Download Presentation - School of Mathematics and Physics

Tim Lamberton
and Dr Katrina Hibberd
Centre for Mathematical Physics
Talk Outline
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Motivation
 Analogies provide new
ways of looking at a
problem
home.tiscali.nl
Talk Outline
●
●
Motivation
 Analogies provide new
ways of looking at a
problem
An analogue model
 The “acoustic metric”
home.tiscali.nl
Talk Outline
●
●
●
Motivation
 Analogies provide new
ways of looking at a
problem
An analogue model
 The “acoustic metric”
General relativity
home.tiscali.nl
 Metrics, black hole horizon, Hawking radiation
Talk Outline
●
●
●
●
●
Motivation
 Analogies provide new
ways of looking at a
problem
An analogue model
 The “acoustic metric”
General relativity
home.tiscali.nl
 Metrics, black hole horizon, Hawking radiation
Bose-Einstein condensates (BECs)
Future directions – quantum gravity
An analogue model of gravity
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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
An analogue model of gravity
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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
An analogue model of gravity
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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
Advances in analogue gravity
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Condensed matter-based models – Superfluids, BECs
Analogue gravity [1]
Advances in analogue gravity
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Condensed matter-based models – Superfluids, BECs
Wormholes
Slow light
Faster-than-light travel
Analogue gravity [1]
Advances in analogue gravity
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Condensed matter-based models – Superfluids, BECs
Wormholes
Slow light
Faster-than-light travel
Rotating black holes
Back-reaction
Cosmological particle creation
Analogue gravity [1]
Advances in analogue gravity
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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]
Advances in analogue gravity
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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]
Model – The Acoustic Metric
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First, the black hole and event horizon
www.aip.org
Model – The Acoustic Metric
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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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First, the black hole and event horizon
Our model – sound waves propagating
in a perfect fluid
www.aip.org

Equation of continuity

Euler's equation for adiabatic, irrotational fluid

This is describes a 'steady flow'
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
●
●
●
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
●
●
●
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
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and rewrite the
wave equation
General relativity
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Gravity is curved space-time
www.zarm.uni-bremen.de
www.math.sk
jilawww.colorado.edu/bec/
General relativity
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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/
General relativity
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Gravity is curved space-time
The metric – distance between
objects in curved space-time
Einstein's equations

Geometry of space
determined by matter
www.zarm.uni-bremen.de
www.math.sk
jilawww.colorado.edu/bec/
General relativity
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Black holes are described by Schwarzschild metric
www.ifa.hawaii.edu
www.scielo.br
www.dailytech.com
General relativity
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Black holes are described by Schwarzschild metric
www.ifa.hawaii.edu
www.scielo.br
www.dailytech.com
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Hawking radiation
 thermal radiation from black hole horizon due to
quantum fluctuations (Black hole explosions S. W.
Hawking 1974)
General relativity
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Black holes are described by Schwarzschild metric
www.ifa.hawaii.edu
www.scielo.br
www.dailytech.com
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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
The Bose-Einstein Condensate
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Predicted in 1920, created in 1995
The Bose-Einstein Condensate
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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/
The Bose-Einstein Condensate
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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/
Future directions – quantum gravity
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Quantum gravity – the idea that general relativity is
a low-energy approximation of a more fundamental
theory
www.liftport.com
Future directions – quantum gravity
●
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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
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
References
1.
2.
3.
4.
5.
6.
7.
8.
"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 – grqc/0703117