Micro Black Holes beyond EinsteinJulien GRAIN, Aurelien BARRAU
Panagiota Kanti, Stanislav Alexeev
What micro-black holes “say” about new physics
• Astrophysics and Cosmology : Primordial Black Holes (power spectrum, dark matter, etc.)
• Gauss-Bonnet Black holes at the LHC
• Black hole’s evaporation in a non-asymptotically flat space-time
Black Holes evaporate
• Radiation spectrum
• Hawking evaporation law
kGM
hcT
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3
2
)(
M
M
dt
dM
stGeVTgM
stGeVTgM
11010
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stGeVTgM
stGeVTgM
11010
10101049
21116
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QM
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)1(
sTBk
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Micro Black holes at the LHC
• Gauss-Bonnet Black holes at the LHC
• Black hole’s evaporation in a non-asymptotically flat space-time
A. Barrau, J. Grain & S. Alexeev
Phys. Lett. B 584, 114-122 (2004)
S. Alexeev, N. Popov, A. Barrau, J. Grain
In preparation
We will see…
Let’s hope!!!
We will see…
Let’s hope!!!
Black Holes at the LHC ?
Hierarchy problem in standard physics:
One of the solutions:
Large extra dimensions
Arkani-Hamed, Dimopoulos, Dvali Phys. Lett. B 429, 257 (1998)
Black Holes Creation
• Two partons with a center-of-mass energy moving in opposite direction
• A black hole of mass and horizon radius
is formed if the impact parameter is lower than
s
From Giddings & al. (2002)
sM BH hrhr
Precursor Works
• Computation of the black hole’s formation cross-section
• Derivation of the number of black holes produced at the LHC
• Determination of the dimensionnality of space using Hawking’s law
From Dimopoulos & al. 2001
Giddings, Thomas Phys. Rev. D 65, 056010 (2002)
Dimopoulos, Landsberg Phys. Rev. Lett 87, 161602 (2001)
Gauss-Bonnet Black Holes?
• All previous works have used D-dimensionnal Schwarzschild black holes
• General Relativity:
• Low energy limit of String Theory:
Gauss-Bonnet Black Holes’ Thermodynamic (1)
Properties derived by:
Expressed in function of the horizon radius
Boulware, Deser Phys. Rev. Lett. 83, 3370 (1985)
Cai Phys. Rev. D 65, 084014 (2002)
Gauss-Bonnet Black holes’ Thermodynamic (2)
Non-monotonic behaviour
taking full benefit of evaporation process
(integration over black hole’s lifetime)
The flux Computation
• Analytical results in the high energy limit
The grey-body factors are constant
• is the most convenient variable
Harris, Kanti JHEP 010, 14 (2003)
The Flux Computation (ATLAS detection)
• Planck scale = 1TeV
• Number of Black Holes produced at the LHC derived by Landsberg
• Hard electrons, positrons and photons sign the Black Hole decay spectrum
• ATLAS resolution
The Results -measurement procedure-
• For different input values of (D,), particles emitted by the full evaporation process are generated
spectra are reconstructed for each mass bin
• A analysis is performed2χ
The Results-discussion-
• For a planck scale of order a TeV, ATLAS can distinguish between the case with and the case without Gauss-Bonnet term.
