search for catalysis of black holes formation in hight energy collisions irina aref’eva

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R.Penrose, unpublished, 1974D.M.Eardley and S.B. Giddings, 2002H.Yoshino and Y. Nambu, 2003S.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