black hole radiation spectrum in loop quantum gravityblack hole radiation spectrum in lqg jacobo...

Black hole radiation spectrum in LQG Jacobo Díaz-Polo

Work in collaboration with:

Alejandro Corichi

Enrique Fernandez-Borja

Black hole

radiation spectrum

in

Loop Quantum Gravity

Jacobo Díaz-PoloDept. Astronomía y Astrofísica

Universidad de Valencia

Jacobo Díaz-PoloDept. Astronomía y Astrofísica

Universidad de Valencia

Loops ’07Morelia, June 2007

Black hole radiation spectrum in LQG Jacobo Díaz-Polo

CONTENTS

Introduction

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

CONTENTS

Introduction

Black holes in Loop Quantum Gravity

Black hole entropy

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

CONTENTS

Introduction

Black holes in Loop Quantum Gravity

Black hole entropy

Computational counting

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

CONTENTS

Introduction

Black holes in Loop Quantum Gravity

Black hole entropy

Computational counting

Discretization

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

CONTENTS

Introduction

Black holes in Loop Quantum Gravity

Black hole entropy

Computational counting

Discretization

Spectroscopy

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

CONTENTS

Introduction

Black holes in Loop Quantum Gravity

Black hole entropy

Computational counting

Discretization

Spectroscopy

Conclusions

Future lines

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

INTRODUCTION

Bekenstein-Mukhanov ’95 ⇒ Discrete equidistant spectrum on the basis of heuristical arguments

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

INTRODUCTION

Bekenstein-Mukhanov ’95 ⇒ Discrete equidistant spectrum on the basis of heuristical arguments

Barreira, Carfora, Rovelli ’96 ⇒ Continuous spectrum within LQG

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

INTRODUCTION

Bekenstein-Mukhanov ’95 ⇒ Discrete equidistant spectrum on the basis of heuristical arguments

Barreira, Carfora, Rovelli ’96 ⇒ Continuous spectrum within LQG

Krasnov ’99 ⇒ Discrete spectrum within LQG

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

INTRODUCTION

Bekenstein-Mukhanov ’95 ⇒ Discrete equidistant spectrum on the basis of heuristical arguments

Barreira, Carfora, Rovelli ’96 ⇒ Continuous spectrum within LQG

Krasnov ’99 ⇒ Discrete spectrum within LQG

Ansari ’06 ⇒ Continuous spectrum but with some discrete “brighter” lines

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

INTRODUCTION

Bekenstein-Mukhanov ’95 ⇒ Discrete equidistant spectrum on the basis of heuristical arguments

Barreira, Carfora, Rovelli ’96 ⇒ Continuous spectrum within LQG

Krasnov ’99 ⇒ Discrete spectrum within LQG

Ansari ’06 ⇒ Continuous spectrum but with some discrete “brighter” lines

Black hole radiation is still an open problem in LoopQuantum Gravity

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

INTRODUCTION

Bekenstein-Mukhanov ’95 ⇒ Discrete equidistant spectrum on the basis of heuristical arguments

Barreira, Carfora, Rovelli ’96 ⇒ Continuous spectrum within LQG

Krasnov ’99 ⇒ Discrete spectrum within LQG

Ansari ’06 ⇒ Continuous spectrum but with some discrete “brighter” lines

Black hole radiation is still an open problem in LoopQuantum Gravity

Here: Some different new results.3 / 12

Black hole radiation spectrum in LQG Jacobo Díaz-Polo

BLACK HOLES IN LQG

Inner boundary introduced in the spacetime manifoldbefore quantization procedure (effective treatment)

Isolated horizon boundary conditions

Hilbert space splitting: Hv ⊗ Hs

[A.Ashtekar, J.Baez, A.Corichi, K.Krasnov]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

BLACK HOLES IN LQG

Inner boundary introduced in the spacetime manifoldbefore quantization procedure (effective treatment)

Isolated horizon boundary conditions

Hilbert space splitting: Hv ⊗ Hs

Surface states: U(1) Chern-Simons theory over a punctured sphere

Spin network pierces the horizon at punctures

Punctures carry some quantum labels satisfying

(projection constraint)0=∑i

im

[A.Ashtekar, J.Baez, A.Corichi, K.Krasnov]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

BLACK HOLES IN LQG

Inner boundary introduced before quantizationprocedure (effective treatment)

Isolated horizon boundary conditions

Hilbert space splitting: Hv ⊗ Hs

Surface states: U(1) Chern-Simons theory over a punctured sphere

Spin network pierces the horizon at punctures

Punctures carry some quantum labels satisfying

(projection0=∑i

im

[A.Ashtekar, J.Baez, A.Corichi, K.Krasnov]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

BLACK HOLE ENTROPY

Entropy arises from the surface degrees of freedom

[A.Ashtekar, J.Baez, K.Krasnov]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

BLACK HOLE ENTROPY

Entropy arises from the surface degrees of freedom

Question: How many different horizon states compatible with the horizon area and the boundary conditions are there?

