Can we see super-Planckian domains? Takehara Workshop June 6-8, 2011 Ken-ichi Nakao (Osaka City...
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Transcript of Can we see super-Planckian domains? Takehara Workshop June 6-8, 2011 Ken-ichi Nakao (Osaka City...
Can we see super-Planckian domains?
Takehara Workshop June 6-8, 2011
Ken-ichi Nakao(Osaka City Unviersity)
In collaboration with Tomohiro Harada and Umpei Miyamoto (Rikkyo University)
Hirotada Okawa and Masaru Shibata (YITP)
If GR correctly describes gravitational phenomena…
Concentration of mass Collapse due to self-gravity
Large spacetime curvature, large energy density, large stress
All know theories of physics including GR are not available
→ New Physics (Superstring? Brane World? …..)
Generation of spacetime singularities
Near spacetime singularities
§Introduction
by Penrose(1965), Hawking & Penrose (1970)…..
Are spacetime singularities observable?
Cosmic censorship hypothesis by Penrose (1969)
Weak version: spacetime singularities generated by gravitational collapses are hiden behind event horizons
Strong version : spacetime is globally hyperbolic
?
×
in 4-dim spaecetime.
§Cosmic censorship hypothesis
““Domain of super-Planckian (SP) scale Domain of super-Planckian (SP) scale = Border of spacetime”= Border of spacetime”
4
Domain A is called the border or SP domain, if
EP = fundamental Planck scale = a positive consitant of
Practical spacetime singularity = Domain in which GR is not available
Harada and Nakao, PRD70, 041501 (2004)
where
Visible super-Planckian domain ≈ Naked singularity
Large extra-dimension scenario Large extra-dimension scenario
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Arkani-Hammed, Dimopoulos and Dvali 1998
Relation between D(>4)-dimensional Planck energy and 4-dimensional one:
(R: length scale of extra-dimansions)
Collisions of high energy particles Collisions of high energy particles in large extra-dimension scenario in large extra-dimension scenario
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Giddings & Thomas (2001), Dimopoulos and Landsberg (2001)
Gravitational radius of the center of mass energy E
Production rate much larger than 4-dimansional theory
Cross section of black hole production
Visible SP Domains generated by Visible SP Domains generated by collisions of high energy particlescollisions of high energy particles
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particle
particle
Domain into which two particles can enter at once
If ≤a black hole forms.If no black hole forms.
Nakao, Harada and Miyamoto (2010)
We call this the “collision domain”.
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Volume of the collision domain in (D-1)-dimensional space
Area of the base of the cylinder Height
of the cylinder
Volume in extra-dimensions
Average energy density in the collision domain
(VN : Volume of an N-dim sphere)
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Condition of visible SP domain formation
from 00-component of Einstein’s equations
If max >1, then is allowed.SP domain with no black hole can
form !
『 Gravitational radius=Compton length, if M = EP. 』
: max2
where SN = Area of N dim sphere.
The value of The value of maxmax
Generation rate of visible SP domainsGeneration rate of visible SP domains
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Generation rate of visible SP domain >> Generation rate of BH
Generation rate of black Generation rate of black holesholes
Practically, the weak version of cosmic censorship is not satisfied.
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High speed scattering of two black holes by higher dimensional numerical relativity
Scattering or merger of high speed BH’s( e.g., classical counterpart of high energy scattering of elementary particles )
Numerical relativity
Method to study various phenomena with strong gravity by numeically integrating Einsteinn’s equations
Evolution of binary composed of compact objects (NS, BH)
Main target of GW physics
==
New target of numerical relativityNew techniques are necessary
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Scatter or merger of high speed BH’s
BH
BH
b
Rg
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For large impact parameter b
After scattering, two BH’s go apart to infinity
Scatter or merger of high speed BH’s
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BH horizon
For small impact parameter b
Formation of one larger BH
Scatter or merger of high speed BH’s
Initial data
If the distance between two BH’s is large enough, each BH and its neighborhood is very similar to
Schwarzschild-Tangherlini spacetime
Rg = EP (M/EP)1/2 : gravitational radius
Scattering of high speed BH’s in 5 dimensions (equal mass M )
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by Shibata, Okawa, Yamamoto (2008)
Boost transformation
translation
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Extrinsic curvature of t = const. hypersurface
Other components vanish.17
Initial data for two BH’s approaching to each other with velocity v
andKij are determined so that constraint equations are satidfied.
4-dim. spatial metric
Extrinsic curvature
However here, we have set Kij .This is a good approximation for the case of large enough distance between the two BH’s.
ここで、
In this initial data, there is almost no junk radiation. 18
on the horizon of a spherically symmetric BH with M= EP in 5-dim spacetime.
SP domain:
is shown in the unit of (EP/M)1/2.
by Okawa, Shibata & KN (2011)
BH’s
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Example: b=3.38Rg, v=0.7
Scattering of high speed BH’s in 5 dimensions (equal mass M )
Visible SP domain
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After scattering, two BH’s will go apart to infinity
K2
[EP
/M]2
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Kv
[EP
/M]
23
If EP < M < 19EP , visible SP domain forms by the scattering of classical BH’s !
The largest value of K in our simulations is
If finer simulations becomes possible, we may find larger K.
v
Scatter
Simulations break down.
(Naked singularity?)Merger
b [
Rg]
bC
bB
Summary and discussionSummary and discussion We can see super-Planckian physics if We can see super-Planckian physics if
the spacetime dimension is larger than the spacetime dimension is larger than four (Naked singularity might form).four (Naked singularity might form).
It is unclear why visible super-It is unclear why visible super-Planckian domain forms by the Planckian domain forms by the scattering of 5-dim BH’s.scattering of 5-dim BH’s.
What is observed ?What is observed ?
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潮汐力による加速
L = 時空の曲率半径
mm
X = 粒子間の距離
大雑把に
重力源 9
Geodesic deviation equations
mm
粒子間の距離がコンプトン長でも、プランク時間内でプランクエネルギーまで加速される
時空の曲率半径 L が プランク長さ lpl より短いとき
量子論的粒子生成で生まれた粒子は、高エネルギー衝突によりブラックホールを形成?
10