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Dynamical black rings with a positive Masashi Kimura

( Osaka City University )

2009 12/24

PRD 80, 044012 (2009)

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Introduction Black ring sol. (Emparan & Reall 2002) is one of the most i

mportant 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

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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

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Contents・ Introduction

・ Kastor-Traschen coalescing BH solution

・ Dynamical black rings with a positive

・ Summary

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・ Kastor-Traschen coalescing BH solution

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Setup・ 5D Einstein-Maxwell system with positive

・ anzats

where

unknown function

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(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

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If

this metric describes coalescence of two BHs

the metric becomes

(Kastor, Traschen 1993, London 1995 )Kastor-Traschen solution

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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

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We know where the BH horizon locates at late time

We can find the location of horizon at each time

by solving null geodesics

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Time evolution of event horizon

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Time evolution of event horizon

(almost proper length)

we can see the coalescence process

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・ Dynamical black rings with a positive

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We show that the metric

describes dynamical

black ring

Next, we focus on the ring source harmonics

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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

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Time evolution of event horizon

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At early time, we can see the event

horizon locate near source of

ring harmonics

～ black string

Near

Early time behavior

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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

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We can see singularities are hidden by horizon

at the least finite past time

Null geodesics obey

Focus on 2D part

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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

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A thin black ring at early

time shrinks and changes

into a single BH

as time increases

singular

Summary

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・ 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

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で として

： horizon： singularity

Charged Black String (Horowitz - Maeda 2002)