Count all possible combinations of labels

[A.Ashtekar, J.Baez, K.Krasnov]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

BLACK HOLE ENTROPY

Entropy arises from the surface degrees of freedom

Question: How many different horizon states compatible with the horizon area and the boundary conditions are there?

Count all possible combinations of labels

Pay attention to: -Distinguishability of punctures

[A.Ashtekar, J.Baez, K.Krasnov]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

BLACK HOLE ENTROPY

Entropy arises from the surface degrees of freedom

Question: How many different horizon states compatible with the horizon area and the boundary conditions are there?

Count all possible combinations of labels

Pay attention to: -Distinguishability of punctures

-Quantum labels: two models ([Domagala, Lewandowski] and [Ghosh, Mitra])

[A.Ashtekar, J.Baez, K.Krasnov]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

BLACK HOLE ENTROPY

Entropy arises from the surface degrees of freedom

Question: How many different horizon states compatible with the horizon area and the boundary conditions are there?

Count all possible combinations of labels

Pay attention to: -Distinguishability of punctures

-Quantum labels: two models ([Domagala, Lewandowski] and [Ghosh, Mitra])

Result: up to γ.AAS ln21

41

−=

[A.Ashtekar, J.Baez, K.Krasnov]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

COMPUTATIONAL COUNTING

In order to make an exact counting we use an explicitenumeration algorithm

Computer generates all possible combinations of labelsand counts only those satisfying the requiredconditions

A.Corichi, E.Fernandez-Borja, J.D. [Class. Quantum Grav. 24, 243 (2007)]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

COMPUTATIONAL COUNTING

In order to make an exact counting we use an explicitenumeration algorithm

Computer generates all possible combinations of labelsand counts only those satisfying the requiredconditions

Problem: Running time only allows a low area regime(few hundreds of Planck areas)

ABCK framework formulated for large area limit

A.Corichi, E.Fernandez-Borja, J.D. [Class. Quantum Grav. 24, 243 (2007)]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

COMPUTATIONAL COUNTING

In order to make an exact counting we use an explicitenumeration algorithm

Computer generates all possible combinations of labelsand counts only those satisfying the requiredconditions

Problem: Running time only allows a low area regime(few hundreds of Planck areas)

ABCK framework formulated for large area limit

But linear dependence and logarithmic correction are obtained ⇒ some confidence

A.Corichi, E.Fernandez-Borja, J.D. [Class. Quantum Grav. 24, 243 (2007)]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

DISCRETIZATION

Surprising new behaviour of entropy as an areafunction: stair-like structure

A.Corichi, E.Fernandez-Borja, J.D. [Phys. Rev. Lett. 98, 181301 (2007)]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

DISCRETIZATION

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A.Corichi, E.Fernandez-Borja, J.D. [Phys. Rev. Lett. 98, 181301 (2007)]

Black hole radiation spectrum in LQG Jacobo Díaz-Polo

DISCRETIZATION

Surprising new behaviour of entropy as an areafunction: stair-like structure

The width of the steps (∆A) is constant

A.Corichi, E.Fernandez-Borja, J.D. [Phys. Rev. Lett. 98, 181301 (2007)]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

DISCRETIZATION

Surprising new behaviour of entropy as an areafunction: stair-like structure

The width of the steps (∆A) is constant

This behaviour is reproduced with both counting models

A.Corichi, E.Fernandez-Borja, J.D. [Phys. Rev. Lett. 98, 181301 (2007)]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

DISCRETIZATION

Surprising new behaviour of entropy as an areafunction: stair-like structure

The width of the steps (∆A) is constant

This behaviour is reproduced with both counting models

Step width proportional to γ in each model

2PA lχγ=∆

A.Corichi, E.Fernandez-Borja, J.D. [Phys. Rev. Lett. 98, 181301 (2007)]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

DISCRETIZATION

Surprising new behaviour of entropy as an areafunction: stair-like structure

The width of the steps (∆A) is constant

This behaviour is reproduced with both counting models

Step width proportional to γ in each model

Where this behaviour comes from?

2PA lχγ=∆

A.Corichi, E.Fernandez-Borja, J.D. [Phys. Rev. Lett. 98, 181301 (2007)]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

DISCRETIZATION

Structure of the horizon area eigenstate degeneracywhen introducing the “projection constraint”

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

DISCRETIZATION

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

DISCRETIZATION

Structure of the horizon area eigenstate degeneracywhen introducing the “projection constraint”

Structure with “bands” or peaks of degeneracy

Degeneracy at the peaks several orders of magnitudehigher than the rest of the spectrum

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

DISCRETIZATION

Structure of the horizon area eigenstate degeneracywhen introducing the “projection constraint”

Structure with “bands” or peaks of degeneracy

Degeneracy at the peaks several orders of magnitudehigher than the rest of the spectrum

With this: - Explanation for the staircase

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

DISCRETIZATION

Structure of the horizon area eigenstate degeneracywhen introducing the “projection constraint”

