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QUARKS-2008 15th International Seminar on High Energy Physics Sergiev Posad, Russia, 23-29 May, 2008 MICRO-BLACK HOLES and WORMHOLES AT THE LHC I.Ya.Aref`eva Steklov Mathematical Institute, Moscow 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) Outlook: • • • • TeV gravity Quantum Gravity Black holes Wormhole (WH) solutions • TIME MACHINES (CTCs) I.Volovich’s talk • Cross-sections and signatures at the LHC N. Arkani-Hamed, S. Dimopoulos, G.R. Dvali, I. Antoniadis, 1998 Hierarchy problem TeV Gravity M SM 1 TeV M D 1 TeV 1 D S d x g R( g ) GD GD 1 M S 1 D 4n D 2 D 1 Vn L n Mc n c If M 2 Pl M Pl 1.2 1016 TeV GNewton Vn M D 2 D 1 GNewton Vn GD MD n M ( ) Mc 2 D MD 1 M D2 M Pl2 Mc 4 d x g R( g ) GNewton 1 2 M Pl Extra Dimensions M 2 Pl MD n M ( ) Mc 2 D M Pl 2 / n Lc M ( ) MD 1 Lc Mc 1 D M Pl 1016 TeV 1 n 2, Lc 10 cm M D TeV n 4, Lc 10 9 cm n 6, Lc 10 12 cm LPl 10 33 cm, LSM 2 10 17 cm, Modification of the Newton law GNewton F m1m2 2 r GNewton F m1m2 2 r Vn GNewton F n m1m2 2 r r for r Lc for r Lc Possible signatures of TeV higherdimensional gravity: • Black Hole/Worm Hole production • Signs of strong quantum gravity • KK modes TeV Gravity = Quantum Gravity i h" , " , "| h' , ' , ' exp{ S[ g , ]} dg d, Sum over topol ogies ": hij " , " ; ': hij ' , ' , g |" h " , |" "; g | ' h ' , | ' ' I.A., K.S.Viswanathan, I.V.Volovich, Nucl.Phys., B 452,1995, 346 Wave functions: ' [h ', '] "[h ", "] Quantum Gravity =Summation over Topologies h" , "| h' , ' sum i exp{ S[ g , ]} dg , over topologies g |" h "; g | ' h ' No a coupling constant to suppress-out channels with nontrivial topology Summation over topologies h" , "| h' , ' sum i exp{ S[ g , ]} dg , over topologies g |" h "; g | ' h ' Theorem (Geroch, Tipler): Topology-changing spacetimes must have CTC (closed timelike curve) Particles to Black Holes/Worm holes particles | BH dh " d " dh ' d ' "[h ", "] h ", ", " | h ', ', ' ' [h ', '] Wave functions: ' [h ', '] particles "[h ", "] black hole BH in Collisions • 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 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 rs of a BH of mass E. • The Thorn's hoop conjecture gives a rough estimate for classical geometrical cross-section (1 1 BH ) ~ rS2 rS M BH M D2 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 D-dimensional Schwarzschild Solution 1 R g R T , , 0,1...D 1 2 1 rS D 3 2 rS D 3 2 2 2 ds 1 ( ) dt 1 ( ) dr r d D 2 r r 2 rS is the Schwarzschild radius 1 M BH BH rS BH ( D ) ( ) MD MD M BH E Meyers,… 1 BH D 3 1/( D 3) BH ( D) 1 8( D 1 / 2) D2 D-dimensional Aichelburg-Sexl Shock Waves c 2 i2 i 2 i ds dudv dx ( x ) (u) du , ( x ) D 4 Penrose, D’Eath, Eardley, Giddings,… Shock waves, Classical geometric cross-section rs2 BH Production in Particle Collisions at Colliders and Cosmic Rays b rS E D7 100 pb 1 / D 3 Thermal Hawking Radiation Decay via Hawking Radiation Emit particles following an approximately black body thermal spectrum M D 1/( D 3) D 3 D 3 TH MD( ) 4 rS 4 BH ( D) M BH Astronomic BH – cold - NO Evaporation Micro BH -- hot -- Evaporation microBH lifetime 1027 1025 s ec onds Micro-BH at Accelerators and parton structure ppBH 1 1 dx d fi ( x) f j ( / x) ij BH ( s) ij m x S – the square of energy (in c.m.) x , / x are the parton momentum fractions the parton distribution functions fi 2 2 m M min / s, M min minimum mass Similar to muon pair production in pp scattering, Matveyev - Muradyan-Tavkhelidze, 1969, JINR Drell-Yan process: pp-->e+e- + X Parton Distribution Functions pp X dx1 dx2 fi ( x1 ) fi ( x2 ) ij X ( x1 , x2 ) ij Q = 2 GeV for gluons (red), up (green), down (blue), and strange (violet) quarks 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 r0 (the Schwarzschild radius) Eardley, Yoshino, Randall Catalyze of BH production due to an anisotropy Dvali, Sibiryakov Colliding Plane Gravitational Waves I.A, Viswanathan, I.Volovich, 1995 Plane coordinates; Kruskal coordinates ds 2 = 4m 2 [1 + sin(uq(u)) + vq(v)]dudv - [1 - sin(uq(u)) + vq(v)][1 + sin(uq(u)) + vq(v)]-1dx 2 -[1 + sin(uq(u)) + vq(v)]2 cos 2 (uq(u)) - vq(v))dy 2 , where u < p /2, v < p /2, v + u < p /2 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? 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 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. Einstein-Rosen bridge Take Schwarzschild BH Take 2 copies of the region Kruskal diagram of the WH Discard the region inside the event horizon Glue these 2 copies of outside event horizon regions 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 The traveler just as a worm could take a shortcut to the opposite side of the universe through a topologically nontrivial tunnel. 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 Schwarzschild WH rS 2 rS 1 2 2 2 ds (1 )dt (1 ) dr r d2 r r 2 the coordinate change u 2 r rS 2 u 2 2 2 2 2 2 2 ds 2 dt 4(u rS )du (u rS ) d2 u rS Traversable Wormholes Morris, Thorne, Yurtsever, Visser,.. ds e 2 2 ( r ) 2 dr dt r 2 (d 2 sin 2 d 2 ) b( r ) 1 2 r 2 Traversable Wormholes ds e 2 WH throat 2 ( r ) dr 2 dt r 2 (d 2 sin 2 d 2 ) b( r ) 1 r 2 r0 r R b( r0 ) r0 For asymptotically flat WH R b' r b 0 1 b' r b b ' pr 2(1 ) 3 M Pl r r r Absence of the event horizon The embedding condition together with the requirement of finiteness of the redshift function lead to the NEC violation on the WH throat Energy Conditions NEC : T k k 0, k k 0 Singularit y theorems Penrose, Hawking w p / 1; 1.1 w 0.9 DE WMAP NEC is violated on the wormhole throat WH in particles collisions DE shell BH WH BH / WH Production at Accelerators ppBH 1 1 1 1 dx d f i ( x ) f i ( / x ) ijBH (s ) x ij m dx ppW H d f i ( x ) f i ( / x ) ijW H (s ) x ij m ILC Possible signatures of TeV higherdimensional gravity: • Black Hole/Worm Hole production Thermal Hawking radiation • Signs of strong quantum gravity “In more spherical” final states • KK modes Extra heavy particles BH/WH production. Assumptions • Extra dimensions at TeV • Classical geometric cross-section • “Exotic” matter (Dark energy w<-1, Casimir, non-minimal coupling, …) 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 experimental signatures of spacetime nontrivial objects deserves further explorations