Strings & Gravity at University of Barcelona
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1 Strings & Gravity at University of Barcelona Higher-dimensional black holes [R. Emparan, M.J. Rodríguez, J. Camps, M. Caldarelli, M. Ortaggio, B. Fiol, O. Dias] Microscopic description of black holes [R. Emparan, O. Dias, A. Maccarrone] Classification of SUGRA solutions [D. Roest, A. Celi, M. Caldarelli] Non-relativistic strings [J. Gomis] Symmetries of string & M-theory [J. Gomis, D. Roest] UV properties of strings and SUGRA [J. Russo] Decay of massive string states [J. Russo] Strings in magnetic backgrounds [J. Russo, J. López] AdS/CFT [AdS/QCD: J.M. Pons; Wilson loops: B. Fiol; etc]
2 Strings & Gravity at University of Barcelona Higher-dimensional black holes [R. Emparan, M.J. Rodríguez, J. Camps, M. Caldarelli, M. Ortaggio, B. Fiol, O. Dias] Microscopic description of black holes [R. Emparan, O. Dias, A. Maccarrone] Classification of SUGRA solutions [D. Roest, A. Celi, M. Caldarelli] Non-relativistic strings [J. Gomis] Symmetries of string & M-theory [J. Gomis, D. Roest] UV properties of strings and SUGRA [J. Russo] Decay of massive string states [J. Russo] Strings in magnetic backgrounds [J. Russo, J. López] AdS/CFT [AdS/QCD: J.M. Pons; Wilson loops: B. Fiol; etc]
3 Strings & Gravity at University of Barcelona Higher-dimensional black holes [R. Emparan, M.J. Rodríguez, J. Camps, M. Caldarelli, M. Ortaggio, B. Fiol, O. Dias] Microscopic description of black holes [R. Emparan, O. Dias, A. Maccarrone] Classification of SUGRA solutions [D. Roest, A. Celi, M. Caldarelli] Non-relativistic strings [J. Gomis] Symmetries of string & M-theory [J. Gomis, D. Roest] UV properties of strings and SUGRA [J. Russo] Decay of massive string states [J. Russo] Strings in magnetic backgrounds [J. Russo, J. López] AdS/CFT [AdS/QCD: J.M. Pons; Wilson loops: B. Fiol; etc]
4 Strings & Gravity at University of Barcelona Higher-dimensional black holes [R. Emparan, M.J. Rodríguez, J. Camps, M. Caldarelli, M. Ortaggio, B. Fiol, O. Dias] Microscopic description of black holes [R. Emparan, O. Dias, A. Maccarrone] Classification of SUGRA solutions [D. Roest, A. Celi, M. Caldarelli] Non-relativistic strings [J. Gomis] Symmetries of string & M-theory [J. Gomis, D. Roest] UV properties of strings and SUGRA [J. Russo] Decay of massive string states [J. Russo] Strings in magnetic backgrounds [J. Russo, J. López] AdS/CFT [AdS/QCD: J.M. Pons; Wilson loops: B. Fiol; etc]
5 Strings & Gravity at University of Barcelona Higher-dimensional black holes [R. Emparan, M.J. Rodríguez, J. Camps, M. Caldarelli, M. Ortaggio, B. Fiol, O. Dias] Microscopic description of black holes [R. Emparan, O. Dias, A. Maccarrone] Classification of SUGRA solutions [D. Roest, A. Celi, M. Caldarelli] Non-relativistic strings [J. Gomis] Symmetries of string & M-theory [J. Gomis, D. Roest] UV properties of strings and SUGRA [J. Russo] Decay of massive string states [J. Russo] Strings in magnetic backgrounds [J. Russo, J. López] AdS/CFT [AdS/QCD: J.M. Pons; Wilson loops: B. Fiol; etc]
6 Strings & Gravity at University of Barcelona Higher-dimensional black holes [R. Emparan, M.J. Rodríguez, J. Camps, M. Caldarelli, M. Ortaggio, B. Fiol, O. Dias] Microscopic description of black holes [R. Emparan, O. Dias, A. Maccarrone] Classification of SUGRA solutions [D. Roest, A. Celi, M. Caldarelli] Non-relativistic strings [J. Gomis] Symmetries of string & M-theory [J. Gomis, D. Roest] UV properties of strings and SUGRA [J. Russo] Decay of massive string states [J. Russo] Strings in magnetic backgrounds [J. Russo, J. López] AdS/CFT [AdS/QCD: J.M. Pons; Wilson loops: B. Fiol; etc]
7 Microscopic analysis of Black Hole superradiance Alessandro Maccarrone 3rd RTN Workshop, Valencia 2007 Based on work with R. Emparan & O. Dias
8 Motivation String theory provides a microscopic description of some properties of BHs: Entropy matching [A. Strominger & C. Vafa (1996),etc] Hawking radiation [C.G. Callan & J.M. Maldacena (1996)]
9 Motivation String theory provides a microscopic description of some properties of BHs: Entropy matching [A. Strominger & C. Vafa (1996),etc] Hawking radiation [C.G. Callan & J.M. Maldacena (1996)] Superradiance?
10 Superradiance Classical effect in rotating BHs due to the presence of an Ergoregion, so negative energy states are allowed. A wave can be scattered off the BH with a reflection coefficient greater than one (Superradiance) If ª(x ¹ )» f(r; µ)e i(²t má)! H SR condition: ² <! H m
11 Superradiance Classical effect in rotating BHs due to the presence of an Ergoregion, so negative energy states are allowed. A wave can be scattered off the BH with a reflection coefficient greater than one (Superradiance) If ª(x ¹ )» f(r; µ)e i(²t má)! H SR condition: ² <! H m This is the stimulated process, but there is also superradiant spontaneous emission.
12 D1-D5-P system For concreteness let us focus on D1-D5-P rotating BHs. The system can be described in terms of the CFT of an effective string carrying momentum excitations in two sectors (Left & Right). Bulk angular momentum is provided by coherent polarization of the fermionic excitations on the string. R L
13 Microscopic Hawking radiation In this picture Hawking Radiation is explained as emission of closed strings due to the collision of a Right and a Left mode. R L
14 Microscopic Hawking radiation In this picture Hawking Radiation is explained as emission of closed strings due to the collision of a Right and a Left mode. R R L BPS limit
15 Hawking vs. Superradiant emission The same mechanism allows to describe Superradiance. In rotating black holes, Hawking and superradiant emission are highly entangled. Extremal ( T H = 0) solutions are a suitable set-up to focus on superradiance, since Hawking radiation is not present in these backgrounds.
16 Non-BPS Extremal Black-Hole Rotating solution! H 6= 0
17 Non-BPS Extremal Black-Hole Rotating solution! H 6= 0 One sector described by polarized fermionic excitations filling up a Fermi Sea T H! 0
18 Non-BPS Extremal Black-Hole Rotating solution! H 6= 0 One sector described by polarized fermionic excitations filling up a Fermi Sea T H! 0 R L
19 Superradiance condition Fermi Sea is described by a distribution of the form: ( is the Fermi Energy) ½ F (²; m)! µ(! H m ²)! H m T H! 0
20 Superradiance condition Fermi Sea is described by a distribution of the form: ½ F (²; m)! µ(! H m ²) T H! 0! H m ( is the Fermi Energy) Excitations in this sector verify: ² <! H m
21 Superradiance condition Fermi Sea is described by a distribution of the form: ½ F (²; m)! µ(! H m ²) T H! 0! H m ( is the Fermi Energy) Excitations in this sector verify: ² <! H m This is the Superradiance condition.
22 Thanks for your attention.
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