1. MICRO-BLACK HOLES and WORMHOLES AT THE LHC I.Ya.Aref`eva Steklov Mathematical Institute, Moscow QUARKS-2008 15th International Seminar on High Energy Physics Sergiev Posad, Russia, 23-29 May, 2008

2. PREDICTIONS Micro-Black hole production at CERN's Large Hadron Collider (LHC) Micro-Wormhole/time machine production at LHC I.A. and I.V.Volovich, Time Machine at the LHC, arXiv: 07102696, Int.J.Geom.Meth.Mod.Phys. (2008)

3. Outlook: TeV gravity Quantum Gravity Black holes Wormhole (WH) solutions TIME MACHINES (CTCs) I.Volovich’s talk Cross-sections and signatures at the LHC

4. TeV Gravity N. Arkani-Hamed, S. Dimopoulos, G.R. Dvali, I. Antoniadis, 1998 Hierarchy problem

5. Extra Dimensions

6. Modification of the Newton law

7. Possible signatures of TeV higher- dimensional gravity: Black Hole/ Worm Hole production Signs of strong quantum gravity KK modes

8. TeV Gravity = Quantum Gravity I.A., K.S.Viswanathan, I.V.Volovich, Nucl.Phys., B 452,1995, 346 Wave functions:

9. No a coupling constant to suppress-out channels with nontrivial topology Quantum Gravity =Summation over Topologies

10. Summation over topologies Theorem (Geroch, Tipler): Topology-changing spacetimes must have CTC (closed timelike curve)

11. Particles to Black Holes/Worm holes Wave functions: particles black hole

12. A possibility of production in ultra-relativistic particle collisions of some objects related to a non-trivial space-time structure is one of long-standing theoretical questions In 1978 collision of two classical ultra relativistic particles was considered by D'Eath and Payne and the mass of the assumed final BH also has been estimated In 1987 Amati, Ciafaloni, Veneziano and 't Hooft 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 Gr Waves ----- > BH I.A., Viswanathan, I.Volovich, 1995 BH in Collisions

13. BLACK HOLE PRODUCTION Collision of two fast point particles of energy E. BH forms if the impact parameter b is comparable to the Schwarzschild radius r s of a BH of mass E. The Thorn's hoop conjecture gives a rough estimate for classical geometrical cross-section

14. BLACK HOLE PRODUCTION To deal with BH creation in particles collisions we have to deal with trans-Planckian scales. Trans-Planckian collisions in standard QG have inaccessible energy scale and cannot be realized in usual conditions. 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

15. D-dimensional Schwarzschild Solution Meyers,…

16. D-dimensional Aichelburg-Sexl Shock Waves Shock waves, Penrose, D’Eath, Eardley, Giddings,… Classical geometric cross-section

17. BH Production in Particle Collisions at Colliders and Cosmic Rays

18. Thermal Hawking Radiation Decay via Hawking Radiation Emit particles following an approximately black body thermal spectrum Astronomic BH – cold - NO Evaporation Micro BH -- hot -- Evaporation

19. Micro-BH at Accelerators and parton structure S – the square of energy (in c.m.) are the parton momentum fractions the parton distribution functions Drell-Yan process: pp--> e + e - + X Similar to muon pair production in pp scattering, Matveyev - Muradyan-Tavkhelidze, 1969, JINR

20. Parton Distribution Functions Q = 2 GeV for gluons (red), up (green), down (blue), and strange (violet) quarks

21. Inelasticity The ratio of the mass of the BH/WH to the initial energy of the collision as a function of the impact parameter divided by r 0 (the Schwarzschild radius) Eardley, Yoshino, Randall Catalyze of BH production due to an anisotropy Dvali, Sibiryakov

22. Colliding Plane Gravitational Waves I.A, Viswanathan, I.Volovich, 1995 Plane coordinates; Kruskal coordinates Regions II and III contain the approaching plane waves. In the region IV the metric (4) is isomorphic to the Schwarzschild metric. D-dim analog of the Chandrasekhar-Ferrari-Xanthopoulos duality?

23. Wormholes Lorentzian Wormhole is a region in spacetime in which 3-dim space-like sections have non-trivial topology. By non-trivial topology we mean that these sections are not simply connected In the simplest case a WH has two mouths which join different regions of the space-time. We can also imagine that there is a thin handle, or a throat connected these mouths. Sometimes people refer to this topology as a 'shortcut' through out spacetime

25. Wormholes The term WH was introduced by J. Wheeler in 1957 Already in 1921 by H. Weyl ( mass in terms of EM) The name WH comes from the following obvious picture. The worm could take a shortcut to the opposite side of the apple's skin by burrowing through its center, instead of traveling the entire distance around.

26. Einstein-Rosen bridge The embedding diagram of the Schwarzschild WH seems to show a static WH. However, this is an illusion of the Schwarzschild coordinate system, which is ill-behaved at the horizon Kruskal diagram of the WH Take Schwarzschild BH Take 2 copies of the region Discard the region inside the event horizon Glue these 2 copies of outside event horizon regions

27. The traveler just as a worm could take a shortcut to the opposite side of the universe through a topologically nontrivial tunnel.

28. Wormholes The first WH solution was found by Einstein and Rosen in 1935 (so-called E-R bridge) There are many wormhole solutions in GR. A great variety of them! With static throat, dynamic throat, spinning, not spinning, etc Schwarzschild WHs (E-R bridges) The Morris-Thorne WH The Visser WH Higher-dimensional WH Brane WH

29. Schwarzschild WH the coordinate change

30. Traversable Wormholes Morris, Thorne, Yurtsever, Visser,..

31. Traversable Wormholes WH throat Absence of the event horizon For asymptotically flat WH The embedding condition together with the requirement of finiteness of the redshift function lead to the NEC violation on the WH throat

32. Energy Conditions Penrose, Hawking NEC is violated on the wormhole throat

33. WH in particles collisions DE shell WHBH

34. BH / WH Production at Accelerators ILC

35. Possible signatures of TeV higher- dimensional gravity: Black Hole/ Worm Hole production Thermal Hawking radiation Signs of strong quantum gravity “In more spherical” final states KK modes Extra heavy particles

36. BH/WH production. Assumptions Extra dimensions at TeV Classical geometric cross-section “Exotic” matter (Dark energy w<-1, Casimir, non-minimal coupling, …)

37. Conclusion TeV Gravity opens new channels – BHs, WHs WH production at LHC is of the same order of magnitude as BH production The important question on possible expe- rimental signatures of spacetime nontrivial objects deserves further explorations