Exterior Structures of Black Holes
and
Another History of the Universe
NCTS/NTHU at 6/Dec/2007
Yukinori NAGATANI
Okayama Institute for Quantum Physics
永谷 幸則 ＠ 岡山光量子科学研究所
PRD 59 041301 (1999),
hep-th/0307295,
hep-ph/0104160,
hep-th/0312060,
NPB 679 363-381 (2004),
and several unpublished things...
Yukinori Nagatani [ / - . / Back ]
1
Exterior Structures of Black Holes
P.1/62
The Essence of Idea
A High Temperature Object (e.g. Iron Ball : T 1000K)
T >>1000K
Hot
Object
may be Iron Ball....
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.2/62
1
The Essence of Idea
A High Temperature Object (e.g. Iron Ball : T 1000K)
in Water
T >>1000K
Hot
Object
Vapor
Bubble
⇒ Vapor Bubble surrounding the Object Appears.
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.2/62
1 The Essence of Idea
A High Hawking Temperature Black Hole (TBH 100 GeV)
TBH >> 100GeV
B.H.
High Temperature
Mini Black Hole
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.2/62
1 The Essence of Idea
A High Hawking Temperature Black Hole (TBH 100 GeV)
in Electroewak
Broken Phase
TBH >> 100GeV
B.H.
φ =0
Domai
n Wall
φ ≠0
Symmetric
Phase
⇒ E.W. Domain Wall surrounding the B.H. Appears.
Yukinori Nagatani [ / - . / Back ]
2
Exterior Structures of Black Holes
P.2/62
Plan of the Talk
1. Thermal Structure around a BH
2. Two types of Spherical Domain Wall by a BH
— Thermal & Dynamical —
3. Baryon Number Creation by a BH
4. Spontaneous Charging-up of a BH
5. Application to Cosmology
Baryogenesis & Dark Matter
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.3/62
Parameters of a Black Hole
3
For a Schwarzschild Black Hole:
Hawking Temp.
2
1 mpl
=
8π mBH
: TBH
Schwarzschild Radius : rBH = 1/(4πTBH )
Luminosity
π2
4
120 g∗ TBH ×
π
2
g
T
∗
BH
480
: JBH =
=
2
20 mpl
π2 g∗ TBH 3
: τBH =
Life Time
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.4/62
Parameter Table
4
100 kg
10
8
GeV
1t
10
9
10
10 t
7
10
GeV
10
GeV
8
100 t
6
GeV
100 TeV
7
10
GeV
1000
10
GeV
6
GeV
7
10
t
10 TeV
kg
1 TeV
100 TeV
10
10
8
-12
10
4
sec
-9
10
2
10
sec
-6
10
1
Yukinori Nagatani [ / - . / Back ]
sec
-3
10
-2
10
sec
1 sec
-4
10
10
3
1
TeV
-6
10
sec
kg
100GeV
TeV
1year
1min 1hour 1day
10
2
4πrBH
10
6
-8
10
sec
Black Hole
Mass
Hawking
Temperature
Schwarzschild
-1
Radius
Black Hole
Life Time
Luminosity
par Solar one
Exterior Structures of Black Holes
P.5/62
5
Thermal Structure around a BH
In the Thermal EW Plasma with Temperature T
Mean Free Path:
"
#−1
βf
λ f = ∑ nF σF, f
'
T
F
√
n ∝ T 3 , σ ' α/s, s ' T
(αY ) lR , Bµ
(αW ) lL , νL , W µ , φ
(αS ) quark, gluon
βY '1000
βW ' 100
} Energy
Transfer
βS ' 10 Thermalization
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.6/62
Inject a Particle with Energy E into the Plasma:
Stopping Depth:
−1
βf E
'
λ̃ f = ∑F nF σF, f
2
T
√
√
s ' ET
A Black Hole heats-up its neighborhood ⇒ T < TBH
Closely Neighborhood of the BH is NOT Thermalized.
rBH =
1 1
4π TBH
BH Radius
λf =
βf
T
MFP
λ̃ f =
β f TBH
T2
Stoping Depth
⇒ The Black Hole Freely Hawking-Radiates.
⇒ Ballistic Particle Region around the BH.
