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. 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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Black-Hole Bombs @LHC

Jong-Phil Lee (Yonsei Univ.)

Based on 1104.0496

연세대 특강



  • 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 Star”

Pierre-Simon Laplace


If gravity is strong enough,

even light could not escape the star.

General Relativity

“Matter tells spacetime

how to curve,


spacetime tells matter

how to move.”

John Wheeler


Schwarzschild geometry

Karl Schwarzschild (1873~1916)

“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).


John Wheeler (1911~2008)

Schwarzschild black hole

Schwarzschild radius

Sun: R=2.95km

Earth: R=8.86mm

Other black holes

Bekensteinand BH entropy

The black hole area never decreases.

  • Black holes have entropy.

  • Black hole entropy is proportional to its area.


Jacob Bekenstein(1947~)

Generalized 2nd Law

Hawking Radiation

entropy ~ heat ~ radiation

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.



  • 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.

Black-hole bomb(BHB)


Rotational energy is extracted to the scattered particle.



angular velocity

Superradiance occurs when

w < mW

Scattering by Kerr BHs

Black-Hole Bomb?!

Press & Teukolsky, Nature 238(1972)

Press-Teukolsky Black-Hole Bomb


Mini black holes

Hierarchy Problem


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

Planck mass

Mp =$ @c/GN

~ 1019GeV~ 10-5g

Extra Dimensions

MP =(spatial effect)X M0

New fundamental scale


Gravity is extended

to extra dim’s.

Randall-Sundrum Model(1999)

  • 5D-theory

  • 5th dimension is warped.


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!

“Mini Black Holes”:properties

Schwarzschild radius

Hawking temperature

Typical lifetime

Searches for mini BH @LHC(CMS)

CMS, PLB697(2010)

CMS results

s upper limit

Below the curves is excluded.

Scalar emission by mini BH

Kanti & Papps, PRD82


Bhb @LHC



Kerr BH in higher dim’s


Schwarzschild radius

(angular velocity)

Scalar scattering

Klein-Gordon equation in curved space

Separation of variables

radial equation

angular equation

Near-horizon region

Change of variable

Near-horizon solution

Hypergeometric function

Far-field region

Change of variable

Bessel function

Matching the two regions

Near-horizon solution = Far-field solution

Mirror boundary condition



For a very small value of w :

Zeros of Bessel function

Imaginary part of frequency

Field amplification


Range of w

Minimum value of the mirror location

dvswrh(Brane emission)

Some parameters

Brane emission for m0=120 GeV

Bulk emission (preliminary)

m0=0.14 GeV

m0=120 GeV

BHB efficiency

BH thermodynamics


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.

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