Mini Black Holes and extra-dimensions

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Mini Black Holes and extra-dimensions
Aurélien BARRAU Julien GRAIN
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Black Holes evaporate

• Radiation spectrum
• Hawking evaporation law

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Small black holes in astrophysics PBHs
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PBH could have formed in the early universe

• Standard mass spectrum in the early universe
• Softening of the equation of state (Canuto ,
  Khlopov)
• Quasi-critical phenomenon (Choptuik)
• Double inflation (Khlopov)
• Phase transition (Hawking , Steinhardt , Khlopov)

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Direct antiprotons emission

• Individual emission
• Convoluted with the mass spectrum today

Initial spectrum
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Source flux
(1)
(2)
(3)
FLUX
(4)
main contribution from
antiprotons kinetic energy (GeV)
No influence of the details of the formation
mechanism
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Let antiprotons propagate in the Milky Way
Diffusive halo with convection and nuclear
reactions
Galactic disc where sources are located
Drawing by D. Maurin
Maurin, Taillet, Donato, Salati, Barrau, Boudoul,
review article for Research Signapost (2002)
astro-ph/0212111
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Primary and secondary antiprotons

• Solve a diffusion equation for PBHs antiprotons
  AND secondary antiprotons coming from nuclear
  reaction on the ISM
• And taking into account the diffusion in energy
  (tertiary contribution)

p-p interaction
p-He interaction
He-p interaction
He-He interaction
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TOA fluxes and upper limit on PBH density
Experimental data points
Secondary antiprotons flux standard physics
only
PBH antiprotons flux for different values of
PBHs density
F.Donato, D. Maurin, P. Salati, A. Barrau, G.
Boudoul, R.Taillet Astrophy. J. (2001) 536, 172
A. Barrau, G. Boudoul et al., Astronom.
Astrophys., 388, 767 (2002)
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Another probe gamma rays

• Data
• EGRET flux at 100 MeV
• Gamma rays noise
• (Pavlidou Fields, ApJ 575, L5-8 (2002))
• - galaxies
• - quasars

PBH emission (direct neutral pions decay),
with an integration over redshift

?PBH lt 3.3??10 9 A. Barrau G. Boudoul, ICRC
2003 proc., astro-ph/0304528
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Cosmological consequences
Unlike the CMB or the large scale structures, PBH
give informations on small scale
PRIMORDIAL BLACK HOLES ARE A UNIQUE COSMOLOGICAL
PROBE
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Cosmological constrainPBH fraction ß
PBHs are the only way to constrain small scales
in the primordial power spectrum
Hypothesis bump in the mass variance (
Starobinsky , Polarski )
Antiprotons constrains
Barrau, Blais, Boudoul, Polarski, Phys. Lett. B,
551, 218 (2003)
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Particle physics beyond the standard model with
black holes ?

• To avoid entropy overproduction, an upper limit
  on Trh is obtainted with gravitinos
• If cosmic-rays from PBHs are detected, it leads
  to an upper limit on the Hubble mass at reheating
  so it leads to a lower limit on Trh
• Combining both lead to constrains on the
  gravitino mass

Lower limit on the gravitino mass as a function
of the PBH induced cosmic rays flux
A. Barrau N. Ponthieu Phys. Rev. D 69, 085010
(2004) , hep-ph/0402187
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PERSPECTIVES
Gravitinos emission from PBHs

• nlt1.18 the most stringent limit at small scale
• Positive running excluded

M. Khlopov, A. Barrau, astro-ph/0406621
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Detection of PBHAntideuterons

• Future experiment like AMS will measure the
  antideuteron flux
• Improvement factor 10 in sensitivity

evaporation
Window for detection
New physics
Secondary anti(D)
A. Barrau, S. Alexeyev, et al. Class. Quantum
Grav. 19 (2002) 4431
A. Barrau, G. Boudoul, et al. Astronom.
Astrophys. 398, 403 (2003)
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Mini Black holes at the LHC a delight for new
physics !

• A. Barrau, J. Grain S. Alexeev
• Phys. Lett. B 584, 114-122 (2004)

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Black Holes at the LHC ?

• Hierarchy problem in standard physics
• One of the solutions
• Large extra dimensions

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Black Holes Creation
From Giddings al. (2002)

• Two partons with a center-of-mass energy
  moving in opposite direction
• A black hole of mass and
  horizon radius is formed if the impact
  parameter is lower than

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Precursor Works
Giddings, Thomas Phys. Rev. D 65, 056010
(2002) Dimopoulos, Landsberg Phys. Rev. Lett 87,
161602 (2001)

• Computation of the black holes formation
  cross-section
• Derivation of the number of black holes produced
  at the LHC
• Determination of the dimensionnality of space
  using Hawkings law

From Dimopoulos al. 2001
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Interesting idea using mini black holes a
resonances
Sigma 1 TeV -2 400 pbarn !