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.7/62
6
Heat transfer analysis
in the region not near to the BH
a) Local Thermal Equilibrium (L.T.E.) Approximation
MFP system size ⇒ T (r)
b) Diffusion Parameters:
D f (x) = 13 λ f (T (x))
c) Boundary Condition:
Spherically Symmetric T (r)
Hawking Flux ≡ Diffusion Flux
Background Plasma with Temperature Tbg
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.8/62
Solution of the Heat Transfer Equation:
1/3
2
9 1 TBH
T (r) = Tbg 3 +
256π2 β r
i
h
2
2
T
(r)
T
(r)
2
v(r) = 1024π
× cbg Tbg
81 β
TBH
⇒ Thermal Plasma Flow from near-BH to far-BH
log T
?
T bg
Τ∝
r −1/3
Di
ff
Flo usio
w n
T bg
Equilibrium
rdif
Yukinori Nagatani [ / - . / Back ]
[ Lengths ]
log r
Exterior Structures of Black Holes
P.9/62
7
Energy transfer from ballistic to thermal
Hawking-radiated Particles are Injected to Thermal Plasma
Ballistic Particles
TBH
Thermal Plasma
⇒
Tinit
σ(TBH , Tinit ) '
α
TBH Tinit
Tinit : Initial Plasma Temperature
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.10/62
Time evolution to stationary situation:
Radiation Start
Tinit = Tbg
Tinit = T (rinit )
Plasma Flow Sol.
log ρ
Local
Heat-up
Tinit
−2
r
llis
Ba
ρ ∝ tic
log ρ
Put BH into Tbg Plasma
Stationary
⇒
T bg
T bg
Thermal
rBH
log r
rBH rinit
log r
Heat-up Depth: rinit ' λ̃(TBH , Tinit ) :Stopping Depth
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.11/62
Results from Self-Consistent Analysis:
Stationary Initial Thermalization at
Tinit
=
rinit
=
9ζ(3) g∗ α
TBH
256π4 β
262144π11 β2
r
81ζ(3)3 g3∗ α3 BH
TBH /(2.3 × 104 ),
'
5.5 × 109 rBH .
'
Yukinori Nagatani [ / - . / Back ]
8
Exterior Structures of Black Holes
P.12/62
Overview around a Black Hole
Diffusion F
MFP
Ballistic Region Transfer
Region
−2
r
p & Density
c
sti
∝
Yukinori Nagatani [ / - . / Back ]
Tbg
Thermal Plasma
lli
ρ
Tinit
Thermal Diffusing
Plasma Region Background
Plasma
Ba
log T
log ρ
Ballistic
ront
Diffusion Flow
BH
Tinit
Diff
usio
Τ∝
n
r −1/3
ρ ∝ −4
r /3
[ Lengths , HeatSol , TimeEvol ]
Equilibrium
Tbg
Exterior Structures of Black Holes
P.13/62
Thermal Diffusing
Plasma Region Background
Plasma
Ballistic Region Transfer
Region
Thermal Plasma
lli
Diff
sti
∝
−2
r
Tinit
Tinit
Equilibrium
r −1/3
ρ ∝ −4
r /3
rdif
ront
Flow
rDiffusion
init
Diffusion F
rBH
n
Τ∝
MFP
Tbg
BH
usio
c
ρ
Temp & Density
Ballistic
Ba
log T
log ρ
i on Fr ont
Diffusion Flow
BH
Tbg
ρbg
log r
Distance
from
BH of Black Holes
Plasma
Ballistic
Yukinori
Nagatani [ /Region
- . / Back ] [ Transfer
Lengths , HeatSol
, TimeEvolRegion
]
Exterior Structures
Background
Thermal Diffusing
Region
Thermal Plasma
c
sti
lli
ρ
∝
−2
Tinit
r
Temp & Density
Ballistic
Ba
log T
log ρ
Plasma
P.14/62
Tinit
Tbg
rBH
Diff
usio
Τ∝
n
Equilibrium
r −1/3
ρ ∝ −4
r /3
rinit
rdif
Distance from BH
Tbg
ρbg
log r
Spherical Electroweak Domain Wall with
1.
Thermal Formation
Tinit > TEW > Tbg
2.
Dynamical Formation
TBH > TEW > Tinit
Yukinori Nagatani [ / - . / Back ]
[ Lengths , HeatSol , TimeEvol ]
Exterior Structures of Black Holes
P.15/62
9
Electroweak Domain Wall around a BH
L.T.E. Higgs VEV hφi (r)i = hφi iT =T (r)
Black Hole in the EW Broken Phase Plasma
Tinit
> T (rnear ) >
TW
> T (rfar ) >
Tbg
Sym. Phase
///
Broken Phase
⇒ An Electroweak Domain Wall is formed
without 1st order phase transition.
