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Search for Catalysis of Black Holes Formation in Hight Energy Collisions Irina Aref’eva Steklov Mathematic al Institute , Moscow Kolomna, QUARKS’2010, June 6-12, 2010. Outlook. Theoretical problems of BH formation: Geometrical cross-section; Trapped surface arguments; - PowerPoint PPT Presentation
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Search for Catalysis of Black Holes Formation in Hight
Energy Collisions
Irina Aref’eva
Steklov Mathematical Institute, Moscow
Kolomna, QUARKS’2010, June 6-12, 2010
Outlook
• Theoretical problems of BH formation:
• Geometrical cross-section;
• Trapped surface arguments;
• Simple calculations that support BH
formation;
Search for catalysis.
• Colliding Hadron as Cosmic Membrane
• Known:
BH formation in transplankian collision of particles – semiclassical process
Classical geometrical cross-section
• Question: can we increase geometrical cross-section?
• Answer: IA, 0912.5481
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
2 2 2S(1 1 BH ) ~ ~ E R G
1+1 BH Modified Thorn's hoop conjecture: BH forms if the impact parameter b is comparable to the
Schwarzschild radius Rs of a BH of mass E.
• Classical geometrical cross-section
Sl R 2SR Gm
BLACK HOLE FORMATION in D>4
( )1( ) ( ) DBH
SD D
MR D
M M
1( )
3D
D
1/( 3)1 8 ( 1 / 2)
( )2
DD
DD
4D
2
1D D
D
GM
2( )SR E
Classical geometric cross-section
• 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R.Penrose, unpublished, 1974D.M.Eardley and S.B. Giddings, 2002H.Yoshino and Y. Nambu, 2003S.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
………
Classical geometric cross-section
1/ 3DSb r E
6 1 15D nb
Numbers ?
1tt nb
37 210nb m
I.Antoniadis, 1998 N. Arkani-Hamed, S. Dimopoulos, G.R. Dvali; Hierarchy problem
Micro-BH at Accelerators and Parton Structure 1 1
( ) ( / ) ( )m
pp BH i j ij BHij
dxd f x f x s
x
S – the square of energy (in c.m.)
if
xx /, are the parton momentum fractionsthe parton distribution functions
massimumnmiMsMm 2min
2min ,/
NUMBERS are small!
• Motivation: small cross-section of micro BH production at the LHC
• Question: what we can do to increase cross-section
• Answer: modify the conditions of collisions
8 (NG G T ))(catalystT1
,2
R g R G
Search for Catalysis of BH Production
Search for a catalyst
• find effects related with nontrivial dynamics of 3-brane embedding in D-dim spacetime.
• Change the background (4-dim/D-dim),
in particular, we can add the cosmological constant (AdS/dS)
• D-dim tail of 4-dim particles made from closed string excitations
Framework of a search for a catalyst
• D-dim gravitational model of relativistic particles
• D-dim gravitational model of particles on brane with “tails” in the bulk.
• Shock-waves as an approx. for ultrarelativistic particles.
• “dilaton” shock-wave
Lambda Modifications:
TGG N (8 ))catalyst(T
gT )catalyst(
0
0
Colliding objects - shock waves with e,s,…
I.A., A.Bagrov,E.Guseva,0905.1087
Nastase;Gubser, Pufu, Yarom, 2008,2009;Alvarez-Gaume,Gomes,.. 2008;Shuryak 2008-9,…….
With charge and Lambda: 0909.1292 I.A., A.Bagrov, L.Joukowskaya
In flat space with charge: Yoshino, Mann 06; Spin - Yoshino, Zelnikov, V.Frolov 07.
D-dim gravitational model of relativistic particles
2 3 2 3 1 2 2 22, (1 ( ) ) (1 ( ) )D DS S
S D
R RR R ds dt dR R d
R R
SR RTolman-Florides interior incompressible perfect fluid solution
Static spherical symmetric solitonic solution of gravity-matter E.O.M. (boson stars)
or
Numerical calculations byM.Choptuik and F.PretoriusPRL, 2010
2 2
2.9
1 / 1 /v c
Boost flattening of the Schwarzschild sphere
,p
m p fixed
Modified Thorn's hoop conjecture:
• It is not obvious that the hoop conjecture is applicable.
