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R.Penrose, unpublished, 1974D.M.Eardley and S.B. Giddings, 2002H.Yoshino and Y. Nambu, 2003S.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