Important progress in the construction of a full quantum theory of gravity
• The results can be refined by taking into account more carefully the endpoint of Hawking evaporation
• The statistical significance of the analysis should be taken with care
2χ
Barrau, Grain & Alexeev
Phys. Lett. B 584, 114 (2004)
Kerr Gauss-bonnet Black Holes
• Black Holes formed at colliders are expected to be spinning
The previous study should be done for spinning Black Holes
• Solve the Einstein equation with the Gauss-Bonnet term in the static, axisymmetric case
RRRRRR
RRRRRRRggRgR
244
242
1
2
1 2
RRRRRR
RRRRRRRggRgR
244
242
1
2
1 2
S. Alexeev, N. Popov, A. Barrau, J. GrainIn preparation
Let’s add a cosmological constant
P. Kanti, J. Grain, A. Barrauin preparation
• Gauss-Bonnet Black holes at the LHC
• Black hole’s evaporation in a non-asymptotically flat space-time
(A)dS Universe
• Positive cosmological constant
• Presence of an event horizon at
• Negative cosmological constant
• Presence of closed geodesics
TgRgR 82
1 TgRgR 8
2
1
2
)2)(1( ddRdS
2
)2)(1( ddRdS
De Sitter (dS) Universe Anti-De Sitter (AdS) Universe
Cosmological constant
Black Holes in such a space-time
• Two event horizons and
• No solution for with
• One event horizon
• Exist only for with
22
22
)2)(1(2
222
)2)(1(22
)1()1(
1
1
dddr
ddrdr
r
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d
Metric function h(r)
critH RR critH TT
De Sitter (dS) Universe Anti-De Sitter (AdS) Universe
2
)2)(3( ddRcrit )2(
)3(2
2
1
d
dTcrit
HR HRdSR
Calculation of Greybody factors (1)
• A potential barrier appears in the equation of motion of fields around a black hole:
• Black holes radiation spectrum is decomposed into three part:
0)1(
)(1
222
2
Rr
rhdy
dRr
dy
d
r
0)1(
)(1
222
2
Rr
rhdy
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dy
d
r
kd
edt
dN
HT
3)(
1
1
kd
edt
dN
HT
3)(
1
1
Potential barrierTortoise coordinate
Break vacuum fluctuations
Cross the potential barrier
Phase space term
Black hole’s horizon
De Sitter horizon
Calculation of Greybody factors (2)
)(
)(
)(
)(
1
in
out
in
hin
F
F
F
FA )(
)(
)(
)(
1
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out
in
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F
FA
2
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A
Analytical calculations Numerical calculations
)(inF
)(outF
)(hinF
Equation of motion analytically solved at the black hole’s and the
de Sitter horizon
Equation of motion numerically solved from black hole’s horizon
to the de Sitter one
De Sitter horizon
Calculation of Greybody factors -results for scalar in dS universe-
d=4 210
The divergence comes from the presence of two horizons
P. Kanti, J. Grain, A. Barrauin preparation
Conclusion
Big black holes are fascinating…Big black holes are fascinating…
But small black holes are far more fascinating!!!But small black holes are far more fascinating!!!
Primordial Black holes in our Galaxy
F.Donato, D. Maurin, P. Salati, A. Barrau, G. Boudoul, R.TailletAstrophy. J. (2001) 536, 172
A. Barrau, G. Boudoul et al., Astronom. Astrophys., 388, 767 (2002)
Astrophys. 398, 403 (2003)
Barrau, Blais, Boudoul, Polarski, Phys. Lett. B, 551, 218 (2003)
Cosmological constrain using PBH
• Small black holes could have been formed in the early universe
• Stringent constrains on the amount of PBH in the galaxy:
The anti-proton flux emitted by PBH is evaluating using an improved propagation scheme for cosmic rays
• This leads to constrain on the PBH fraction
• New window of detection using low energy anti-deuteron
9104 PBH
9104 PBH
2710PBH
Derivation of the Kerr Gauss-Bonnet black holes solution
S. Alexeev, N. Popov, A. Barrau, J. GrainIn preparation
The Kerr-Schild metric-work in progress-
• Most convenient metric for axisymmetric problem:
• Black hole’s angular momentum is paramatrized by a
23
22
222
222222222
cos
)sin)(,(sin2
)()cos()(
Ddr
dadurdrda
darardrdrduds
23
22
222
222222222
cos
)sin)(,(sin2
)()cos()(
Ddr
dadurdrda
darardrdrduds
Radial coordinate
Zenithal coordinate
Unknown metric function
Deriving the metric function
• Method:– The kerr-schild metric is injected in the Einstein’s
equation– The ur equation verified by β is solved
– Compatibility for the other component is finally checked
• Boundary conditions
0),(),(),(),(),( 012
201 rgrgrgdr
drhrh 0),(),(),(),(),( 01
2201 rgrgrg
dr
drhrh
)2)(1(
)4)(3(8)4)(3(411
)4)(3(2),(lim
1
22
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dd
r
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dd
rr
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)2)(1(
)4)(3(8)4)(3(411
)4)(3(2),(lim
1
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dd
dd
r
dd
dd
rr
dr
Results and temperature calculation
• functions have been numerically obtained for
• The temperature is obtain from the gravity surface at the event horizon
),( r
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