MICRO-BLACK HOLES and WORMHOLES AT THE LHC

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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I.A., K.S.Viswanathan,I.V.Volovich,Nucl.Phys., B 452,1995, 346

Wave functions: '[ ', ']h "[ ", "]h

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dggSi

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No a coupling constant to suppress-out channels with nontrivial topology

Quantum Gravity =Summation over Topologies

Summation over topologies

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'" hghg

dggSi

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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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particles BH

dh d dh d h

h h h

Wave functions:'[ ', ']h particles

"[ ", "]h black hole

• 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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2BH

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Mr

M

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

22

221

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D-dimensional Schwarzschild Solution

Schwarzschild radiusSr is the

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BH

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D-dimensional Aichelburg-Sexl Shock Waves

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Shock waves, Penrose, D’Eath, Eardley, Giddings,…

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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MD DT M

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Astronomic BH – cold - NO EvaporationMicro BH -- hot -- Evaporation

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Micro-BH at Accelerators and parton structure 1 1

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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 ,/

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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dtrr

ds SS

22

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22

2

)()(4

drudurudtru

uds

rru

SSS

S

the coordinate change

Traversable Wormholes

Morris, Thorne, Yurtsever, Visser,..

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1

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2

22)(22 ddr

rrb

drdteds r

Traversable Wormholes

)sin()(

1

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2)(22 ddr

rrb

drdteds r

WH throat

Rrr 0

00 )( rrb

0' brbAbsence of the event horizon

For asymptotically flat WH

R

rrb

rbrb

Mp

Plr

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'13

The embedding condition together with the requirement of finiteness of theredshift function lead to the NEC violation on the WH throat

Energy Conditions

theoremsySingularitkkkkTNEC 0,0:

Penrose, Hawking

WMAPDEw

pw

9.01.1

;1/

NEC is violated on the wormhole throat

WH in particles collisions

DE shell

WH BH

BH / WH Production at Accelerators

)()/()(1 1

sxfxfxdx

d BHijiiij

BHpp

m

)()/()(1 1

sxfxfxdx

d WHijiiij

WHpp

m

ILC

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