1 / 10

The Attractor Mechanism in Extremal Black Holes

The Attractor Mechanism in Extremal Black Holes. Alessio MARRANI Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Rome, Italy & INFN – LNF, Frascati, Italy. Prima Conferenza di Progetto del Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”,

paki-estes
Download Presentation

The Attractor Mechanism in Extremal Black Holes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Attractor Mechanism in Extremal Black Holes Alessio MARRANI Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Rome, Italy & INFN – LNF, Frascati, Italy Prima Conferenza di Progetto del Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Salone delle Conferenze, Ministero dell’Interno, Viminale, Rome, 30 November 2007

  2. Dr. S. Bellucci (INFN -- LNF, Italy) • Dr. A. Ceresole (Turin Univ. & INFN – Turin, Italy) • Prof. S. Ferrara (CERN, Switzerland & UCLA, USA & INFN -- LNF, Italy) • Prof. M. Gunaydin (Penn State Univ., PA, USA) • Dr. E. Orazi(Turin Politecnico & INFN – Turin, Italy) • Dr. A. Shcherbakov(JINR, Dubna, Russia & INFN – LNF, Italy) • Dr. A. Yeranyan (Yerevan State Univ., Armenia & INFN – LNF, Italy) Collaborators: Papers on Attractors: • On some properties of the attractor equations, PLB 635, 172 (2006), hep-th/0602161 • Charge orbits of symmetric special geometries and attractors, IJMP A21,5043 (2006), hep-th/0606209 • Mirror Fermat Calabi-Yau Threefolds and Landau-Ginzburg Black Hole Attractors, Riv. Nuovo Cim. 029, 1 (2006), hep-th/0608091 • Attractor Horizon Geometries of Extremal Black Holes, XVII SIGRAV Conf. 2006, hep-th/0702019 • N=8 non-BPS Attractors, Fixed Scalars and Magic Supergravities, NPB 2007, in press, arXiv:0705.3866 • On the Moduli Space of non-BPS Attractors for N=2 Symmetric Manifolds, PLB 652, 111 (2007), arXiv:0706.1667 • 4d/5d Correspondence for the Black Hole Potential and its Critical Points, CQG 2007, in press, arXiv:0707.0964 • Attractors with Vanishing Central Charge, PLB 2007 (in press), arXiv:0707.2730 • Black Hole Attractors in Extended Supergravity, PASCOS07, arXiv:0708.1268 Book : Supersymmetric mechanics. Vol. 2: The attractor mechanism and space time singularities, LNP 701, Springer – Verlag, 2006 A. Marrani, SIF 2006

  3. N=2, d=4 Supergravity coupled to nV Abelian vector multiplets: Maxwell-Einstein Supergravity Theory (MESGT) Field content : Graviphoton  Supergravity Multiplet Vielbein SU(2)doublet of gravitinos  nV Abelian Vector Multiplets Complex scalar fields (MODULI) U(1) gauge boson Doublet of gauginos Gauge Symmetry Overall No Hypermultiplets will be considered : they decouple from the system A. Marrani, SIF 2006 Only scalars from vector multiplets are relevant for the ATTRACTOR MECHANISM

  4. What is the Attractor Mechanism? • Bekenstein – Hawking Entropy – Area Formula (Macroscopic Approach to Black Hole Thermodynamics) • We consider an Extremal (T=0), dyonic, asymptotically flat, spherically symmetric, static Black Hole (BH) A priori the BH entropy will depend on the following variables : BH Magnetic charges BH Electric charges Values of the moduli fields at the Event Horizon of the black hole: Notice : they willin generaldepend on theinitial dataof their deterministic, classical evolution dynamics, i.e. on theasymptotical values are UNCONSTRAINED; they can take any possible complex value A. Marrani, SIF 2006

