1 / 23

Francisco Navarro-Lérida 1 , Jutta Kunz 1 , Dieter Maison 2 , Jan Viebahn 1

Charged Rotating Black Holes in Higher Dimensions. Francisco Navarro-Lérida 1 , Jutta Kunz 1 , Dieter Maison 2 , Jan Viebahn 1. MG11 Meeting, Berlin 25.7.2006. Outline. Introduction Einstein-Maxwell Black Holes Einstein-Maxwell-Dilaton Black Holes

janae
Download Presentation

Francisco Navarro-Lérida 1 , Jutta Kunz 1 , Dieter Maison 2 , Jan Viebahn 1

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. Charged Rotating Black Holes in Higher Dimensions Francisco Navarro-Lérida1, Jutta Kunz1, Dieter Maison2, Jan Viebahn1 MG11 Meeting, Berlin 25.7.2006

  2. Outline • Introduction • Einstein-Maxwell Black Holes • Einstein-Maxwell-Dilaton Black Holes • Einstein-Maxwell-Chern-Simons Black Holes • Conclusions

  3. Introduction • 4D Einstein-Maxwell (EM) black holes • D>4 Einstein-Maxwell black holes

  4. Introduction • Aim: Higher dimensional Abelian black holes asymptotically flat and with regular horizon • Black rings are allowed for D>4 Emparan&Reall 2002 • D>4 EM +

  5. Einstein-Maxwell Black Holes Einstein-Maxwell action • Maxwell field strength tensor Einstein equations with stress-energy tensor Maxwell equations

  6. Einstein-Maxwell Black Holes • General black holes: characterized by mass M N=[(D-1)/2] angular momenta Ji and charge Q(no magnetic charge for D>4) • No analytical charged rotating solutions for D>4 • Numerical approach: too complicated in the general case • Restricted case: odd dimensional black holes with equal-magnitude angular momenta • Simplification=field equations reduce to a system of 5 ODE’s Kunz, Navarro-Lérida, Viebahn 2006 • Similar procedure for EMD and EMCS theories

  7. Einstein-Maxwell Black Holes (odd D) • Ansätze (D=2N+1)

  8. Einstein-Maxwell Black Holes (odd D) • Regular horizon at r=rH with f(rH)=0 • Killing vector null at the horizon=horizon angular velocity • Removing a0 : first integral • Mass formulaGauntlett, Myers, Townsend 1999

  9. Einstein-Maxwell Black Holes (odd D) Domain of existence (scaled quantities) Angular momentum Mass

  10. Einstein-Maxwell Black Holes (odd D) • Gyromagnetic ratio • g=2 for D=4 but ... • Perturbative value g=(D-2) Aliev 2006

  11. Einstein-Maxwell-Dilaton Black Holes Einstein-Maxwell-Dilaton action (units 16  GD=1) h=dilaton coupling constant Field equations • Analytical solutions!!! Kaluza-Klein black holesKunz, Maison, Navarro-Lérida, Viebahn 2006

  12. Einstein-Maxwell-Dilaton Black Holes (Kaluza-Klein) • Myers-Perry solution as seed • Fixed dilaton coupling constant

  13. Einstein-Maxwell-Dilaton Black Holes (Kaluza-Klein) • Some quantities • Horizon: • Surface gravity: • Domains of existance: Extremal solutions sg=0 • Scaled quantities:

  14. Einstein-Maxwell-Dilaton Black Holes (Kaluza-Klein)

  15. Einstein-Maxwell-Dilaton Black Holes (Kaluza-Klein) • Similar pattern for D>6

  16. Einstein-Maxwell-Dilaton Black Holes (odd D) Einstein-Maxwell-Dilaton Black Holes (odd D) • Restricted case: odd D, equal-magnitude angular momenta • Same ansatz as in EM theory + =(r) • No constraint on the dilaton coupling constant

  17. Einstein-Maxwell-Chern-Simons Black Holes • Just for odd D(=2N+1): Chern-Simons term AFN Einstein-Maxwell-Chern-Simons action Einstein equations Maxwell equations Kunz, Navarro-Lérida 2006

  18. Einstein-Maxwell-Chern-Simons Black Holes • Black hole solutions: regular horizon r=rH • Restricted case: same ansatz as for EM black holes • First integral of the system of ODE’s • Mass formula • Scaling

  19. Einstein-Maxwell-Chern-Simons Black Holes (D=5) • Redefinition: • Cases: • Analytical solutions: only for =1Breckenridge, Myers, Peet, Vafa 1997 • Good for testing the numerical scheme(restricted case: |J1|=|J2|) • Very high accuracy!!! =0: Einstein-Maxwell theory =1: bosonic sector of minimal D=5 supergravity >1

  20. Einstein-Maxwell-Chern-Simons Black Holes (D=5) • Domain of existence(extremal solutions) Extremal =1 EMCS (supersymmetric branch) • Mass saturates • Angular momentum satisfies • Vanishing horizon angular velocity • Instability beyond =1 (up to =2)supersymmetry marks a borderline between stability and instability • =2 is a special caseinfinite set of extremal black holes with the same charges?

  21. Einstein-Maxwell-Chern-Simons Black Holes (D=5) Four types of black holes • Type I: Corrotating  J ¸ 0 and =0 , J=0 • Type II: Static horizon =0 but non-vanishing J  0 (¸ 1 and =1 ) extremal) • Type III: Counterrotating  J < 0 (  > 1) • Type IV: Rotating horizon  0 but J=0 (¸ 2 and =2 ) extremal)

  22. Einstein-Maxwell-Chern-Simons Black Holes (D=5) The horizon mass may be negative !!! Black holes are not uniquely determined by M, Ji, Q (non-uniqueness even for horizons of spherical topology)

  23. Conclusions • Abelian higher dimensional charged rotating BH’s • Restricted case: odd D + equal-magnitude angular momenta ) system of ODE’s • EM theory: non-constant gyromagnetic ratio for D>4 • Analytical Kaluza-Klein solutions in EMD theory • (Odd-D) EMCS theory: D=5 is a special case • =1: supersymmetry marks a borderline between stability and instability • Four types of black holes (for >2) • Non-uniqueness (for >2)

More Related