Assumption
2nd order Phase Transition
of the Simplest Critical Curve
Yukinori Nagatani [ / - . / Back ]
| φ |
v
Tw
T
Exterior Structures of Black Holes
P.16/62
The Resultant Structure
Domain Wall
Symmetric
Phase
Broken
Phase
dDW
BH
rDW
| φ |
v
Domain Wall Radius: rDW =
Yukinori Nagatani [ / - . / Back ]
r
1 1
9
2
256π βcW TW3
TBH 2
Exterior Structures of Black Holes
P.17/62
10
Validity of the Wall
I. Stationary Domain Wall Condition
Time Scale of Wall Creation Lifetime of BH
τDW = rDW /vDW
3 (m2 T 5 /T 7 )
1 τBH /τDW = (5 · 220 π2 /36 g∗ ) β3 cW
BH
pl W
=⇒
TBH < 1.4 × 108 GeV (mBH > 76 kg)
II. Thermalized Wall Condition
Thickness of Wall Heating-up Depth
1 rDW /rinit = (9ζ(3)/256π4 ) (g∗ α/β) (TBH /TW )
=⇒
TBH > 2.3 × 106 GeV (mBH < 4600 kg)
Yukinori Nagatani [ / - . / Back ]
[ OverView3 ]
Exterior Structures of Black Holes
P.18/62
Allowed Regions
pp
ppp
ppp
pp pppp pp
Lifetime of BH is too Short.
pp
pp
ppp
ppp
Non-Stationary
Wall
pp
pp
pp
ppp
p
p
p
p
p
p
p
p
ppppppppp 1.4 × 108 GeV
76 kg ppp
ppp
ppp
pp
pp
ppp
Stationary
Thermalized
Wall
ppp
ppp
pp
pppppppppp
p
p
p
p
p
p
p
p
4600 kg pppp
ppp 2.3 × 106 GeV
pp
ppp
ppp
pp
Stationary
Dynamical
Wall
pp
ppp
ppp
ppp
p
pppppppppp 100 GeV
108 kgppppppppppp
ppp
ppp
ppp
ppp
Wall by Atomic Structure Model of BH
ppp
ppp
p
ppp
ppp
pp
T (r) ∼ 1/ g00 (r) × TBH
ppp pppp pp
ppp
pp mBH
p
Yukinori Nagatani [ / - . / Back ]
Mass of BH
Hawking Temperature
TBH
[ OverView3 ]
Exterior Structures of Black Holes
P.19/62
11
Baryon Number Creation by a BH
p p pp p p
p
p
p
p
p
p
p
p
Assume p CP Phase ∆θCP in Wall:
hφ(r)i = v f (r) exp [ i∆θCP (1 − f (r)) ]
Sakharov’s 3 Criteria for Baryogenesis
p pp p
1. ppBaryon
: Sphaleron Process in the SM
pp pp p ppp pp ppp ppp pp pp
ppp pp ppp
p
pp pp
2. pC
: The SM is Chiral Theory
p p pp p p
p pppp ppp : Extension of the SM
ppCP
Assume more than 2 Higgs Doublets
3. Non-Equilibrium : Plasma Flow from the BH
Yukinori Nagatani [ / - . / Back ]
[ EWSakharov ]
Exterior Structures of Black Holes
P.20/62
Sakharov’s Criteria around a BH
Domain Wall
Symmetric
Phase
CP
BH
Plasma Flow
rDW
Broken
Phase
dDW
Sphaleron
Working
| φ |
v
r
Yukinori Nagatani [ / - . / Back ]
[ Sakharov ]
Exterior Structures of Black Holes
P.21/62
12
Amount of Baryon Number Creation
Thermalized Wall (M.F.P. < dDW )
⇔ Thick Wall ⇒ Spontaneous Baryogenesis by CKN
CPv Phase on Plasma Flow:
d
d
θCP = vDW θCP
dt
dr
⇒ Baryon # Chemical Potential:
µB = N
d
dt θCP
= N vDW
d
dr θCP
c.f. Thin Wall / Charge Transport Scenario → µB = Ñ Y /T 2
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.22/62
Sphaleron Rate:
i
h
hφ(r)i
5
4
Γsph = κ αW TW exp −100 × v
Baryon # Creation Rate:
Z
Ḃ = −
Sphaleron Vol.
dV
Γsph
µB
TW
Total Baryon Number Creation by a BH:
B =
Z BH lifetime
' 10
−9
× ∆θCP
dt Ḃ =
mBH
TW
− 4π153 g N
∗
5
καW
m2pl
ε∆θCP TW TBH
This result is valid for 76 kg < mBH < 4600 kg.
e.g. When the maximum CPv (∆θCP = π) is assumed,
a black hole of mBH = 300kg produces 3µg baryon matter.