  5. Can the moduli be stabilizedat the Event Horizon of the BH? Can theybe made INDEPENDENTon the UNCONSTRAINED asymptotical values? S. Ferrara, R. Kallosh, Phys.Rev. D54 (1996),1514, Phys.Rev. D54 (1996),1525, S. Ferrara, G. Gibbons, R. Kallosh, Nucl.Phys. B500 (1997),75 ATTRACTOR MECHANISM: In approaching the Event Horizon, the moduli completelylose memoryof the initial data, and take values dependentONLYon theelectric/magnetic charges of the BH: Regardless of the initial conditions, the Horizon values depend ONLY on the charges, but nevertheless the evolution remains DETERMINISTIC! Conserved charges, from gauge-inv. A. Marrani, SIF 2006

  6. Thus, which is the criterion to determine the purely charge-dependent configs. of the moduli? How can the ATTRACTOR MECHANISM be implemented? Critical implementation(Ferrara, Gibbons, Kallosh, Nucl. Phys. B500 (1997), 75): actually are non-degenerate critical points of an “effective black hole potential” Z is the N=2 Kaehler-covariantly holomorphic “central charge function” Regular contravariant metric of the Special Kaehler moduli space : Covariant derivative of Z: Horizon moduli configs. characterized as critical pts. of VBH CLASSICAL BLACK HOLE ENTROPY A. Marrani, SIF 2006

  7. General classification of BH Attractors in N=2, d=4 MESGT: • ½-BPS Attractors:they preserve the maximum number of SUSYs (4 out of 8), and • they do saturate the Bogomol’ny – Prasad – Sommerfeld (BPS) bound: Characterizing conditions: Known since the mid 90’s, starting from the cited seminal paper by Ferrara, Gibbons and Kallosh. 2. non-BPS Attractors with non-vanishing central charge: they do not preserve any SUSY of the asymptotical Minkowskian bkgd.,and do NOT saturate the BPS bound: Characterizing conditions: Recently discovered (Goldstein et al., hep-th/0507096, Tripathy and Trivedi, hep-th/0511117, and many others…), they correspond to BH backgrounds breaking all SUSYs, but in the framework of a SUSY theory : important phenomenological implications! A. Marrani, SIF 2006

  8. 3. non-BPS Attractors with vanishing central charge: they do not preserve any SUSY of the asymptotical Minkowskian background,and do NOTsaturate the BPS bound: It can be traced back to the regularity of the SKG of the moduli space Characterizing conditions: Until June 2006, the unique explicit example of such a kind of extremal BH Attractors was given by Giryavets in hep-th/0511215. Since then, the non-BPS, Z=0 Attractors have been studied by S.Bellucci, S.Ferrara, A.M., E. Orazi and A. Shcherbakov in a number of frameworks:  Homogeneous Symmetric Special Kaeheler Geometries;  Special Kaeheler Moduli Spaces arising from compactifications of d=10 Superstrings on Fermat CY3;  Peculiar Homogeneous Symmetric Models, the so-called st2 (nV =2) and stu (nV =3) Models. Such a kind of Attractors turns out to be really interesting, since it gives rise to a BH background breaking all SUSYs in the framework of N=2, d=4 MESGT, butwithout central extension of the N=2 SUSY algebra pertaining the asymptotical Minkowskian background. A. Marrani, SIF 2006

  9. Outlook and further developments: • Study of BH Attractors in particular classes of Special Kaeheler Geometries (SKGs) • of the scalar manifold of Maxwell-Einstein supergravities, such as: SKGs with “deformed” periods, arising from dimensional compactifications on complex 3-folds which are CY3s only LOCALLY (for recent studies on SKG related to LOCAL CY3s, see e.g. Bilal and Metzger, hep-th/0503173) • Analysis of the (SK?) geometries of the moduli spaces arising from • compactifications on (CY) Supermanifolds  SUSY extension of the moduli space: What is the supersymmetrized analogue of the Attractor Mechanism?  Need for extension of Symplectic Geometry on Supermanifolds (recently studied, see Lavrov and Radchenko, arXiV : 0708.3778)  for recent advances on compactifications on supermanifolds, see e.g. Grassi and Marescotti, hep-th/0607243 • Going beyond the Static case : • Rotating • and/or Asymptotically non-flat (AdS) • and/or with non-vanishing Cosmological Constant • Extremal BHs A. Marrani, SIF 2006

  10. Thank You! A. Marrani, SIF 2006

More Related