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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  4n
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) 


  D2 
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
D7

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
1027  1025 s ec onds
Micro-BH at Accelerators and parton structure
 ppBH
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 d2
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 ) d2
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
 ppBH
1
1
1
1
dx
   d 
f i ( x ) f i ( / x ) ijBH (s )
x
ij  m

dx
 ppW H    d 
f i ( x ) f i ( / x ) ijW 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