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Stefano Bellucci
Editor
Supersymmetric
Gravity and Black
Holes
Proceedings
of the INFN-Laboratori Nazionali
di Frascati School on the Attractor
Mechanism 2009
With 16 Figures
123
Editor
Stefano B ellucci
Laboratori Nazionali di Frascati
Istituto Nazionale di Fisica Nucleare
Frascati RM
Italy
SpringerProceedings inPhysics ISSN0930-8989
ISBN978-3-642-31379-0 ISBN978-3-642-31380-6 (eBook)
DOI10.1007/978-3-642-31380-6
SpringerHeidelbergNew York Dordrecht London
Library of Congress Control Number: 2012953495
© Springer-Verlag Berlin Heidelberg 2013
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To Mario,agreat physicist,a modelof
loyalty,integrity,coherence, andjustthebest
DirectorIever met.
(cid:127)
Preface
This book is based upon lectures held from 29 June to 3 July 2009 at the
INFN-Laboratori Nazionali di Frascati School on Attractor Mechanism, directed
by Stefano Bellucci, with the participation of prestigious lecturers, including
M. Cvetic, G. DallAgata, S. Ferrara, J.F. Morales, G. Moore, A. Sen, J. Simon,
andM.Trigiante,aswellasinvitedscientistsofthecaliberofM.Bianchi,C.Nappi,
A. Sagnotti, and E. Witten. All lectures were given at a pedagogical,introductory
level, a feature which reflects itself in the specific “flavor” of this volume, which
alsobenefitedmuchfromextensivediscussionsandrelatedreworkingofthevarious
contributions.
This is the fifth volume in a series of books on the general topics of
supersymmetry, supergravity, black holes, and the attractor mechanism. Indeed,
basedonpreviousmeetings,fourvolumeswerealreadypublished:
Bellucci S. (2006). Supersymmetric Mechanics – Vol.1: Supersymmetry, Non-
commutativity and Matrix Models. (vol.698, pp.1–229). ISBN: 3-540-33313-4.
(Springer,BerlinHeidelberg)LectureNotesinPhysicsVol.698.
Bellucci S., S. Ferrara, A. Marrani. (2006). Supersymmetric Mechanics – Vol.2:
The Attractor Mechanism and Space Time Singularities. (vol.701, pp.1–242).
ISBN:978-3-540-34156-7.(Springer,BerlinHeidelberg)LectureNotesinPhysics
Vol.701.
Bellucci S. (2008). Supersymmetric Mechanics – Vol.3: Attractors and Black
HolesinSupersymmetricGravity.(vol.755,pp.1–373).ISBN:978-3-540-79522-3.
(Springer,BerlinHeidelberg)LectureNotesinPhysicsVol.755.
BellucciS.(2010).TheAttractorMechanism.ProceedingsoftheINFN-Laboratori
Nazionali di Frascati School 2007. ISSN 0930-8989, ISBN 978-3-642-10735-1,
e-ISBN 978-3-642-10736-8. DOI 10.1007/978-3-642-10736-8. (Springer
HeidelbergDordrechtLondonNewYork)ProceedingsinPhysicsVol.134.
vii
viii Preface
I wish to thank all lecturers, invited scientists, and participants at the School
for contributing to the success of the School, which prompted the realization of
this volume. I wish to thank especially Mario Calvetti for giving vital support
to the School and for personal trust and enduring encouragement. Lastly, but
mostimportantly,my gratitudegoesto mywife Gloriaandourbeloveddaughters
Costanza,Eleonora,Annalisa,Erica,andMaristellaforloveandinspiration,inwant
ofwhichIwouldhaveneverhadthestrengthtocompletethisbook.
Frascati,Italy StefanoBellucci
Contents
1 BlackHolesinSupergravity:FlowEquationsandDuality ............. 1
GianguidoDall’Agata
2 IntersectingAttractors...................................................... 47
JoseFranciscoMorales
3 Extremality,HolographyandCoarseGraining .......................... 89
JoanSimo´n
4 IssuesonBlackHolesinFourDimensionalSupergravity............... 143
L.Andrianopoli,R.D’AuriaandM.Trigiante
5 OntheClassificationofTwoCenterOrbitsforMagical
BlackHoles ................................................................... 181
LauraAndrianopoli,RiccardoD’Auria,andSergioFerrara
ix
Chapter 1
Black Holes in Supergravity: Flow Equations
and Duality
GianguidoDall’Agata
1.1 Introduction
Theanalysisofblackholesolutionsandthestudyoftheirphysicsisanactiveand
importantbranchofcontemporarytheoreticalphysics.Infact,notonlyblackholes
areanexcellenttheoreticallaboratoryforunderstandingsomefeaturesofquantum
gravity,but they can also be successfully used as a tool in applicationsto nuclear
physics,condensedmatter,algebraicgeometryandatomicphysics.Forthisreason,
black holes are considered the “Hydrogen atom” of quantum gravity [67] or the
“harmonicoscillatorofthe21stcentury”[77].
TheexistenceofblackholesseemstobeanunavoidableconsequenceofGeneral
Relativity (GR) and of its extensions (like supergravity). Classically, the horizon
of black holes protects the physics in the outer region from what happens in the
vicinity of singular field configurations that can arise in GR from smooth initial
data. However, already at the semiclassical level, black holes emit particles with
a thermalspectrum[7,58]. A thermodynamicbehaviourcan also be associated to
blackholesfromthelawsgoverningtheirmechanics[79]and,inparticular,onecan
associatetoablackholeanentropyS proportionaltotheareaAofitseventhorizon
(measuredinPlanckunitsl2 DG„=c3)
P
k A
B
S D : (1.1)
l2 4
P
In most physical systems the thermodynamicentropy has a statistical interpre-
tationintermsofcountingmicroscopicconfigurationswiththesamemacroscopic
G.Dall’Agata((cid:2))
DipartimentodiFisica“GalileoGalilei”,Universita`diPadova,ViaMarzolo8,35131,
Padova,Italy
INFN,SefionediPadova,ViaMarzolo8,35131,Padova,Italy
e-mail:[email protected]
S.Bellucci(ed.),SupersymmetricGravityandBlackHoles,SpringerProceedings 1
inPhysics142,DOI10.1007/978-3-642-31380-6 1,
©Springer-VerlagBerlinHeidelberg2013
