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

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

Black Holes evaporate Radiation spectrum Hawking evaporation law

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, 114-122 (2004) S. Alexeev, N. Popov, A. Barrau, J. Grain In preparation

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

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

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

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

Gauss-Bonnet Black Holes’ Thermodynamic (1) Properties derived by: Boulware, Deser Phys. Rev. Lett. 83, 3370 (1985) Cai Phys. Rev. D 65, 084014 (2002) Propriété dérive par Cai Toujours exprimer en terme de l’horizon du trou noir. Expressed in function of the horizon radius

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

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

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

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

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)

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

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

(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

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

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

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

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

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

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)

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

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

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

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

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