Structure with “bands” or peaks of degeneracy

Degeneracy at the peaks several orders of magnitudehigher than the rest of the spectrum

With this: - Explanation for the staircase

- Implications in spectroscopy

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

DISCRETIZATION

Structure of the horizon area eigenstate degeneracywhen introducing the “projection constraint”

Structure with “bands” or peaks of degeneracy

Degeneracy at the peaks several orders of magnitudehigher than the rest of the spectrum

With this: - Explanation for the staircase

- Implications in spectroscopy

Consider all possible transitions regardless of theconcrete quantum configuration (unknown dynamics)

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

DISCRETIZATION

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

SPECTROSCOPY (“toy model”)

First approximation: consider only states at the peaks

Equidistant area spectrum with a gap 2PA lχγ=∆

E.Fernandez-Borja, J.D. [arXiv: 0706.1979 [gr-qc]]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

SPECTROSCOPY (“toy model”)

First approximation: consider only states at the peaks

Equidistant area spectrum with a gap

Fundamental frequency

2PA lχγ=∆

Mπγχω

320 =

E.Fernandez-Borja, J.D. [arXiv: 0706.1979 [gr-qc]]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

SPECTROSCOPY (“toy model”)

First approximation: consider only states at the peaks

Equidistant area spectrum with a gap

Fundamental frequency

Discrete spectrum: integer multiples of

2PA lχγ=∆

Mπγχω

320 =

0ω

E.Fernandez-Borja, J.D. [arXiv: 0706.1979 [gr-qc]]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

SPECTROSCOPY (“toy model”)

First approximation: consider only states at the peaks

Equidistant area spectrum with a gap

Fundamental frequency

Discrete spectrum: integer multiples of

Analogous to Bekenstein-Mukhanov picture

2PA lχγ=∆

Mπγχω

320 =

0ω

E.Fernandez-Borja, J.D. [arXiv: 0706.1979 [gr-qc]]

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

SPECTROSCOPY

But some important qualitative differences if we takeinto account the structure of the bands:

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

SPECTROSCOPY

But some important qualitative differences if we takeinto account the structure of the bands:

- The spectrum is not discrete

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

SPECTROSCOPY

But some important qualitative differences if we takeinto account the structure of the bands:

- The spectrum is not discrete

- Statistically preferred frequencies

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

SPECTROSCOPY

But some important qualitative differences if we takeinto account the structure of the bands:

- The spectrum is not discrete

- Statistically preferred frequencies

- Equidistant “brighter” lines sticking out from a continuous background spectrum

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

SPECTROSCOPY

But some important qualitative differences if we takeinto account the structure of the bands:

- The spectrum is not discrete

- Statistically preferred frequencies

- Equidistant “brighter” lines sticking out from a continuous background spectrum

- The bands are not narrow ⇒ Broadening of the lines

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

CONCLUSIONS

We make an spectroscopical analysis at the kinematicallevel (we don’t know dynamics)

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

CONCLUSIONS

We make an spectroscopical analysis at the kinematicallevel (we don’t know dynamics)

Considering all possible transitions, IH introduce a quantum gravity imprint in the black hole radiationspectrum

Observable qualitative effects in the spectrum

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

CONCLUSIONS

We make an spectroscopical analysis at the kinematicallevel (we don’t know dynamics)

Considering all possible transitions, IH introduce a quantum gravity imprint in the black hole radiationspectrum

Observable qualitative effects in the spectrum

ω0 proportional to γ ⇒ hypothetical observational determination (GRB’s ???)

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

FUTURE LINES

Optimization of the algorithm in order to reach largerarea values

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

FUTURE LINES

Optimization of the algorithm in order to reach largerarea values

Analytical study of the degeneracy structure ⇒ Find the analytical value of χ ( 8 ln3 ??? )

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

FUTURE LINES

Optimization of the algorithm in order to reach largerarea values

Analytical study of the degeneracy structure ⇒ Find the analytical value of χ ( 8 ln3 ??? )

Complete detailed spectroscopical analysis ⇒ Thermal behaviour ???

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

FUTURE LINES

Optimization of the algorithm in order to reach largerarea values

Analytical study of the degeneracy structure ⇒ Find the analytical value of χ ( 8 ln3 ??? )

Complete detailed spectroscopical analysis ⇒ Thermal behaviour ???

Search for possible primordial black holes in GRB’s to test the model (In collaboration with the GACE (INTEGRAL) at the Universidad de Valencia)

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Black hole radiation spectrum in LQG Jacobo Díaz-Polo

FUTURE LINES

Optimization of the algorithm in order to reach largerarea values

Analytical study of the degeneracy structure ⇒ Find the analytical value of χ ( 8 ln3 ??? )

Complete detailed spectroscopical analysis ⇒ Thermal behaviour ???

Search for possible primordial black holes in GRB’s to test the model (In collaboration with the GACE (INTEGRAL) at the Universidad de Valencia)

THE END

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