• Search for SUSY particles
• Search for light Higgs

From Dimopoulos al. 2001
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Gauss-Bonnet Black Holes?

• All previous works have used D-dimensionnal
  Schwarzschild black holes
• General Relativity
• Low energy limit of String Theory

A. Barrau, J. Grain S. Alexeev Phys. Lett. B
584, 114-122 (2004)
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Gauss-Bonnet Black Holes Thermodynamic (1)

• Properties derived by

• Boulware, Deser Phys. Rev. Lett. 83, 3370
  (1985)
• Cai Phys. Rev. D 65, 084014 (2002)

Expressed in function of the horizon radius
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Gauss-Bonnet Black holes Thermodynamic (2)

• Non-monotonic behaviour
• taking full benefit of evaporation process
• (integration over black holes lifetime)

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The flux Computation

• Analytical results in the high energy limit
• The grey-body factors are constant
• is the most convenient variable

Harris, Kanti JHEP 010, 14 (2003)
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The Flux Computation (ATLAS detection)

• Planck scale 1TeV
• Number of Black Holes produced at the LHC derived
  by Landsberg
• Hard electrons, positrons and photons sign the
  Black Hole decay spectrum
• ATLAS resolution

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The Results -measurement procedure-

• For different input values of (D,?), particles
  emitted by the full evaporation process are
  generated
• spectra are reconstructed for each mass
  bin
• A analysis is performed

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The Results-discussion-

• For a planck scale of order a TeV, ATLAS can
  distinguish between the case with and the case
  without Gauss-Bonnet term.
• Important progress in the construction of a full
  quantum theory of gravity
• The results can be refined by taking into account
  more carefully the endpoint of Hawking
  evaporation

Barrau, Grain Alexeyev Phys. Lett. B 584, 114
(2004)
Dark matter candidate
Barrau et al., Ann. Phys. (2004)
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Lets add a cosmological constant
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(A)dS Universe
Cosmological constant
De Sitter (dS) Universe
Anti-De Sitter (AdS) Universe

• Positive cosmological constant
• Presence of an event horizon at

• Negative cosmological constant
• Presence of closed geodesics

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Black Holes in such a space-time
Metric function h(r)

• One event horizon
• Exist only for with

• Two event horizons and
• No solution for with

De Sitter (dS) Universe
Anti-De Sitter (AdS) Universe
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Calculation of Greybody factors (1)

• A potential barrier appears in the equation of
  motion of fields around a black hole
• Black holes radiation spectrum is decomposed into
  three part

De Sitter horizon
Potential barrier
Tortoise coordinate
Black holes horizon
Break vacuum fluctuations
Cross the potential barrier
Phase space term
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Calculation of Greybody factors (2)
De Sitter horizon
Analytical calculations
Numerical calculations
Equation of motion analytically solved at the
black holes and the de Sitter horizon
Equation of motion numerically solved from black
holes horizon to the de Sitter one
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Calculation of Greybody factors -results for
scalar in dS universe-
d4
The divergence comes from the presence of two
horizons
P. Kanti, J. Grain, A. Barrau, Phys. Rev. D 71
(2005) 104002
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Flux
Greybody factors in dS spacetime
http//lpsc.in2p3.fr/ams/greybody
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Perspectives
Compatibility with astrophysical and cosmological
data OK
A. Barrau, C. feron, J. Grain, in press for
Astrophys. J. (2005)

• Computations for fermions in dS spacetime (Grain,
  Kanti, Barrau)
• Computations for bosons and fermions in AdS
  spacetime (Grain, Kanti, Barrau)
• Investigation of the LHC signals (Labbé, Grain,
  Barrau)
• Gravitationnal blueshift (Barrau, Muteau-Jaouen)

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Conclusion
Big black holes are fascinating
But small black holes are far more fascinating!!!
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Primordial Black holes in our Galaxy

• F.Donato, D. Maurin, P. Salati, A. Barrau, G.
  Boudoul, R.Taillet
• Astrophy. J. (2001) 536, 172
• A. Barrau, G. Boudoul et al.,
• Astronom. Astrophys., 388, 767 (2002)
• Astrophys. 398, 403 (2003)
• Barrau, Blais, Boudoul, Polarski,
• Phys. Lett. B, 551, 218 (2003)

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Cosmological constrain using PBH

• Small black holes could have been formed in the
  early universe
• Stringent constrains on the amount of PBH in the
  galaxy
• The anti-proton flux emitted by PBH is evaluating
  using an improved propagation scheme for cosmic
  rays
• This leads to constrain on the PBH fraction
• New window of detection using low energy
  anti-deuteron