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Black-Hole Bombs @LHC

Black-Hole Bombs @LHC. Jong -Phil Lee ( Yonsei Univ.) Based on 1104.0496. 연세대 특강 2011.5.12. Outlook. What is a Black Hole? Black-Hole Bomb(BHB) Mini Black Holes BHB @LHC. What is a black hole?. Escape velocity. What happens if gravity becomes very strong?. “Dark S tar”.

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Black-Hole Bombs @LHC

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  1. Black-Hole Bombs @LHC Jong-Phil Lee (Yonsei Univ.) Based on 1104.0496 연세대 특강 2011.5.12.

  2. Outlook • What is a Black Hole? • Black-Hole Bomb(BHB) • Mini Black Holes • BHB @LHC

  3. What is a black hole?

  4. Escape velocity What happens if gravity becomes very strong?

  5. “Dark Star” Pierre-Simon Laplace (1749~1827) If gravity is strong enough, even light could not escape the star.

  6. General Relativity “Matter tells spacetime how to curve, and spacetime tells matter how to move.” John Wheeler (1911~2008)

  7. Schwarzschild geometry Karl Schwarzschild (1873~1916)

  8. “Black Hole” by J. Wheeler The term black hole was coined in 1967 during a talk he gave at the NASA Goddard Institute of Space Studies (GISS). ---wikipedia John Wheeler (1911~2008)

  9. Schwarzschild black hole Schwarzschild radius Sun: R=2.95km Earth: R=8.86mm

  10. Other black holes

  11. Bekensteinand BH entropy The black hole area never decreases. • Black holes have entropy. • Black hole entropy is proportional to its area. SBH=A/4 Jacob Bekenstein(1947~) Generalized 2nd Law

  12. Hawking Radiation entropy ~ heat ~ radiation

  13. Summary of basic BH properties • There is a singularity inside a BH with infinite gravity. • There are event horizons for every BHs. • Even light cannot escape • from the inside of the horizon to outside. • Time goes slower as a clock approaches the horizon, • and stops at the horizon, for an outside observer. R=2GM/c2

  14. Cont’d • Black holes can have angular momentum and charges. • Black holes have ENTROPY. • The BH entropy is proportional to its horizontal area. • Black holes emit Hawking radiation. • The Hawking temperature is • inversely proportional to the BH mass.

  15. Black-hole bomb(BHB)

  16. Superradiance Rotational energy is extracted to the scattered particle. w W angular velocity Superradiance occurs when w < mW

  17. Scattering by Kerr BHs

  18. Black-Hole Bomb?! Press & Teukolsky, Nature 238(1972) Press-Teukolsky Black-Hole Bomb Mirror

  19. Mini black holes

  20. Hierarchy Problem WHY MW ~100GeV<<<< MP ~1019GeV? Planck mass Mp =$ @c/GN ~ 1019GeV~ 10-5g

  21. Extra Dimensions MP =(spatial effect)X M0 New fundamental scale ~1TeV Gravity is extended to extra dim’s.

  22. Randall-Sundrum Model(1999) • 5D-theory • 5th dimension is warped. 22

  23. Easy to make BH in XDs • Actual Planck mass is not so large. • >>> Actual gravitational constant is not so small. • >>> Small mss is enough to produce BH. • >>> BH can be produced at low energy. • >>> LHC can produce BH!

  24. “Mini Black Holes”:properties Schwarzschild radius Hawking temperature Typical lifetime

  25. Searches for mini BH @LHC(CMS) CMS, PLB697(2010)

  26. CMS results s upper limit Below the curves is excluded.

  27. Scalar emission by mini BH Kanti & Papps, PRD82 superradiance

  28. Bhb @LHC

  29. Superradiance+Mirror=BHB Mirror

  30. Kerr BH in higher dim’s metric Schwarzschild radius (angular velocity)

  31. Scalar scattering Klein-Gordon equation in curved space Separation of variables

  32. radial equation angular equation

  33. Near-horizon region Change of variable

  34. Near-horizon solution Hypergeometric function

  35. Far-field region Change of variable Bessel function

  36. Matching the two regions Near-horizon solution = Far-field solution

  37. Mirror boundary condition

  38. Approximation ~ For a very small value of w : Zeros of Bessel function

  39. Imaginary part of frequency Field amplification

  40. Setup Range of w Minimum value of the mirror location

  41. dvswrh(Brane emission)

  42. Some parameters

  43. Brane emission for m0=120 GeV

  44. Bulk emission (preliminary) m0=0.14 GeV m0=120 GeV

  45. BHB efficiency BH thermodynamics D MBH =W D J At some point the superradiance stops when

  46. Conclusions • Rotating mini BHs can undergo the superradiance. • If the emitted particles are reflected by a mirror, • the system can be a Bomb. • LHC could produce the BHB.

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