1. Moulting Black Holes KEK, 22 June 2011 Masaki Shigemori (KMI, Nagoya U) Iosif Bena, Borun Chowdhury, Jan de Boer, Sheer El-Showk and MS: 103.nnnn

2. 2

3. Introduction 3

4. No hair theorem 4 Black holes have no “hair” Unique BH solution

5. 5

6. “Moulting” black holes 6  AdS BH can spit out excessive charges to “hair” and increase entropy  Einstein-Maxwell has BH with charged condensate [Gubser]  AdS 5 BH with R-charge [Bhattacharyya+Minwalla+Papadodimas]  “Enigmatic” BHs in 4d N=2 sugra / MSW [Denef+Moore] “moults” hair “hair” — but not under very good control

7. 7

8. AdS 3 /CFT 2 : ideal arena 8

9. 9

10. What we do 10

11. Outline 11  Introduction  Boundary CFT side  Bulk gravity side  Discussion  Conclusion

12. Boundary CFT side of the story 12

13. 13 bulkboundary The AdS 3 /CFT 2 correspondence

14. Some facts about D1-D5 CFT 14 “Standard lore” phase diagram Cardy formula

15. States of D1-D5 CFT 15 charges add up

16. Example: BMPV ensemble 16 BMPV BH

17. The question 17

18. Maximizing entropy 18

19. The new CFT phase diagram 19 P=N/5 Applies for both T 4 & K3 old new

20. Numerical check 20 Confirmed!

21. Comments 21  Absolute # of states  Not protected  Not absolute # of states  Protected

22. Summary — CFT side 22

23. Bulk sugra side of the story 23

24. The goal 24

25. Supersymmetric sugra solutions 25  Assume two isometries  reduces to 4d N=2 sugra  Most general timelike susy solutions in 4D known [Bates-Denef] [Gauntlett-Gutowski] [Bena-Warner]

26. Ansatz 26 2-center configs. Play with parameters and maximize BH entropy Parameters constrained to give desired total charges

27. Result: max-entropy 2-center configs. 27 P=N/5

28. Bulk phase diagram 28  2-center configs very barely dominates over BMPV P=N/5 BMPV CFT enigmatic BMPV+tube BR BMPV BMPV+tube BMPV BMPV+tube BR

29. Summary — gravity side 29 gravityCFT

30. Discussion 30

31. Discussion 31  Found configs whose entropy is larger than BMPV  BMPV is unstable, in spite of susy  BH configs exist even outside the BMPV parabola!  Elliptic genus doesn’t capture this BH Cf. Matching of CFT and sugra elliptic genera [de Boer] It was believed that there are no BHs in the gray region, but there are!

32. Partial lifting (1) 32 Standard lore CFT gravity contribute to index don’t contribute to index protected pairwise lift

33. Partial lifting (2) 33 The reality CFT gravity contribute to index don’t contribute to index pairwise lift protected don’t lift! “enigmatic” states Protected for dynamical reasons, not susy?

34. Conclusion 34

35. Conclusion 35

36. 36 Thanks!

37. 37

38. A new index? 38 We are not turning on generic moduli — There may be an index protected only on special loci other moduli special locus generic locus moduli space of T 4 /K3

39. Unsolved issues 39  Black rings (susy)  Microscopics (CFT state) not understood [Bena+Kraus]  Dipole charge?  Multi-center solutions  Zoo of solutions, no organizing principle  Microscopics unclear  Fuzzballs / gravity microstate