Presentation is loading. Please wait.

Presentation is loading. Please wait.

T. Delsate University of Mons-Hainaut Talk included in the Rencontres de Moriond 2009 – La Thuile (Italy).

Published byBeryl Logan Modified over 8 years ago

Similar presentations

Presentation on theme: "T. Delsate University of Mons-Hainaut Talk included in the Rencontres de Moriond 2009 – La Thuile (Italy)."— Presentation transcript:

1 T. Delsate University of Mons-Hainaut Talk included in the Rencontres de Moriond 2009 – La Thuile (Italy).

2  Motivations  Asymptotically flat space:  Black Strings and the GL instability  Phase diagram of higher dimensional black strings  Asymptotically AdS space:  Uniform black string in AdS  Still a GL instability ?  Perturbative non uniform black string in AdS: a first step in the phase diagram  Non-perturbative analysis : hint for localised black holes  Conclusion

3  Suppose d>4. Gravity propagates in ED.

4  Black Objects = theoretical labs for gravity. NB : No more uniqueness thm in ED.

5  Suppose d>4. Gravity propagates in ED.  Black Objects = theoretical labs for gravity. NB : No more uniqueness thm in ED.  If ED are compact, possible black strings

6  Suppose d>4. Gravity propagates in ED.  Black Objects = theoretical labs for gravity. NB : No more uniqueness thm in ED.  If ED are compact, possible black strings  Better understanding of Black String phases.  Relatively well understood in asymptotically flat space.

7  Suppose d>4. Gravity propagates in ED.  Black Objects = theoretical labs for gravity. NB : No more uniqueness thm in ED.  If ED are compact, possible black strings  Better understanding of Black String phases.  Relatively well understood in asymptotically flat space.  Why AdS ?

8  Suppose d>4. Gravity propagates in ED.  Black Objects = theoretical labs for gravity. NB : No more uniqueness thm in ED.  If ED are compact, possible black strings  Better understanding of Black String phases.  Relatively well understood in asymptotically flat space.  Why AdS ?  AdS / CFT duality

9  Suppose d>4. Gravity propagates in ED.  Black Objects = theoretical labs for gravity. NB : No more uniqueness thm in ED.  If ED are compact, possible black strings  Better understanding of Black String phases.  Relatively well understood in asymptotically flat space.  Why AdS ?  AdS / CFT duality  Why not ?

10  d-dim Black string solution to Einstein equation, R MN = 0: r z L r0r0 (d-1) Tangherlini

11  d-dim Black string solution to Einstein equation, R MN = 0: r z L (d-1) Tangherlini+ 1 Ricci flat direction

12 Black Strings are unstable towards long wavelength perturbations (R. Gregory, R. Laflamme – 1993)

13 Black Strings are unstable towards long wavelength perturbations (R. Gregory, R. Laflamme – 1993)  k

14 Black Strings are unstable towards long wavelength perturbations (R. Gregory, R. Laflamme – 1993)  k kckc UnstableStable

15 For a given mass, long black string are unstableshort black strings are stable  k kckc UnstableStable

16 For a given mass, long black string are unstableshort black strings are stable  k kckc UnstableStable

17 -> Unstable black strings. What should they decay to? r z L

18 -> Unstable black strings. What should they decay to ? Localised Black Hole ? r z LL ?

19  Answer : NO ! ->Takes an infinite proper time at the horizon for such a transition… (Horowitz and Maeda, 2001)

20  Answer : NO ! ->Takes an infinite proper time at the horizon for such a transition… (Horowitz and Maeda, 2001) -> Suggests the existance of something else L Non uniform Black String (Gubser 2002, Wiseman 2003)

21 Thermodynamical quantities : Mass M (time translation), Entropy S (quarter horizon area), Temperature T H (regular Euclidean sections), Tension T (z translation)

22 Thermodynamical quantities : Mass M (time translation), Entropy S (quarter horizon area), Temperature T H (regular Euclidean sections), Tension T (z translation) Dimensionless quantities : n = T /ML  = G d M/L d-3

