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
Jan 14, 2016
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
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
TeV Gravity
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Possible signatures of TeV higher-dimensional gravity:
• Black Hole/Worm Hole production
• Signs of strong quantum gravity
• KK modes
TeV Gravity = Quantum Gravity
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Quantum Gravity =Summation over Topologies
Summation over topologies
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Theorem (Geroch, Tipler):Topology-changing spacetimes must have CTC (closed timelike curve)
Particles to Black Holes/Worm holes
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Wave functions:'[ ', ']h particles
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• 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
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
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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
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Classical geometric cross-section 2sr
BH Production in Particle Collisions at Colliders and Cosmic Rays
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Thermal Hawking Radiation
Decay via Hawking Radiation
Emit particles following an approximately black body thermal spectrum
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Micro-BH at Accelerators and parton structure 1 1
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xx /, are the parton momentum fractionsthe parton distribution functions
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Drell-Yan process: pp-->e+e- + X
Similar to muon pair production in pp scattering,Matveyev - Muradyan-Tavkhelidze, 1969, JINR
1 2 1 2 1 2( ) ( ) ( , )pp X i i ij Xij
dx dx f x f x x x
Parton Distribution Functions
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
Regions II and III contain the approaching plane waves. In the region IV the metric (4) is isomorphic to the Schwarzschild metric.
2 2
-1 2
2 2 2
ds = 4m [1 + sin(u (u)) + v (v)]dudv
- [1 - sin(u (u)) + v (v)][1 + sin(u (u)) + v (v)] dx
-[1 + sin(u (u)) + v (v)] cos (u (u)) - v (v))dy ,
q q
q q q q
q q q qwhere u < /2, v < /2, v + u < /2p p p
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 itscenter, instead of traveling the entire distance around.
Einstein-Rosen bridge
The embedding diagram of the Schwarzschild WH seems to show a static WH. However, this is an illusionof 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
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
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Traversable Wormholes
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For asymptotically flat WH
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The embedding condition together with the requirement of finiteness of theredshift function lead to the NEC violation on the WH throat
Energy Conditions
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NEC is violated on the wormhole throat
WH in particles collisions
DE shell
WH BH
BH / WH Production at Accelerators
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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 modesExtra 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 expe-
rimental signatures of spacetime nontrivial objects deserves further explorations