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Black-Hole Bombs @LHC

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Black-Hole Bombs @LHC

Jong-Phil Lee (Yonsei Univ.)

Based on 1104.0496

연세대 특강

2011.5.12.

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

What happens if gravity

becomes very strong?

Pierre-Simon Laplace

(1749~1827)

If gravity is strong enough,

even light could not escape the star.

“Matter tells spacetime

how to curve,

and

spacetime tells matter

how to move.”

John Wheeler

(1911~2008)

Karl Schwarzschild (1873~1916)

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)

Schwarzschild radius

Sun: R=2.95km

Earth: R=8.86mm

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

entropy ~ heat ~ radiation

- 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

- 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.

Rotational energy is extracted to the scattered particle.

w

W

angular velocity

Superradiance occurs when

w < mW

Press & Teukolsky, Nature 238(1972)

Press-Teukolsky Black-Hole Bomb

Mirror

WHY

MW ~100GeV<<<< MP ~1019GeV?

Planck mass

Mp =$ @c/GN

~ 1019GeV~ 10-5g

MP =(spatial effect)X M0

New fundamental scale

~1TeV

Gravity is extended

to extra dim’s.

- 5D-theory
- 5th dimension is warped.

22

- 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!

Schwarzschild radius

Hawking temperature

Typical lifetime

CMS, PLB697(2010)

s upper limit

Below the curves is excluded.

Kanti & Papps, PRD82

superradiance

Mirror

metric

Schwarzschild radius

(angular velocity)

Klein-Gordon equation in curved space

Separation of variables

radial equation

angular equation

Change of variable

Hypergeometric function

Change of variable

Bessel function

Near-horizon solution = Far-field solution

~

For a very small value of w :

Zeros of Bessel function

Field amplification

Range of w

Minimum value of the mirror location

m0=0.14 GeV

m0=120 GeV

BH thermodynamics

D MBH =W D J

At some point the superradiance stops when

- 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.