heavy ions collisions and black holes production irina aref’eva steklov mathematical institute,...
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Heavy Ions Collisions
andBlack Holes Production
Irina Aref’eva
Steklov Mathematical Institute, Moscow
Round Table IV Italy-Russia@ DubnaBlack Holes in Mathematics and Physics
December 16-17, 2011
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Outlook
• Dual description of QCD:• QGP in dual description;• Trapped surface area and multiplicity;• BH charge and chemical potential
• Theoretical problems of BH formation:• Semiclassical approach and geometrical cross section;• Trapped surface arguments
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• 4-dim (astrophysics)
• TeV Gravity (micro-black holes)
D-dim, D= 5, 6,…
• 5-dim AdS to 4-dim QCD
BH formation in collision of matter
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BLACK HOLE FORMATION
• Thorn's hoop conjecture:
BH forms if the linear size of clumping matter l is
comparable to the Schwarzschild radius
Rs of a BH of mass m
Sl R 2SR Gm
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BLACK HOLE FORMATION
2 2 2S(1 1 BH ) ~ ~ E R G
Modified Thorn's hoop conjecture (for colliding particles):
BH forms if the impact parameter b is comparable to the Schwarzschild radius Rs of a BH of mass E.
• Classical geometrical cross-section
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• In 1987 't Hooft and Amati, Ciafaloni and Veneziano conjectured that in string theory and in QG at energies much higher than the Planck mass BH emerges.
Aichelburg-Sexl shock waves to describe particles,
Shock Waves ------ > BH
• Colliding plane gravitation waves to describe particles
Plane Gravitational Waves ----- > BH I.A., Viswanathan, I.Volovich, Nucl.Phys., 1995
• Boson stars (solitons) to describe particles M.Choptuik and F.Pretorius, Phys.Rev.Lett, 2010
4-dim Gev19Pl 10 M
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D-dim, D= 5, 6,…
• TeV Gravity (1998) N. Arkani-Hamed, S. Dimopoulos, G.R. Dvali, I. Antoniadis, 1998
• TeV Gravity to produce BH at Labs (1999) Banks, Fischler, hep-th/9906038 I.A., hep-th/9910269, Giuduce, Rattazzi, Wells, hep-ph/0112161 Giddings, hep-ph/0106219 Dimopolos, Landsberg, hep-ph/0106295, ……………………………
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• Classical geometric cross-section has got support from trapped surface estimations
R.Penrose, unpublished, 1974D.M.Eardley and S.B. Giddings, 2002H.Yoshino and Y. Nambu, 2003S. B. Giddings and V. S. Rychkov, 2004
………
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Trapped Surface
• A trapped surface is a two dimensional spacelike surface whose two null normals have negative expansion (=Neighbouring light rays, normal to the surface, must move towards one another)
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• MD with a shock wave (Aichelburg-Sexl metric)
Metric of the space-time with shock wave
M. Hotta, M. Tanaka – 1992
2 2 24
( ) ( ) , ( )i i iD
cds dudv dx F x u du F x
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+ ….
Guidice, Rattazzi,Well, hep-ph/0112161,Lodone, Rychkov,0909.3519
Barbashov,Kuleshov, Matveev,Sissakian, TMP,1970
Kadyshevskii at al, TMP,1971
Eikonal approximation
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X
Geodesics in the space-time with shock wave
2
( ) ( )
( ) ( ) 2 ( ) ( )
X b v
V v F b
)(bFv
V
U
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• 2 Aichelburg-Sexl shock waves
2 Ultrarelativistic particles = 2 shock waves
M. Hotta, M. Tanaka – 1992
4
2 2 2 21 2
2 20
( )( ) ( ) ( ) ( ) ,
( )
| ( ) |D
i i i i
i kk
i ik
ds dudv dx F x x u du F x v dv
cF x
x x
Smooth coordinates: P.D’Eath coordinates, Dray and ‘t Hooft
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VU
X
Trapped Surface for two shock waves
,][ )2()2()1()1(2 jiijjkikjkik dXdXHHHHdUdVds
1,2 1,2
2 ( 2)1,2 (1,2)
1 2
0, , 0,
( ), ,
4,
D
the outer null normals have zero
convergenc
X D X D
X X
e
no function in convergence
X D
X D
Eardley, Giddings; Kang, Nastase,….
(1)1
1( )
2ij ij i jH F u u
TS comprises two halves,which are matched along a “curve”
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The TS has two parts which lie in the regions
They are defined in terms of two functions
0Wand0
Boundary condition:
Trapped Surface for two shock waves
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Black Hole production in AdS5 as Quark-Gluon-Plasma formation in 4-dim QCD
Conjecture: Total entropy production in a heavy-ion collision = entropy of a trapped surface.
Goal: construct colliding nuclei in a holographic dual to QCD (an exact holographic dual to QCD is unavailable)
Nastase, hep-th/0501068; Shuryak, Sin, Zahed; Grumiller, Romatschke; Albacete, Kovchegov,Taliotis(09)
Gold ions colliding with √sNN ~200 GeV produces entropy ~ 38 000:
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z=0Our 4-dim worldN=4 SYM
5-dim SUGR in AdS space
L is the radius of the AdS space= -6/L2
5th coord. z 22
2
22 2 dzdxdxdx
z
Lds
2
30 xxx
Shock-waves in AdS5 & 4-dim QCD
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Single Nucleus in AdS/CFT
An ultrarelativistic nucleus is a shock wave in 4d with the energy-momentum tensor
)(~ xT
The metric of a shock wave in AdS corresponding to the ultrarelativistic nucleus in 4d is
22242
2
2
22 )(
22 dzdxdxzxT
Ndxdx
z
Lds
C
Janik, Peschanksi ‘05
x
x
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Colliding Nuclei in AdS/CFT
x
x
24
22
224
12
222
2
22 )(
2)(
22 dxzxT
NdxzxT
Ndzdxdxdx
z
Lds
CC
Nothing happens before the collision
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Multiplicity
GQP = BH
Lattice calculations
Gubser, Pufu, Yarom, 0805.1551, Alvarez-Gaume, C. Gomez, Vera, Tavanfar, and Vazquez-Mozo, 0811.3969
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Different profiles and multiplicities
An arbitrary gravitational shock wave in AdS5
Lin and Shuryak, 09
The Einstein equation
Plane shock waves
Cai,Ji,Soh, gr-qc/9801097
IA, 0912.5481
Kiritis,Taliotis, 1111.1931
Dilaton shock waves
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“Trapped Surface” for two shock waves
Regularization
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Critical trapped surfaces formation in the collision of ultrarelativistic charges in (A)dS
IA, A.Bagrov, E. Guseva, JHEP (2010) (dS, AdS)
IA, A.Bagrov, L.Joukovskaya, JHEP (2010) (charged particles in AdS,dS)
Formation of trapped surfaces on the past light cone is only possible when
crQ Q
A trapped surface forms if
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The trapped surface decreases with growth of a charge.
Critical trapped surfaces formation in the collision of charged shock waves in (A)dS
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Conclusion• BH production in AdS5 as QGP formation in 4-dim QCD• Techniques of trapped surfaces
Plans
• Classification of shock waves (to get details formula for multiplicity for heavy-ion collisions at RHIC and LHC)
• Try to use plane gravitational waves to calculate multiplicity• Simplification of techniques of trapped surface
• May be numerical calculations in AdS5 with “stars”