연세대 특강

2 What is a Black Hole? Black-Hole Bomb(BHB) Mini Black Holes

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4 What happens if gravity becomes very strong?

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

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

7 Karl Schwarzschild (1873~1916)

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

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

10 chargeangular momentumspecies XX Schwarzschild BH XO Kerr BH OX Reissner-Nordström BH OO Kerr-Newman BH

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

12 entropy ~ heat ~ radiation

13 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 / c 2

14 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.

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16    m  Superradiance occurs when Rotational energy is extracted to the scattered particle. angular velocity

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

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20 WHY M W ~100GeV <<<< M P ~10 19 GeV? Planck mass Mp = G N   GeV   g

21 M P =(spatial effect)X M 0 New fundamental scale ~ 1TeV Gravity is extended to extra dim’s.

22 5D-theory 5 th dimension is warped.

23 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 Schwarzschild radius Hawking temperature Typical lifetime

25 CMS, PLB697(2010)

26  upper limit Below the curves is excluded.

27 Kanti & Papps, PRD82 superradiance

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29 Mirror

30 metric Schwarzschild radius(angular velocity)

31 Klein-Gordon equation in curved space Separation of variables

32 radial equation angular equation

33 Change of variable

34 Hypergeometric function

35 Change of variable Bessel function

36 Near-horizon solution = Far-field solution

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38 For a very small value of  ~ Zeros of Bessel function

39 Field amplification

40 Range of  Minimum value of the mirror location

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44 m 0 =0.14 GeVm 0 =120 GeV

45  M BH =  J BH thermodynamics At some point the superradiance stops when

46 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.