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

16

3

2

)(

M

M

dt

dM

stGeVTgM

stGeVTgM

11010

10101049

21116

stGeVTgM

stGeVTgM

11010

10101049

21116

sTBk

Q

eh

QM

dQdt

Nd2

222

)1(

sTBk

Q

eh

QM

dQdt

Nd2

222

)1(

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

drdtrds

d

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

dRr

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

in

out

in

hin

F

F

F

FA

2

2

12)(

A

2

2

12)(

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

dd

dd

r

dd

dd

rr

dr

)2)(1(

)4)(3(8)4)(3(411

)4)(3(2),(lim

1

22

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

11,6d

221 )()(1),( hh rrbrrbr 2

21 )()(1),( hh rrbrrbr

hrrttjttiijtt gggg

))((

4

12