Table Of ContentSpringer Proceedings in Physics 176
Renata Kallosh
Emanuele Orazi E ditors
Theoretical
Frontiers in
Black Holes and
Cosmology
Theoretical Perspective in High Energy
Physics
Springer Proceedings in Physics
Volume 176
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Renata Kallosh Emanuele Orazi
(cid:129)
Editors
Theoretical Frontiers in Black
Holes and Cosmology
Theoretical Perspective in High Energy
Physics
123
Editors
Renata Kallosh Emanuele Orazi
Department ofPhysics EscoladeCiências eTecnologia
StanfordUniversity Universidade FederalRioGrande doNorte
Stanford, CA Natal, RN
USA Brazil
ISSN 0930-8989 ISSN 1867-4941 (electronic)
SpringerProceedings in Physics
ISBN978-3-319-31351-1 ISBN978-3-319-31352-8 (eBook)
DOI 10.1007/978-3-319-31352-8
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Preface
This volume aims at providing a pedagogical review on recent developments and
applications of black hole physics in the context of high energy physics and cos-
mology. The contributions are based on lectures delivered at the school
“Theoretical Frontiers in Black Holes and Cosmology”, held at the “International
Institute of Physics” (IIP) in Natal, Brazil, in June 2015. The lectures give a
panoramicviewofmainstreamresearchlinessharingblackholesolutionstogravity
and supergravity as common denominator. Starting with accessible and introduc-
tory concepts, the newcomer to the field will be brought to a level suitable to face
cutting-edge research in the various topics considered in this book.
The only prerequisite for the reader is a working knowledge in field theory and
group theory, and the knowledge of general relativity and supersymmetry is
desirable. The primary audience is intended to be postgraduate students but the
well-establishedtechniquespresentedinthisvolumeformsausefulreviewforany
scientistworkinginthefield.Theselectionofauthorshasbeenbasedonworldwide
recognized contributions on geometric approaches to fundamental problems in the
field of black hole physics.
The book is organized as follows: Chapter “Three Lectures on the FGK
Formalism and Beyond” introduces the key role of dualities and the attractor
mechanism in the context of singular solutions in ungauged supergravities. These
concepts are further developed in Chap. “Introductory Lectures on Extended
SupergravitiesandGaugings”,whichisareviewofthepresentmethodstobuildup
a gauged supergravity. A basic knowledge on how to gauge a supergravity is the
necessary ingredient for Chap. “Supersymmetric Black Holes and Attractors in
Gauged Supergravity” that deals with the construction of black hole solutions in a
gauged supergravity. The relevance of these solutions is due to applications to
gauge/gravityduality,whereblackholebackgroundsinthebulkareusedtomodel
finite temperature condensed matter systems on the boundary. In this framework,
theasymptoticalAdSspace,generatedbythegaugingprocedure,providestheright
symmetries to describe a conformal system on the boundary. These first three
contributionsareintendedtobeaprimerforthecommunityofscientistsworkingin
v
vi Preface
the field of gauge/gravity duality that want to embed more complicated bulk
backgrounds in the holographic settings. In Chap. “Lectures on Holographic
Renormalization”, we selected the holographic renormalization among the many
topicsingauge/gravityduality,duetothestrongoverlappingwithtechniquesused
to find the scalar flows for black holes backgrounds in supergravity. Chapter
“Nonsingular Black Holes inPalatini Extensions of General Relativity” introduces
the reader to a different formulation of gravity based on metric-affine spaces. This
approach allows to remove the singularity of general relativity giving rise to a
wormhole structure. Finally, Chap. “Inflation: Observations and Attractors” is an
introduction to inflation both from theoretical and experimental points of view,
aimed at describing the role of cosmological attractors for inflationary model
building.
We acknowledge the staff at the IIP for the support in organizing the school
“Theoretical Frontiers in Black Holes and Cosmology” where these lectures have
been delivered.