23 Thermodynamical quantities : Mass M (time translation), Entropy S (quarter horizon area), Temperature T H (regular Euclidean sections), Tension T (z translation) Dimensionless quantities : n = T /ML  = G d M/L d-3 Harmark, Niarchos and Obers n  Uniform Black String Non Uniform BS Localised BH

24 Thermodynamical quantities : Mass M (time translation), Entropy S (quarter horizon area), Temperature T H (regular Euclidean sections), Tension T (z translation) Dimensionless quantities : n = T /ML  = G d M/L d-3 n  Uniform Black String Non Uniform BS Localised BH cc Merger Point Harmark, Niarchos and Obers

25 Thermodynamical quantities : Mass M (time translation), Entropy S (quarter horizon area), Temperature T H (regular Euclidean sections), Tension T (z translation) Dimensionless quantities : n = T /ML  = G d M/L d-3 cc Topological phase transition = difficult to study n  Uniform Black String Non Uniform BS Localised BH Harmark, Niarchos and Obers Merger Point

26 Do all these phenomenae have an AdS counterpart ?

27  Uniform black string solution in AdS (Mann, Radu, Stelea – 2006)

28  Uniform black string solution in AdS (Mann, Radu, Stelea – 2006)

29  Uniform black string solution in AdS (Mann, Radu, Stelea – 2006)  f 1 =f 1 (r 0,l,d), a 0, b 1 arbitrary constants (fixed by asymptotically AdS requirement)  l² being the AdS radius  No Closed form solution -> numerics

30  Thermodynamics :

31  T H, S as usual

32  Thermodynamics :  T H, S as usual  Mass, Tension : Counter term procedure (Balasubramanian, Kraus 1999) ▪ Involves integration over z from 0 to L.

33  Thermodynamics :  T H, S as usual  Mass, Tension : Counter term procedure (Balasubramanian, Kraus 1999) ▪ Involves integration over z from 0 to L. ▪ NB : No obvious background for background substraction methods

34  2 phases :

35  2 phases :  Small black string (r 0 /l <<1): ▪ Essentially same feature as flat case (thermodynamically unstable)

36  2 phases :  Small black string (r 0 /l <<1): ▪ Essentially same feature as flat case (thermodynamically unstable)  Big black string : ▪ Becomes thermodynamically stable (« AdS acts like a confining box ») NB : This phenomena occurs for AdS black Holes (Hawking, Page 1983)

37  Non-uniform ansatz

38  Non-uniform ansatz

39  Non-uniform ansatz  Xi’s = Fourier modes  k c =2  /L fixes the length of the black string.

40  Order  : Stability. (=static perturbation,  = 0) (Brihaye, Delsate and Radu – 2007)

41  Order  : Stability. (=static perturbation,  = 0) (Brihaye, Delsate and Radu – 2007)  Equations of Motion : Eigen value problem for k c ².  Also numerical (background is numerical…)

42  Order  : Stability. (=static perturbation,  = 0) (Brihaye, Delsate and Radu – 2007)  Equations of Motion : Eigen value problem for k c ².  Also numerical (background is numerical…)  k c ² > 0 = Exists GL instability  k c ² < 0 = Dynamically stable. NB : AdS radius provides a lengthscale -> µ 2 = L/l = 1/(l k c )

43  Results :

44  Results :  Small AdS black string dynamically unstable

45  Results :  Small AdS black string dynamically unstable  Big AdS black string dynamically stable

46  Results :  Small AdS black string dynamically unstable  Big AdS black string dynamically stable THE DYNAMICAL AND THERMODYNAMICAL INSTABILITIES MATCH ! (=Gubser-Mitra conjecture, 2001)

47  Order  ² : (Delsate – 2008)

48  Corrections on thermodynamical quantities

49  Order  ² : (Delsate – 2008)  Corrections on thermodynamical quantities Recall the integration over z from 0 to L=2  /k c :  Order  : linear in cos(k c z)

50  Order  ² : (Delsate – 2008)  Corrections on thermodynamical quantities Recall the integration over z from 0 to L=2  /k c :  Order  : linear in cos(k c z)  Order  ² : ▪Linear in X 0, X 2 cos(2k c z) -> X 2 terms vanish ▪Terms of the form X 1 ²

