1/21 Dynamical black rings with a positive Masashi Kimura ( Osaka City University ) /24 PRD 80, (2009)

2 /21 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 Black Saturn (Elvang et al 2007) Black di-ring (Iguchi and Mishima 2007) Orthogonal Black rings (Izumi 2009, Elvang et al 2009) ・・・・ Recently many black objects are constructed

3 /21 Some people are interested in black rings with in the context of AdS/CFT correspondence (and purely mathematical interest) By now, attempts to obtain a regular stationary black ring sol with did not succeed. we consider a possibility that the solution is dynamical by the existence of (positive) In this talk

4 /21 Contents ・ Introduction ・ Kastor-Traschen coalescing BH solution ・ Dynamical black rings with a positive ・ Summary

5 /21 ・ Kastor-Traschen coalescing BH solution

6 /21 Setup ・ 5D Einstein-Maxwell system with positive ・ anzat s where unknown function

7 /21 (Kastor, Traschen 1993, London 1995 ) Then Einstein eq and Maxwell eq reduce to We just have to solve Laplace eq on If (point source harmonics) the metric becomes 5D Reissner-Nordstroem-de Sitter BH (Q = m) written in cosmological coord

8 /21 If this metric describes coalescence of two BHs the metric becomes (Kastor, Traschen 1993, London 1995 ) Kastor-Traschen solution

9 /21 Late time behavior Same form as RNdS BH with mass We can see that there is a single BH at late time At RNdS BH has a BH horizon at

10 /21 We know where the BH horizon locates at late time We can find the location of horizon at each time by solving null geodesics

11 /21 Time evolution of event horizon

12 /21 Time evolution of event horizon (almost proper length) we can see the coalescence process

13 /21 ・ Dynamical black rings with a positive

14 /21 We show that the metric describes dynamical black ring Next, we focus on the ring source harmonics

15 /21 Late time behavior Same form as RNdS BH So we can see that there is a single BH at late time like Kastor-Traschen sol At RNdS BH has a BH horizon at

16 /21 Time evolution of event horizon

17 /21 At early time, we can see the event horizon locate near source of ring harmonics ～ black string Near Early time behavior

18 /21 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 /21 We can see singularities are hidden by horizon at the least finite past time Null geodesics obey Focus on 2D part

20 /21 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 /21 A thin black ring at early time shrinks and changes into a single BH as time increases singular Summary

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26 /21 ・ 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 /21 で として ： horizon ： singularity Charged Black String (Horowitz - Maeda 2002)