Search for Catalysis of Black Holes Formation in Hight Energy Collisions Irina Aref’eva

1. Search for Catalysis of Black Holes Formation in Hight Energy Collisions Irina Aref’eva Steklov MathematicalInstitute, Moscow Kolomna, QUARKS’2010, June 6-12, 2010

2. 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

3. 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

4. BLACK HOLE FORMATION • Thorn's hoop conjecture: BH forms if the linear size of clumping matter l is comparable to the Schwarzschild radius Rsof a BH of mass m • 1+1  BH • Modified Thorn's hoop conjecture: • BH forms if the impact parameter b is comparable to the Schwarzschild radius Rsof a BH of mass E. • Classicalgeometricalcross-section

5. BLACK HOLE FORMATION in D>4

6. Classical geometric cross-section • Classical geometric cross-section has got support from trapped surface estimations R.Penrose, unpublished, 1974 D.M.Eardley and S.B. Giddings, 2002 H.Yoshino and Y. Nambu, 2003 S. B. Giddings and V. S. Rychkov, 2004 ………

7. I.Antoniadis, 1998 N. Arkani-Hamed, S. Dimopoulos, G.R. Dvali; Hierarchy problem Numbers ? Classical geometric cross-section

8. Micro-BH at Accelerators and Parton Structure are the parton momentum fractions the parton distribution functions S – the square of energy (in c.m.) NUMBERS are small!

9. Search for Catalysis of BH Production • 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

10. 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

11. 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

12. Lambda Modifications: I.A., A.Bagrov, E.Guseva, 0905.1087 Nastase; Gubser, Pufu, Yarom, 2008,2009; Alvarez-Gaume, Gomes,.. 2008; Shuryak 2008-9, ……. Colliding objects - shock waves with e,s,… In flat space with charge: Yoshino, Mann 06; Spin - Yoshino, Zelnikov,V.Frolov 07. With charge and Lambda: 0909.1292 I.A., A.Bagrov, L.Joukowskaya

13. D-dim gravitational model of relativistic particles Tolman-Florides interior incompressible perfect fluid solution or Static spherical symmetric solitonic solution of gravity-matter E.O.M. (boson stars) Boost  flattening of the Schwarzschild sphere Numerical calculations by M.Choptuik and F.Pretorius PRL, 2010

14. ModifiedThorn'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.

15. Choptuik-Pretorius results

16. Metric of the space-time with shock wave • MD with a shock wave (Aichelburg-Sexl metric) Smooth coordinates: P.D’Eath coordinates, Dray and ‘t Hooft M. Hotta, M. Tanaka – 1992

17. Particles and Shock Waves M X Z=(U+V)/2 't Hooft, Kaloper, Terning Shock Waves

18. Metric of the space-time with shock wave • MD with a shock wave (Aichelburg-Sexl metric) M. Hotta, M. Tanaka – 1992

19. Geodesics in the space-time with shock wave U V X

20. Particle in Shock Wave X Shock Wave M Z=(U+V)/2 Target Projectile M is chasing after the shock

21. Escape or not escape M

22. Charged dilaton G.Gibbons, Maeda, Garfinkle, Horowitz, Strominger, Cai,… BH solutions Shock wave Acts as a catalyst

23. Lambda Modifications: I.A., A.Bagrov, E.Guseva, 0905.1087 Nastase; Gubser, Pufu, Yarom, 2008,2009; Alvarez-Gaume, Gomes,.. 2008; Shuryak 2008-9, …….

24. Metric of the space-time with shock wave • dS4 space-time with a shock wave as submanifold ( ) of 5-dim. space-time with metric Hotta-Tanake, 92 Sfetsos, 95 Griffiths, Podolsky, 97 Horowitz, Itzhaki, 99 Emparan. 01 M. Hotta, M. Tanaka – 1992

25. Capture in the presence of the vacuum energy Trapped surface guarantees BH formation only for asymptotical free spacetimes

26. 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

27. 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.

28. 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. ADD RS2

29. 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

30. Colliding Hadron as Cosmic Membrane • Two types of effects of the angle deficit : corrections to the graviton propagation; new channels of decays

31. Colliding Hadron as Cosmic Membrane Corrections to the graviton propagation; New channels of decays Toy model: if we neglect brane, light particle m2M k – momentum of m particle