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

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 Star”

Pierre-Simon Laplace

(1749~1827)

If gravity is strong enough,

even light could not escape the star.


General Relativity

“Matter tells spacetime

how to curve,

and

spacetime tells matter

how to move.”

John Wheeler

(1911~2008)


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).

---wikipedia

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.

SBH=A/4

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.

R=2GM/c2


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.


Black-hole bomb(BHB)


Superradiance

Rotational energy is extracted to the scattered particle.

w

W

angular velocity

Superradiance occurs when

w < mW


Scattering by Kerr BHs


Black-Hole Bomb?!

Press & Teukolsky, Nature 238(1972)

Press-Teukolsky Black-Hole Bomb

Mirror


Mini black holes


Hierarchy Problem

WHY

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

Planck mass

Mp =$ @c/GN

~ 1019GeV~ 10-5g


Extra Dimensions

MP =(spatial effect)X M0

New fundamental scale

~1TeV

Gravity is extended

to extra dim’s.


Randall-Sundrum Model(1999)

  • 5D-theory

  • 5th dimension is warped.

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!


“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

superradiance


Bhb @LHC


Superradiance+Mirror=BHB

Mirror


Kerr BH in higher dim’s

metric

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


Approximation

~

For a very small value of w :

Zeros of Bessel function


Imaginary part of frequency

Field amplification


Setup

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

D MBH =W D J

At some point the superradiance stops when


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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