BlackHole Bombs LHC JongPhil Lee Yonsei Univ Based
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 2
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Escape velocity What happens if gravity becomes very strong? 4
“Dark Star” Pierre-Simon Laplace (1749~1827) If gravity is strong enough, even light could not escape the star. 5
General Relativity “Matter tells spacetime how to curve, and spacetime tells matter how to move. ” John Wheeler (1911~2008) 6
Schwarzschild geometry Karl Schwarzschild (1873~1916) 7
“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) 8
Schwarzschild black hole Schwarzschild radius Sun: R=2. 95 km Earth: R=8. 86 mm 9
Other black holes charge angular momentum species X X Schwarzschild BH X O Kerr BH O X Reissner-Nordström BH O O Kerr-Newman BH 10
Bekenstein and BH entropy The black hole area never decreases. • Black holes have entropy. • Black hole entropy is proportional to its area Jacob Bekenstein(1947~) Generalized 2 nd Law SBH=A/4 11
Hawking Radiation entropy ~ heat ~ radiation 12
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=2 GM/c 2 13
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. 14
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Superradiance Rotational energy is extracted to the scattered particle. w W Superradiance occurs when angular velocity w < m. W 16
Scattering by Kerr BHs 17
Black-Hole Bomb? ! Mirror Press & Teukolsky, Nature 238(1972) Press-Teukolsky Black-Hole Bomb 18
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Hierarchy Problem WHY MW ~100 Ge. V<<<< MP ~1019 Ge. V? Planck mass Mp =$ @c/GN ~ 1019 Ge. V ~ 10 -5 g 20
Extra Dimensions MP =(spatial effect)X M 0 New fundamental scale Gravity is extended to extra dim’s. ~1 Te. V 21
Randall-Sundrum Model(1999) • 5 D-theory • 5 th dimension is warped. 22 22
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! 23
“Mini Black Holes”: properties Schwarzschild radius Hawking temperature Typical lifetime 24
Searches for mini BH @LHC(CMS) CMS, PLB 697(2010) 25
CMS results s upper limit Below the curves is excluded. 26
Scalar emission by mini BH Kanti & Papps, PRD 82 superradiance 27
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Superradiance+Mirror=BHB Mirror 29
Kerr BH in higher dim’s metric Schwarzschild radius (angular velocity) 30
Scalar scattering Klein-Gordon equation in curved space Separation of variables 31
radial equation angular equation 32
Near-horizon region Change of variable 33
Near-horizon solution Hypergeometric function 34
Far-field region Change of variable Bessel function 35
Matching the two regions Near-horizon solution = Far-field solution 36
Mirror boundary condition 37
Approximation For a very small value of ~: w Zeros of Bessel function 38
Imaginary part of frequency Field amplification 39
Setup Range of w Minimum value of the mirror location 40
d vs wrh (Brane emission) 41
Some parameters 42
Brane emission for m 0=120 Ge. V 43
Bulk emission (preliminary) m 0=0. 14 Ge. V m 0=120 Ge. V 44
BHB efficiency BH thermodynamics D MBH = W D J At some point the superradiance stops when 45
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. 46
- Slides: 46