51  Corrections on thermodynamical quantities at fixed length n 

52 n  µ 1 (1) µ 1 (3) µ 1 (2) n UBS (µ 1 (i) ) n pNUBS (µ 1 (i) ) n UBS (µ)/L n 

53  Corrections on thermodynamical quantities at fixed length n  µ 1 (1) µ 1 (3) µ 1 (2) n UBS (µ 1 (i) ) n pNUBS (µ 1 (i) ) n UBS (µ)/L n  Effect of the new Length scale !!

54  Corrections on thermodynamical quantities at fixed length n  µ 1 (1) µ 1 (3) µ 1 (2) n UBS (µ 1 (i) ) n pNUBS (µ 1 (i) ) n UBS (µ)/L n  ?

55  Corrections on thermodynamical quantities at fixed length (S UBS /L independant of L) S/L  µ 1 (1) µ 1 (3) µ 1 (2) S/L UBS (µ 1 (i) ) S/L pNUBS (µ 1 (i) ) S UBS (T H )/L

56  Corrections on thermodynamical quantities at fixed length (S UBS /L independant of L) S/L  µ 1 (1) µ 1 (3) µ 1 (2) µ 1 (0)  S/  T H >0 : new thermodynamically stable phases (T. Delsate – 12/2008)

57  Corrections on thermodynamical quantities at fixed length (S UBS /L independant of L) S/L  µ 1 (1) µ 1 (3) µ 1 (2) µ 1 (0)  S/  T H >0 : new thermodynamically stable phases L large, r 0 small : « Long small NUBS » (T. Delsate – 12/2008)

58  First results in non perturbative approach confirms the perturbative results

59  Regime of strong deformation suggests the existance of localised black holes

60  First results in non perturbative approach confirms the perturbative results  Regime of strong deformation suggests the existence of localised black holes  Only partial results, still under investigation

61 Prediction from perturbative analysis are confirmed within the numerical accuracy d0d0

62 Embedding of the horizon in euclidean space z r

63 Embedding of the horizon in euclidean space Preiodicity in z direction -> Localised black hole phase ? z r

64 Embedding of the horizon in euclidean space Preiodicity in z direction -> Localised black hole phase ? NB : d 0 controls the deformation z r

65  Small black Strings in AdS are unstable - Large black strings are not,  neither thermo nor dynamically (Gubser Mitra)  Small AdS BS follow the same pattern as Flat case  New thermo stable pNUBS  To be confirmed with non perturbative analysis  Hint for the localised AdS black hole phase  First approximation for AdS black rings ?  (thin black rings ; works for  =0).  Connection with boundary CFT in AdS/CFT context?  New backgrounds for the dual theory (S d-3 xS 1 ).  Dual of the new stable long-small black strings?

66  Small black Strings in AdS are unstable - Large black strings are not,  neither thermo nor dynamically (Gubser Mitra)  Small AdS BS follow the same pattern as Flat case  New thermo stable pNUBS  To be confirmed with non perturbative analysis  Hint for the localised AdS black hole phase  First approximation for AdS black rings ?  (thin black rings ; works for  =0).  Connection with boundary CFT in AdS/CFT context?  New backgrounds for the dual theory (S d-3 xS 1 ).  Dual of the new stable long-small black strings?

67  Small black Strings in AdS are unstable - Large black strings are not,  neither thermo nor dynamically (Gubser Mitra)  Small AdS BS follow the same pattern as Flat case  New thermo stable pNUBS  To be confirmed with non perturbative analysis  Hint for the localised AdS black hole phase  First approximation for AdS black rings ?  (thin black rings ; works for  =0).  Connection with boundary CFT in AdS/CFT context?  New backgrounds for the dual theory (S d-3 xS 1 ).  Dual of the new stable long-small black strings?

