Dynamical black rings with a positive

1. Dynamical black rings with a positive PRD 80, 044012 (2009) Masashi Kimura ( Osaka City University ) 2009 12/24

2. Recently many black objects are constructed Black Saturn (Elvang et al 2007) Black di-ring (Iguchi and Mishima 2007) Orthogonal Black rings (Izumi 2009, Elvang et al 2009) ・・・・ Introduction Black ring sol. (Emparan & Reall 2002)is one of the most important discoveries because that means ・uniqueness theorem (in the sence of 4D case) does not hold in higher-dim space-time ・shape of black objects can take various topology in higher-dim space-time

3. By now, attempts to obtain a regular stationary black ring sol with did not succeed. In this talk we consider a possibility that the solution is dynamical by the existence of (positive) Some people are interested in black rings with in the context of AdS/CFT correspondence (and purely mathematical interest)

4. Contents ・ Introduction ・ Kastor-Traschen coalescing BH solution ・ Dynamical black rings with a positive ・ Summary

5. ・ Kastor-Traschen coalescing BH solution

6. unknown function Setup ・5D Einstein-Maxwell system with positive ・anzats where

7. If (point source harmonics) the metric becomes 5D Reissner-Nordstroem-de Sitter BH (Q = m) written in cosmological coord Then Einstein eq and Maxwell eq reduce to (Kastor, Traschen 1993, London 1995 ) We just have to solve Laplace eq on

8. Kastor-Traschen solution (Kastor, Traschen 1993, London 1995 ) If the metric becomes this metric describes coalescence of two BHs

9. Late time behavior At Same form as RNdS BH with mass RNdS BH has a BH horizon at We can see that there is a single BH at late time

10. We can find the location of horizon at each time by solving null geodesics We know where the BH horizon locates at late time

11. Time evolution of event horizon

12. Time evolution of event horizon (almost proper length) we can see the coalescence process

13. ・ Dynamical black rings with a positive

14. Next, we focus on thering source harmonics We show that the metric describes dynamical black ring

15. Late time behavior At Same form as RNdS BH RNdS BH has a BH horizon at So we can see that there is a single BH at late time like Kastor-Traschen sol

16. Time evolution of event horizon

17. Early time behavior At early time, we can see the event horizon locate near source of ring harmonics Near ～ black string

18. If → naked singularity at We investigate whether the singularities are hidden by the horizon i.e. whether the null geodesic generator reach at a finite time

19. Focus on 2D part Null geodesics obey We can see singularities are hidden by horizon at the least finite past time

20. However, as along the horizon This singularity is not so wrong as long as we focus on the region in which the time coordintate takes finite value

21. singular Summary A thin black ring at early time shrinks and changes into a single BH as time increases

26. ・ 5D Reissner-Nordstroem-de Sitter BH metric ( Q = M ) written in cosmological coordinate BH horizon (event horizon) locates where is one of roots a equation ( )

27. Charged Black String (Horowitz - Maeda 2002) ：horizon ：singularity で として