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


CONTENTS

Introduction

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CONTENTS

Introduction

Black holes in Loop Quantum Gravity

Black hole entropy

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CONTENTS

Introduction


Black hole entropy

Computational counting

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CONTENTS

Introduction


Black hole entropy


Discretization

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CONTENTS

Introduction


Black hole entropy


Discretization

Spectroscopy

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CONTENTS

Introduction


Black hole entropy


Discretization

Spectroscopy

Conclusions

Future lines

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INTRODUCTION

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

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INTRODUCTION


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

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INTRODUCTION



Krasnov ’99 ⇒ Discrete spectrum within LQG

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INTRODUCTION




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

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INTRODUCTION





Black hole radiation is still an open problem in LoopQuantum Gravity

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INTRODUCTION





Black hole radiation is still an open problem in LoopQuantum Gravity

Here: Some different new results.3 / 12


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 HOLES IN LQG

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



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


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BLACK HOLES IN LQG

Inner boundary introduced before quantizationprocedure (effective treatment)



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


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BLACK HOLE ENTROPY

Entropy arises from the surface degrees of freedom

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

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BLACK HOLE ENTROPY


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

Count all possible combinations of labels


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BLACK HOLE ENTROPY




Pay attention to: -Distinguishability of punctures


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BLACK HOLE ENTROPY





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


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BLACK HOLE ENTROPY





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

Result: up to γ.AAS ln21

41

−=


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

ABCK framework formulated for large area limit


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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


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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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DISCRETIZATION

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DISCRETIZATION


The width of the steps (∆A) is constant


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DISCRETIZATION



This behaviour is reproduced with both counting models


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DISCRETIZATION




Step width proportional to γ in each model

2PA lχγ=∆


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DISCRETIZATION




Step width proportional to γ in each model

Where this behaviour comes from?

2PA lχγ=∆


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DISCRETIZATION

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

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DISCRETIZATION

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DISCRETIZATION


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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DISCRETIZATION




With this: - Explanation for the staircase

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DISCRETIZATION





- Implications in spectroscopy

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DISCRETIZATION





- Implications in spectroscopy

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

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DISCRETIZATION

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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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Equidistant area spectrum with a gap

Fundamental frequency

2PA lχγ=∆

Mπγχω

320 =


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Discrete spectrum: integer multiples of

2PA lχγ=∆

Mπγχω

320 =

0ω


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Discrete spectrum: integer multiples of

Analogous to Bekenstein-Mukhanov picture

2PA lχγ=∆

Mπγχω

320 =

0ω


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SPECTROSCOPY

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

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SPECTROSCOPY


- The spectrum is not discrete

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SPECTROSCOPY



- Statistically preferred frequencies

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SPECTROSCOPY




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

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SPECTROSCOPY




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

- The bands are not narrow ⇒ Broadening of the lines

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CONCLUSIONS

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

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CONCLUSIONS


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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CONCLUSIONS


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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FUTURE LINES

Optimization of the algorithm in order to reach largerarea values

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FUTURE LINES


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

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FUTURE LINES



Complete detailed spectroscopical analysis ⇒ Thermal behaviour ???

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FUTURE LINES




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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FUTURE LINES




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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