68  Small black Strings in AdS are unstable - Large black strings are not,  neither thermo nor dynamically (Gubser Mitra)  Small AdS BS follow the same pattern as Flat case  New thermo stable pNUBS  To be confirmed with non perturbative analysis  Hint for the localised AdS black hole phase  First approximation for AdS black rings ?  (thin black rings ; works for  =0).  Connection with boundary CFT in AdS/CFT context?  New backgrounds for the dual theory (S d-3 xS 1 ).  Dual of the new stable long-small black strings?

69  Small black Strings in AdS are unstable - Large black strings are not,  neither thermo nor dynamically (Gubser Mitra)  Small AdS BS follow the same pattern as Flat case  New thermo stable pNUBS  To be confirmed with non perturbative analysis  Hint for the localised AdS black hole phase  First approximation for AdS black rings ?  (thin black rings ; works for  =0).  Connection with boundary CFT in AdS/CFT context?  New backgrounds for the dual theory (S d-3 xS 1 ).  Dual of the new stable long-small black strings?

70  Small black Strings in AdS are unstable - Large black strings are not,  neither thermo nor dynamically (Gubser Mitra)  Small AdS BS follow the same pattern as Flat case  New thermo stable pNUBS  To be confirmed with non perturbative analysis  Hint for the localised AdS black hole phase  First approximation for AdS black rings ?  (thin black rings ; works for  =0).  Connection with boundary CFT in AdS/CFT context?  New backgrounds for the dual theory (S d-3 xS 1 ).  Dual of the new stable long-small black strings?

71  Small black Strings in AdS are unstable - Large black strings are not,  neither thermo nor dynamically (Gubser Mitra)  Small AdS BS follow the same pattern as Flat case  New thermo stable pNUBS  To be confirmed with non perturbative analysis  Hint for the localised AdS black hole phase  First approximation for AdS black rings ?  (thin black rings ; works for  =0).  Connection with boundary CFT in AdS/CFT context?  New backgrounds for the dual theory (S d-3 xS 1 ).  Dual of the new stable long-small black strings?

72  Small black Strings in AdS are unstable - Large black strings are not,  neither thermo nor dynamically (Gubser Mitra)  Small AdS BS follow the same pattern as Flat case  New thermo stable pNUBS  To be confirmed with non perturbative analysis  Hint for the localised AdS black hole phase  First approximation for AdS black rings ?  (thin black rings ; works for  =0).  Connection with boundary CFT in AdS/CFT context?  New backgrounds for the dual theory (S d-3 xS 1 ).  Dual of the new stable long-small black strings?

73  Small black Strings in AdS are unstable - Large black strings are not,  neither thermo nor dynamically (Gubser Mitra)  Small AdS BS follow the same pattern as Flat case  New thermo stable pNUBS  To be confirmed with non perturbative analysis  Hint for the localised AdS black hole phase  First approximation for AdS black rings ?  (thin black rings ; works for  =0).  Connection with boundary CFT in AdS/CFT context?  New backgrounds for the dual theory (S d-3 xS 1 ).  Dual of the new stable long-small black strings?

74  Small black Strings in AdS are unstable - Large black strings are not,  neither thermo nor dynamically (Gubser Mitra)  Small AdS BS follow the same pattern as Flat case  New thermo stable pNUBS  To be confirmed with non perturbative analysis  Hint for the localised AdS black hole phase  First approximation for AdS black rings ?  (thin black rings ; works for  =0).  Connection with boundary CFT in AdS/CFT context?  New backgrounds for the dual theory (S d-3 xS 1 ).  Dual of the new stable long-small black strings?

75  Small black Strings in AdS are unstable - Large black strings are not,  neither thermo nor dynamically (Gubser Mitra)  Small AdS BS follow the same pattern as Flat case  New thermo stable pNUBS  To be confirmed with non perturbative analysis  Hint for the localised AdS black hole phase  First approximation for AdS black rings ?  (thin black rings ; works for  =0).  Connection with boundary CFT in AdS/CFT context?  New backgrounds for the dual theory (S d-3 xS 1 ).  Dual of the new stable long-small black strings?

