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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

Jong-Phil Lee (Yonsei Univ.)

Based on 1104.0496

연세대 특강

2011.5.12.


Outlook
Outlook

  • What is a Black Hole?

  • Black-Hole Bomb(BHB)

  • Mini Black Holes

  • BHB @LHC



Escape velocity
Escape velocity

What happens if gravity

becomes very strong?


Dark s tar
“Dark Star”

Pierre-Simon Laplace

(1749~1827)

If gravity is strong enough,

even light could not escape the star.


General relativity
General Relativity

“Matter tells spacetime

how to curve,

and

spacetime tells matter

how to move.”

John Wheeler

(1911~2008)


Schwarzschild geometry
Schwarzschild geometry

Karl Schwarzschild (1873~1916)


Black hole by j wheeler
“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)


Schwarzschild black hole
Schwarzschild black hole

Schwarzschild radius

Sun: R=2.95km

Earth: R=8.86mm



Bekenstein and bh entropy
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


Hawking radiation
Hawking Radiation

entropy ~ heat ~ radiation


Summary of basic bh properties
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


Cont d
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.



Superradiance
Superradiance

Rotational energy is extracted to the scattered particle.

w

W

angular velocity

Superradiance occurs when

w < mW



Black hole bomb
Black-Hole Bomb?!

Press & Teukolsky, Nature 238(1972)

Press-Teukolsky Black-Hole Bomb

Mirror



Hierarchy problem
Hierarchy Problem

WHY

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

Planck mass

Mp =$ @c/GN

~ 1019GeV~ 10-5g


Extra dimensions
Extra Dimensions

MP =(spatial effect)X M0

New fundamental scale

~1TeV

Gravity is extended

to extra dim’s.


Randall sundrum model 1999
Randall-Sundrum Model(1999)

  • 5D-theory

  • 5th dimension is warped.

22


Easy to make bh in xds
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
“Mini Black Holes”:properties

Schwarzschild radius

Hawking temperature

Typical lifetime



Cms results
CMS results

s upper limit

Below the curves is excluded.


Scalar emission by mini bh
Scalar emission by mini BH

Kanti & Papps, PRD82

superradiance


Bhb @lhc
Bhb @LHC



Kerr bh in higher dim s
Kerr BH in higher dim’s

metric

Schwarzschild radius

(angular velocity)


Scalar scattering
Scalar scattering

Klein-Gordon equation in curved space

Separation of variables


radial equation

angular equation


Near horizon region
Near-horizon region

Change of variable


Near horizon solution
Near-horizon solution

Hypergeometric function


Far field region
Far-field region

Change of variable

Bessel function


Matching the two regions
Matching the two regions

Near-horizon solution = Far-field solution



Approximation
Approximation

~

For a very small value of w :

Zeros of Bessel function


Imaginary part of frequency
Imaginary part of frequency

Field amplification


Setup
Setup

Range of w

Minimum value of the mirror location


D vs w r h brane emission
dvswrh(Brane emission)



Brane emission for m 0 120 gev
Brane emission for m0=120 GeV


Bulk emission preliminary
Bulk emission (preliminary)

m0=0.14 GeV

m0=120 GeV


Bhb efficiency
BHB efficiency

BH thermodynamics

D MBH =W D J

At some point the superradiance stops when


Conclusions
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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