Rotating BHs at future colliders: Greybody factors for brane fields

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Rotating BHs at future collidersGreybody
factors for brane fields

• Kin-ya Oda, Tech. Univ. Munich

with S. Park and D. Ida hep-th/0212108, to
appear in PRD

• Why Study BHs at Collider?
• BH at Collider (Basic Facts)
• Production
• BHs are produced with large angular momenta.
• (Black ring formation)
• Evaporation
• Brane-field eqs. are separable in any dim.
• Greybody factors for 5-d BH
• Power spectra from 5-d BH
• Summary

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Why study BHs at collider?
In ADD/RS1 scenario, hierarchy problem is
solvedto result in the fundamental gravitational
scale O(TeV).
Experimentally accessible quantum gravity!!
Truly QG effects will be observed as the
deviationfrom the asymptotic behavior (in BH
picture).
It is essential to predict BH behavior as
precisely as possible!
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BH at collider (basic facts)

• We consider the region where the produced BH is
• large enough to be treated semi-classcially and
• small enough to be spherical in the bulk.

(Both are typically satisfied in LHC energy
range.)
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Rotating BH formation
RHS is decreasing function of J (or b).
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Our formula nicely fits numerical result with
full GR
So what?
There are two direct consequences.
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1. Production cross section becomes larger
Production cross section becomes larger when one
take angular momentum into account.
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2. BHs are produced with large angular momenta
Differential cross sectionincreases linearly
with J.
BHs are really produced with large angular
momenta!!
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Radiation from rotating BH
Once we have established that BHs are produced
with large angular momenta,we want to find out
which signal would result.
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Radiations from rotating BH
Greybody factors are obtained by solving the
brane field equations.

• What we have found
• Brane field equation is separable into angular
  and radial parts for any spin s and in any
  dimensions n.
• We have analytically solved this equation for
  any spin s in 5 dim. and found greybody factors
  in low frequency expansion.
• We show that radiations are highly anisotropic
  (initially).

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Higher dim. Kerr metric(just to show how it
looks)
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Newman Penrose formalism(just to show how it
looks)
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Brane field equations
Same as 4-dim. Can be treated in a standard
manner.
Gives the greybody factor.
Note This term is absent in Kanti, March-Russell
02 (appeared after our work) because they
utilized Cvetic-Larsen equation which essentially
relies on the fact that this term vanishes (in
4-d).
This term vanishes for n1 (5-d). For this case,
we can find greybody factors analytically.
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Greybody factors in 5-d(just to show how it
looks)
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Scalar power spectrum
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Spinor power spectra
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Vector power spectrum
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Scalar ang. power spectrum
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Spinor ang. power spectrum
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Vector ang. power spectrum
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Summary

• What we have done
• Production of rotating BH
• BHs are produced with large aungular momenta.
• Production cross section of BH becomes
  largerwhen one takes angular momentum into
  account.
• Evaporation of rotating BH
• Brane field equation is separable for any spin
  and in any dimensions.
• Analytic expression of greybody factors for n1
• Power spectrum is substantially different
  fromg.o. limit.
• Especially spinor and vector are highly
  anisotropic.
• Works in progress
• Greybody factor in any dimensions without low
  frequency limit
• Complete determination of time integrated power
  and angular spectrum which can be observed in
  real experiment

Usable by experimentalists!!