics and signature change events in Bose gas hydrodynamics” Silke Weinfurtner, Angela White, Matt Visser – gr-qc/0703117