dynamical black rings with a positive
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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)
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