• Counterexample: a single particle boosted beyond the Planck energy -- no black hole formation.
Choptuik-Pretorius results
1.15, 2.75, 4
• 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
Smooth coordinates: P.D’Eath coordinates, Dray and ‘t Hooft
X
Particles and Shock Waves
M
Z=(U+V)/2
Shock Waves
't Hooft, Kaloper, Terning
• 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
X
Geodesics in the space-time with shock wave
2
( ) ( )
( ) ( ) 2 ( ) ( )
X b v
V v F b
)(bFv
V
U
X
Particle in Shock Wave
M
Z=(U+V)/2
Shock Wave
M is chasing after the shock
)(bFv bM
pv
Pl2
Target Projectile
2
2
( )
( ) ( ) ( )2
( ) ( ) ( )2
X b v
vZ F b
vt F b
2
0
( ) ( ) ( )2
X
vZ t Z F b
Escape or not escape
M
2 2 2 22
(1 ) ,1 / 2
R b vb v
2Pl
pv
M b
22min 21
bR
v
2* 4
2
Pl
M pb
M
min( ) ( )SR M R bb b
Charged dilaton
G.Gibbons, Maeda, Garfinkle, Horowitz, Strominger, Cai,…
BH solutions
Acts as a catalyst
Shock wave
Lambda Modifications:
TGG N (8 ))catalyst(T
gT )catalyst(
0
0
I.A., A.Bagrov,E.Guseva,0905.1087
Nastase;Gubser, Pufu, Yarom, 2008,2009;Alvarez-Gaume,Gomes,.. 2008;Shuryak 2008-9,…….
• dS4 space-time with a shock wave as submanifold ( ) of 5-dim. space-time with metric
Metric of the space-time with shock wave
M. Hotta, M. Tanaka – 1992
Hotta-Tanake, 92Sfetsos, 95Griffiths, Podolsky, 97Horowitz, Itzhaki, 99Emparan. 01
Capture in the presence of the vacuum energy
Trapped surface guarantees BH formation only for asymptotical free spacetimes
Conclusion
• Modified Thorn’s conjecture is confirmed; • Results of trapped surface calculations are confirmed
Catalysts:• A particular “dilaton” acts as a catalyst• Lambda<0 acts as a catalyst
Colliding Hadron as Cosmic Membrane
• Hight-energy hadrons colliding on the 3-brane embedding in the 5-dim spacetime with 5th dim smaller than the hadrons size are considered as colliding cosmic membranes.
• This consideration leads to the 3-dim effective model of high energy collisions of hadrons and the model is similar to cosmic strings in the 4-dim world.
Colliding Hadron as Cosmic Membrane
• These membranes are located on our 3-brane. Since 5-gravity is strong enough we can expect that hadrons membranes modified the 5-dim spacetime metric.
5hadronl l
3,5 10PlM TeVADD
RS2,5PlM TeV
Colliding Hadron as Cosmic Membrane
• Due to the presence of the hadron membrane the gravitational background is nontrivial and
describes a flat spacetime with a conical singularity located on the hadron membrane.
• This picture is a generalization of the cosmo-logical string picture in the 4-dim world to the 5-dim world.
• The angle deficit 3 3
5 5, [ ] , [ ] /G G M M S M
Colliding Hadron as Cosmic Membrane • Two types of effects of the angle deficit :
corrections to the graviton propagation;
new channels of decays
5 ,G
Colliding Hadron as Cosmic Membrane
Corrections to the graviton propagation;
5 ,G 9
3 3 2
1 110 ,
10 1
27 1
310l
gfor k M
M
k – momentum of m particle
New channels of decays Toy model: if we neglect brane, light particle m2M