1. Micro Black Holes beyond Einstein
Julien GRAIN, Aurelien BARRAU
Panagiota Kanti, Stanislav Alexeev
Je me presente
Je presente le travail

2. 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 hole’s evaporation in a non-asymptotically flat space-time

3. Black Holes evaporate
Radiation spectrum
Hawking evaporation law

4. Micro Black holes at the LHC
We will see…
Let’s hope!!!
Gauss-Bonnet Black holes at the LHC
Black hole’s evaporation in a non-asymptotically flat space-time
A. Barrau, J. Grain & S. Alexeev
Phys. Lett. B 584, (2004)
S. Alexeev, N. Popov, A. Barrau, J. Grain
In preparation

5. Arkani-Hamed, Dimopoulos, Dvali Phys. Lett. B 429, 257 (1998)
Black Holes at the LHC ?
Hierarchy problem in standard physics:
One of the solutions:
Large extra dimensions
Arkani-Hamed, Dimopoulos, Dvali Phys. Lett. B 429, 257 (1998)
J’explique le pb de la hierarchie
Parmi les solutions:ADD RS
Possibilite d’abaisser l’échelle de planck, expliquer le Vd-4 et Md

6. 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
Processus a seuil: au LHC l’energie > Md
expliquer le schema

7. Precursor Works
Giddings, Thomas Phys. Rev. D 65, (2002)
Dimopoulos, Landsberg Phys. Rev. Lett 87, (2001)
Computation of the black hole’s formation cross-section
Derivation of the number of black holes produced at the LHC
Determination of the dimensionnality of space using Hawking’s law
Parler de Landsberg et giddings
Donner leur resultats:section efficace
nombre de BH produits
evaporation, l’expliquer, peut etre ils ne le savent pas  loi de hawking donne la dimension
prenne en compte une evaporation instantanée
From Dimopoulos & al. 2001

8. Gauss-Bonnet Black Holes?
All previous works have used D-dimensionnal Schwarzschild black holes
General Relativity:
Low energy limit of String Theory:
Toujours utiliser les schwarzschild generalisés
RS et ADD viennent de la theorie des cordes
Le terme de GB vient aussi de cette theorie
 Plus coherent

9. Gauss-Bonnet Black Holes’ Thermodynamic (1)
Properties derived by:
Boulware, Deser Phys. Rev. Lett. 83, (1985)
Cai Phys. Rev. D 65, (2002)
Propriété dérive par Cai
Toujours exprimer en terme de l’horizon du trou noir.
Expressed in function of the horizon radius

10. Gauss-Bonnet Black holes’ Thermodynamic (2)
Non-monotonic behaviour
taking full benefit of evaporation process
(integration over black hole’s lifetime)
Temperature en fonction de la masse
Comportement non monotone donc utiliser le processus d’evaporation dans son ensemble

11. 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)
Hypothese des tres haute energy, ce qui est justifier car les trous npoirs formes sont deja tres chaud
Horizon est la variable la plus adapte
Prise en compte de l’evolution temporelle du BH

12. 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
Exemple de flux
Il semblerait qu’il y ait des degenerescences mais on verra que les valeurs de D et lambda peuvent etre reconstruite
Mplanck=1tev
Utilisation des photons, e+ et e- de hautes energy car: hadron affecte par la fragmentation
phptpn, e+ et e- de hautes energy pas affectes par les produits de la fragmentation
Resolution de ATLAS

13. 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
Valeur differentes du couple D et lambda
Reconstruction des spectres mesure par ATLAS
Analyse de chi2 avec les modeles theoriques
Exemple de D=8 et lambda=5
marche bien, meme resultat dans les autres cas

14. 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
ATLAS pourra mesurer Lambda et D
Prendre mieux en compte la fin de vie
Faire attention au chi2
Barrau, Grain & Alexeev
Phys. Lett. B 584, 114 (2004)

15. 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

16. Let’s add a cosmological constant
Gauss-Bonnet Black holes at the LHC
Black hole’s evaporation in a non-asymptotically flat space-time
P. Kanti, J. Grain, A. Barrau
in preparation

17. (A)dS Universe De Sitter (dS) Universe Anti-De Sitter (AdS) 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

18. 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

19. 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
Tortoise coordinate
Potential barrier
Black hole’s horizon
Break vacuum fluctuations
Cross the potential barrier
Phase space term

20. Calculation of Greybody factors (2)
De Sitter horizon
Analytical calculations
Numerical calculations
Equation of motion analytically solved at the black hole’s and the de Sitter horizon
Equation of motion numerically solved from black hole’s horizon to the de Sitter one

21. Calculation of Greybody factors -results for scalar in dS universe-
The divergence comes from the presence of two horizons
P. Kanti, J. Grain, A. Barrau
in preparation

22. Conclusion Big black holes are fascinating…
But small black holes are far more fascinating!!!

23. 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)

24. 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

25. Derivation of the Kerr Gauss-Bonnet black holes solution
S. Alexeev, N. Popov, A. Barrau, J. Grain
In preparation

26. The Kerr-Schild metric -work in progress-
Most convenient metric for axisymmetric problem:
Black hole’s angular momentum is paramatrized by a
Unknown metric function
Radial coordinate
Zenithal coordinate

27. Deriving the metric function
Method:
The kerr-schild metric is injected in the Einstein’s equation
The ur equation verified by β is solved
Compatibility for the other component is finally checked
Boundary conditions

28. Results and temperature calculation
functions have been numerically obtained for
The temperature is obtain from the gravity surface at the event horizon