Stanford Renata Kallosh
Natal Emanuele Orazi
Contents
Three Lectures on the FGK Formalism and Beyond. . . . . . . . . . . . . . . 1
Tomás Ortín and Pedro F. Ramírez
Introductory Lectures on Extended Supergravities and
Gaugings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Antonio Gallerati and Mario Trigiante
Supersymmetric Black Holes and Attractors in Gauged
Supergravity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Dietmar Klemm
Lectures on Holographic Renormalization . . . . . . . . . . . . . . . . . . . . . . 131
Ioannis Papadimitriou
Nonsingular Black Holes in Palatini Extensions of General
Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Gonzalo J. Olmo
Inflation: Observations and Attractors. . . . . . . . . . . . . . . . . . . . . . . . . 221
Diederik Roest and Marco Scalisi
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
vii
Contributors
Pedro F. Ramírez Instituto de Física Teórica UAM/CSIC C/ Nicolás Cabrera,
Madrid, Spain
Antonio Gallerati Department DISAT, Politecnico di Torino, Torino, Italy
DietmarKlemm DipartimentodiFisica,UniversitàdiMilanoandINFN,Sezione
di Milano, Milano, Italy
Gonzalo J. Olmo Departamento de Física Teórica and IFIC, Centro Mixto
Universidad de Valencia—CSIC, Paterna, Spain; Universidad de Valencia,
Valencia, Spain; Departamento de Física, Universidade Federal da Paraíba, João
Pessoa, Paraíba, Brazil
TomásOrtín InstitutodeFísicaTeóricaUAM/CSICC/NicolásCabrera,Madrid,
Spain
Ioannis Papadimitriou SISSA and INFN—Sezione di Trieste, Trieste, Italy
Diederik Roest Van Swinderen Institute for Particle Physics and Gravity,
University of Groningen, Groningen, The Netherlands
Marco Scalisi Van Swinderen Institute for Particle Physics and Gravity,
University of Groningen, Groningen, The Netherlands
Mario Trigiante Department DISAT, Politecnico di Torino, Torino, Italy
ix
Three Lectures on the FGK
Formalism and Beyond
TomásOrtínandPedroF.Ramírez
Abstract We review the formalism proposed by Ferrara, Gibbons and Kallosh
to study charged, static, spherically symmetric black-hole solutions of d = 4
supergravity-liketheoriesanditsextensiontoobjectsofhigherworldvolumedimen-
sionsinhigherspacetimedimensionsandtheso-calledH-FGKformalismbasedon
variablestransforminglinearlyunderdualityintheeffectiveaction.Wealsoreview
applicationsoftheseformalismsto4-and5-dimensionalsupergravitytheories.
1 TheFGKFormalismfor d = 4 BlackHoles
Manyresultsinblack-holephysics1havebeenderivedfromthestudyoffamiliesof
solutions,thatis,solutionswhosefieldsdependonanumberofindependentphysical
parameters(mass,electricandmagneticcharges,angularmomentumandmoduli).
Obtainingthesefamiliesofsolutionsrequires,typically,agreatdealofeffort.The
FGKformalism[2]thatwearegoingtoreviewinthislecturedramaticallysimplifies
thistaskforthestaticcaseinsupergravity-likefieldtheories.Butitdoesmuchmore
thanthat,sinceitallowsustoderivegenericresultsaboutentirefamiliesofsolutions
without having to find them explicitly. One of these results is the general form of
thecelebratedattractormechanism[3–6]thatcontrolsthebehaviourofscalarfields
in the near-horizon limit for extremal black holes and leads to the conclusion that
theirentropyismoduli-independentandafunctionofquantizedchargesonly,which
stronglysuggestamicroscopicexplanation.
1Mostofthematerialcoveredintheselectures,withadditionalcomplementarymaterialand
referencescanbefoundintherecentbook[1].
B
T.Ortín( )·P.F.Ramírez
InstitutodeFísicaTeóricaUAM/CSICC/NicolásCabrera,13–15,C.U.
Cantoblanco,28049Madrid,Spain
e-mail:[email protected]
P.F.Ramírez
e-mail:[email protected]
©SpringerInternationalPublishingSwitzerland2016 1
R.KalloshandE.Orazi(eds.),TheoreticalFrontiersinBlackHoles
andCosmology,SpringerProceedingsinPhysics176,
DOI10.1007/978-3-319-31352-8_1
