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Asymptotic black hole greybody factors

Asymptotic black hole greybody factors. Jorge Escobedo University of Amsterdam Institute for Theoretical Physics April 2008. Outline. Black hole thermodynamics Two puzzles What are greybody factors? Motivation: Maldacena-Strominger Asymptotic greybody factors. Black hole thermodynamics.

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Asymptotic black hole greybody factors

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  1. Asymptotic black hole greybody factors Jorge Escobedo University of Amsterdam Institute for Theoretical Physics April 2008

  2. Outline • Black hole thermodynamics • Two puzzles • What are greybody factors? • Motivation: Maldacena-Strominger • Asymptotic greybody factors

  3. Black hole thermodynamics • Black holes (BH) are fascinating objects predicted by general relativity.

  4. Black hole thermodynamics • Bekenstein (1973): Conjectures that BH have an associated entropy. • Bardeen, Carter and Hawking (1973): Laws of black hole mechanics Laws of thermodynamics if:

  5. Black hole thermodynamics • Problem: If BH have an associated temperature, they must radiate. However, nothing can escape from a BH! • Hawking (1975): Quantum fields in a BH background. Temperature and entropy of a BH given by: Analogy between BH and thermodynamical systems made consistent!

  6. Black hole thermodynamics • Moreover, Hawking found that BH have a characteristic blackbody radiation spectrum.

  7. Black hole thermodynamics • Everything looks really nice, uh? but…

  8. Two puzzles 1.Quantum description of black holes No-hair theorem: A BH solution is characterized only by its mass, charge and angular momentum. Therefore, there is only one state of the BH that has the observable thermodynamical quantities mentioned above.

  9. Two puzzles Given that BH have an associated entropy, what are the microscopic degrees of freedom that give rise to it? Strominger and Vafa (1996): String theoretical derivation of the Bekenstein-Hawking entropy.

  10. Two puzzles 2.The information loss paradox Pure quantum state Thermal radiation

  11. Two puzzles • If a pure state falls into the black hole, it will be emitted as thermal radiation (mixed state). • Violation of unitarity: Pure states cannot evolve into mixed states! In terms of density matrices: • Where U is an operator that acts on pure states • This is known as the information loss paradox: we started with quantum fields in a BH background and obtained a result that is not allowed by quantum mechanics!

  12. What are greybody factors?

  13. What are greybody factors? Potential barrier: V

  14. Motivation: Maldacena-Strominger calculation D=5 near extremal black hole:

  15. Motivation: Maldacena-Strominger calculation • Results D-brane computation (CFT) = Semiclassical computation • Same result from a theory with gravity and one without it. • A year later (1997), Maldacena proposed the AdS/CFT correspondence.

  16. Asymptotic greybody factors • D=4 Schwarzschild black hole with: • Tortoise coordinate:

  17. Asymptotic greybody factors • Study propagation of a scalar field in the exterior region of the above BH, i.e. • Regge-Wheeler (1957): where:

  18. Asymptotic greybody factors • Solutions of the previous equation describe the scattering of incoming or outgoing waves by the BH geometry. • Now consider:

  19. Asymptotic greybody factors Define the greybody factor as Check:

  20. Asymptotic greybody factors • Results: • So, the blackbody radiation gets modified to:

  21. Asymptotic greybody factors • D=4 Reissner-Nordstrom black hole: • Proposal (Neitzke, 2003): Just as in the case of small frequencies, the results in this regime might have dual descriptions.

  22. Conclusions • The study of greybody factors as part of perturbations around BH in classical gravity. • Moreover, the study of asymptotic greybody factors might help us in understanding the quantum nature of black holes and thus, of quantum gravity.

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