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Micro Black Holes beyond Einstein

Micro Black Holes beyond Einstein. Julien GRAIN, Aurelien BARRAU Panagiota Kanti, Stanislav Alexeev. 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

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Micro Black Holes beyond Einstein

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  1. Micro Black Holes beyond Einstein Julien GRAIN, Aurelien BARRAU Panagiota Kanti, Stanislav Alexeev

  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. 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 Micro Black holes at the LHC We will see… Let’s hope!!!

  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

  6. Black Holes Creation • 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 From Giddings & al. (2002)

  7. 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 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:

  9. 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

  10. Gauss-Bonnet Black holes’ Thermodynamic (2) Non-monotonic behaviour taking full benefit of evaporation process (integration over black hole’s lifetime)

  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)

  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

  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

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

  17. Positive cosmological constant Presence of an event horizon at Negative cosmological constant Presence of closed geodesics (A)dS Universe Cosmological constant De Sitter (dS) Universe Anti-De Sitter (AdS) Universe

  18. Two event horizons and No solution for with One event horizon Exist only for with Black Holes in such a space-time Metric function h(r) 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- d=4 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

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