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HOW TO ESCAPE A MOCK BLACK HOLE TUNE DISPERSION

29 pages


  • saint andrews

  • counter flow

  • gravity analogue

  • tune dispersion


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HOW TO ESCAPE (ENTER)
A MOCK BLACK (WHITE) HOLE ?
TUNE DISPERSION !
Germain Rousseaux, Philippe Maïssa, Christian Mathis and Pierre Coullet
Laboratoire J.-A. Dieudonné, UMR CNRS-UNS 6621,
Université de Nice-Sophia Antipolis, France.
Thomas Philbin and Ulf Leonhardt
University of Saint Andrews, Scotland.
th12 Marcel Grossmann Meeting, BHT6, Paris, 12-18 July 2009.Water Waves as a Gravity AnalogueWave Propagation The Ramp Counter FlowTwo Experimental Regimes
Wave Propagation
Wave Transmission
Counter Flow Wave Blocking
UmaxExperimental White Hole Horizon
T=0.8s ; U =0.94m/s ; A=0.1m ; H=1.4m
max
0.2
Wave Propagation
0.15
0.1
Wave Blocking
0.05
0
-0.05
-0.1
Counter Flow
-0.15
-0.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
x (m)
h (m)Wave blocking as a saddle-node (tangent) bifurcation!
! =!(k)=Uk± gktanh(kh)
!1" !s "
30
White Horizon20
10
!1!k k k k k !m "H R I k B!50 50
!!
!10 =0= cg
!k
!20
21! !! ! 2!(k)=!(k )+ (k!k )
22 !kBlocking Velocity as a function of the wave Period !
! =!(k)=Uk± gk
!1U !m.s "
White Horizon1.0
Wave Blocking = Forbidden Region
0.8
= White Hole
0.6
gT!0.4 U = kh>> 1
8!
0.2
0.0 T !s"
0.0 0.5 1.0 1.5 2.0 2.5
216!!k =
2gTBlue-shifted Phase Velocity at the Horizon
Counter FlowTime
Wave Propagation
Space