Micro Black Holes beyond Einstein

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Micro Black Holes beyond Einstein
Julien GRAIN, Aurelien BARRAU Panagiota Kanti,
Stanislav Alexeev
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What micro-black holes say about new physics

• Astrophysics and Cosmology Primordial Black
  Holes (power spectrum, dark matter, etc.)
• Gauss-Bonnet Black holes at the LHC
• Black holes evaporation in a non-asymptotically
  flat space-time

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Black Holes evaporate

• Radiation spectrum
• Hawking evaporation law

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Micro Black holes at the LHC
We will see Lets hope!!!

• Gauss-Bonnet Black holes at the LHC
• Black holes evaporation in a non-asymptotically
  flat space-time

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

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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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Gauss-Bonnet Black Holes?

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

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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
• The statistical significance of the analysis
  should be taken with care

Barrau, Grain Alexeev Phys. Lett. B 584, 114
(2004)
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Kerr Gauss-bonnet Black Holes

• Black Holes formed at colliders are expected to
  be spinning
• The previous study should be done for
  spinning Black Holes
• Solve the Einstein equation with the Gauss-Bonnet
  term in the static, axisymmetric case

S. Alexeev, N. Popov, A. Barrau, J. Grain In
preparation
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Lets add a cosmological constant

• Gauss-Bonnet Black holes at the LHC
• Black holes evaporation in a non-asymptotically
  flat space-time

• P. Kanti, J. Grain, A. Barrau
• in preparation

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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)

• Two event horizons and
• No solution for with

• One event horizon
• Exist only 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
• in preparation

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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

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Derivation of the Kerr Gauss-Bonnet black holes
solution
S. Alexeev, N. Popov, A. Barrau, J. Grain In
preparation
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The Kerr-Schild metric-work in progress-

• Most convenient metric for axisymmetric problem
• Black holes angular momentum is paramatrized by
  a

Unknown metric function
Radial coordinate
Zenithal coordinate
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Deriving the metric function

• Method
• The kerr-schild metric is injected in the
  Einsteins equation
• The ur equation verified by ß is solved
• Compatibility for the other component is finally
  checked
• Boundary conditions

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Results and temperature calculation

• functions have been numerically
  obtained for
• The temperature is obtain from the gravity
  surface at the event horizon