76

77  R. Gregory and R. Laflamme, `Black strings and p-branes are unstable', Phys. Rev. Lett. 70 (1993) 2837, hep-th/9301052.  R. Mann, E. Radu and C. Stelea, `Black string solutions with negative cosmological constant', JHEP 09 (2006) 073, hep-th/0604205.  S.W. Hawking, D.N. Page, Commun. Math. Phys. 87 (1983) 577.  B. Kol, `The Phase Transition between Caged Black Holes and Black Strings – A review', Phys. Rept. 422 (2006) 119-165,hep-th/0411240.  S. Gubser and I. Mitra, `The evolution of unstable black holes in anti-de Sitter space', JHEP 08 (2001) 018, hep-th/0011127.  S. Gubser, `On non-uniform black branes', Class. Quant. Grav. 19 (2002) 4825- 4844, hep-th/0110193.  T. Wiseman, `Static axisymmetric vacuum solutions and non-uniform black strings', Class. Quant. Grav. 20 (2003) 1137, hep-th/0209051.  T. Harmark, V. Niarchos, N. A. Obers, `Instabilities of black strings and branes‘, Class.Quant.Grav.24:R1-R90,2007  Y. Brihaye, T. Delsate and E. Radu, `On the stability of AdS black strings', 2007, Phys.Lett.B662:264-269,2008, hep-th/00710.4034.  T. Delsate, `Pertubative non uniform string in AdS 6 ', Phys. Lett. B663 (2008) 118- 124, arXiv:0802.1392.  T. Delsate, `New Stable phase of AdS d Black Strings’, JHEP 159 p1008

Download ppt "T. Delsate University of Mons-Hainaut Talk included in the Rencontres de Moriond 2009 – La Thuile (Italy)."

Similar presentations

Towards understanding the final fate of the black string Luis Lehner UBC-CITA-PIMS.

Towards understanding the final fate of the black string Luis Lehner UBC-CITA-PIMS.
ICHEP conference, Paris, 22/07/10. Emergence Current Paradigm FUNDAMENTAL FORCES: carried by elementary particles.

ICHEP conference, Paris, 22/07/10. Emergence Current Paradigm FUNDAMENTAL FORCES: carried by elementary particles.
Martín Schvellinger Instituto de Física de La Plata - CONICET Departamento de Física - UNLP The gauge/gravity duality and Non-Relativistic Quantum Field.

Martín Schvellinger Instituto de Física de La Plata - CONICET Departamento de Física - UNLP The gauge/gravity duality and Non-Relativistic Quantum Field.
Brane-World Inflation

Brane-World Inflation
8/1(Thu), 2013 Parallel talk (Theoretical development) Daisuke Kadoh (KEK) D.K. and Syo Kamata, in preparation TexPoint fonts used in.

8/1(Thu), 2013 Parallel talk (Theoretical development) Daisuke Kadoh (KEK) D.K. and Syo Kamata, in preparation TexPoint fonts used in.
Holographic Superconductors with Higher Curvature Corrections Sugumi Kanno (Durham) work w/ Ruth Gregory (Durham) Jiro Soda (Kyoto) arXiv:0907.3203, to.

Holographic Superconductors with Higher Curvature Corrections Sugumi Kanno (Durham) work w/ Ruth Gregory (Durham) Jiro Soda (Kyoto) arXiv: , to.
(In)Stabilities and Complementarity in AdS/CFT Eliezer Rabinovici The Hebrew University, Jerusalem Based on works with J.L.F Barbon Based on work with.

(In)Stabilities and Complementarity in AdS/CFT Eliezer Rabinovici The Hebrew University, Jerusalem Based on works with J.L.F Barbon Based on work with.
ASYMPTOTIC STRUCTURE IN HIGHER DIMENSIONS AND ITS CLASSIFICATION KENTARO TANABE (UNIVERSITY OF BARCELONA) based on KT, Kinoshita and Shiromizu PRD84 044055.

ASYMPTOTIC STRUCTURE IN HIGHER DIMENSIONS AND ITS CLASSIFICATION KENTARO TANABE (UNIVERSITY OF BARCELONA) based on KT, Kinoshita and Shiromizu PRD
The attractor mechanism, C-functions and aspects of holography in Lovelock gravity Mohamed M. Anber November 27 2007 HET bag-lunch.

The attractor mechanism, C-functions and aspects of holography in Lovelock gravity Mohamed M. Anber November HET bag-lunch.
Quantum Tunneling of Thin Wall Matthew C. Johnson, in collaboration with Anthony Aguirre.

Quantum Tunneling of Thin Wall Matthew C. Johnson, in collaboration with Anthony Aguirre.
Entanglement in Quantum Critical Phenomena, Holography and Gravity Dmitri V. Fursaev Joint Institute for Nuclear Research Dubna, RUSSIA Banff, July 31,

Entanglement in Quantum Critical Phenomena, Holography and Gravity Dmitri V. Fursaev Joint Institute for Nuclear Research Dubna, RUSSIA Banff, July 31,
Elcio Abdalla Perturbations around Black Hole solutions.

Elcio Abdalla Perturbations around Black Hole solutions.
Shock waves in strongly coupled plasmas M. Kruczenski Purdue University Based on: arXiv:1004.3803 (S. Khlebnikov, G. Michalogiorgakis, M.K.) Quantum Gravity.

Shock waves in strongly coupled plasmas M. Kruczenski Purdue University Based on: arXiv: (S. Khlebnikov, G. Michalogiorgakis, M.K.) Quantum Gravity.
Francisco Navarro-Lérida 1, Jutta Kunz 1, Dieter Maison 2, Jan Viebahn 1 MG11 Meeting, Berlin 25.7.2006 Charged Rotating Black Holes in Higher Dimensions.

Francisco Navarro-Lérida 1, Jutta Kunz 1, Dieter Maison 2, Jan Viebahn 1 MG11 Meeting, Berlin Charged Rotating Black Holes in Higher Dimensions.
Black Holes in Extra Dimensions COSMO 2003, Ambleside Toby Wiseman Cambridge (UK) / Harvard Work with B. Kol (Hebrew University) H. Kudoh (Kyoto)

Black Holes in Extra Dimensions COSMO 2003, Ambleside Toby Wiseman Cambridge (UK) / Harvard Work with B. Kol (Hebrew University) H. Kudoh (Kyoto)
Non-uniform black strings/branes: non-linear effects of gauge charge Umpei MIYAMOTO Waseda U. “Einstein's Gravity in Higher Dims” 18-22 Feb

Non-uniform black strings/branes: non-linear effects of gauge charge Umpei MIYAMOTO Waseda U. “Einstein's Gravity in Higher Dims” Feb
AdS4/CFT3+gravity for Accelerating Conical Singularities arXiv:0809.2789 arXiv:0809.2789 Mohamed Anber HET Bag Lunch Novemberr 12th.

AdS4/CFT3+gravity for Accelerating Conical Singularities arXiv: arXiv: Mohamed Anber HET Bag Lunch Novemberr 12th.
JHEP 06 (2004) 053, hep-th/0406002 The Hebrew University July 27 2006 Freie Universität Berlin Class.Quant.Grav. 22 (2005) 3935-3960, hep-th/0505009 Talk.

JHEP 06 (2004) 053, hep-th/ The Hebrew University July Freie Universität Berlin Class.Quant.Grav. 22 (2005) , hep-th/ Talk.
Robert Mann D. Kubiznak, N. Altimirano, S. Gunasekaran, B. Dolan, D. Kastor, J. Traschen, Z. Sherkatgnad D.Kubiznak, R.B. Mann JHEP 1207 (2012) 033 S.

Robert Mann D. Kubiznak, N. Altimirano, S. Gunasekaran, B. Dolan, D. Kastor, J. Traschen, Z. Sherkatgnad D.Kubiznak, R.B. Mann JHEP 1207 (2012) 033 S.
Strings and Black Holes David Lowe Brown University AAPT/APS Joint Fall Meeting.

Strings and Black Holes David Lowe Brown University AAPT/APS Joint Fall Meeting.

Similar presentations

Ads by Google