Yukinori Nagatani [ / - . / Back ]
[ Wall , ParameterTable ]
Exterior Structures of Black Holes
P.23/62
13
Ballistic Picture
Hawking radiated particles near a BH:
mean free path system size > wave-length
⇒ Ballistic Picture of the Radiated Particles
ψ
Wave Function
Ballistic Particle
• A BH radiates ballistic point particles.
• The ballistic point particle has mass
which is proportional to Higgs vev | hφi |
due to Yukawa/Gauge/Higgs couplings.
is available as an effective description.
Yukinori Nagatani [ / - . / Back ]
[ OverView1 , Lengths ]
Exterior Structures of Black Holes
Once a slope of Higgs vev is created,
P.24/62
ψ
φ (r )
Wave Function
v
icle
t
r
a
P low
F
1)
r
(
p
Hawking
Pressure
BH
Yukinori Nagatani [ / - . / Back ]
∆p p
( r 2)
Local
Pressure
Balance
Wall Structure
[ OverView1 , Lengths ]
Ballistic Particle
Wall Tension
+ Potential Force
r
Exterior Structures of Black Holes
P.25/62
Higgs VEV
φ (r )
v
icle
Partlow
F
)
p (r1
Hawking
Pressure
∆p p
( r 2)
Local
Pressure
Balance
Ballistic Particle
Wall Tension
+ Potential Force
r
Wall Structure
BH
p(r) = E 2 − m2 (r),
m(r) = Y h|φ(r)|i
∆p = p(r1 ) − p(r2 ) ' (m/p)∆m
p
⇒ Hawking Radiation Pressure is acting on the wall.
⇒ Balance of the Pressures keeps the Wall Structure.
Idea of Dynamical Wall by a BH.
Yukinori Nagatani [ / - . / Back ]
14
Exterior Structures of Black Holes
P.26/62
Ballistic Model as an effective theory around a BH
Higgs field ⊕ Massive Ballistic Particles
φ(x)
: Higgs Field
µ
{yi (s)} : Trajectories of the Ballistic Particles
Z
i
h
√
S[φ, y] =
d 4 x g |∂φ|2 − 21 V (φ)
Z
q
− ∑ dsi Yi |φ (yi (si )) | |ẏi (si )|2
i
∑i : sum all over particles around the BH
Yi : “Yukawa” coupling constant
V (φ): Higgs Potential
µ2 4
2 2
V (φ) = −µ φ + 2 φ
v
Yukinori Nagatani [ / - . / Back ]
[ BallisticPicture ]
V
φ
Exterior Structures of Black Holes
P.27/62
15
Basic Properties of the Ballistic Model
√
Vacuum: | hφi | = v/ 2
√
Particle Mass in the vacuum: mi = Yi | hφi | = Yi v/ 2
⇒ Reproduce relations in Higgs-Yukawa system
e.g.
mq (x) = Yq hφ(x)i ,
mW (x) =
√g hφ(x)i
2
How about Higgs particles itself?
Yukinori Nagatani [ / - . / Back ]
16
[ BallisticPicture ]
Exterior Structures of Black Holes
P.28/62
Ballistic Higgs Particle
Decomposition of φ:
φ(t, x) =
hφ(x)i
δφ(t, x)
+
expect.value
Higgs field
φ ( t , x)
prop. mode
icle
a s Part
f
o
igg
ion
Motllistic H
Ba
v
vev
Fluctuation of
the Higgs field
BH
Yukinori Nagatani [ / - . / Back ]
Wall Structure
[ BallisticAction , BallisticPicture ]
r
DW
r
Exterior Structures of Black Holes
P.29/62
δφ(t, x) can be regard as the Ballistic Higgs Particles.
ReDefinition of φ and {yi }:
φ(x)
{yi }
≡
≡
hφ(x)i
{yi } ⊕ { Ballistic Higgs Particles }
Effective Yi for the Ballistic Higgs Particle:
√ µ
Yi =
3
v
All particles in Standard Model
are described by the Ballistic Model.
Yukinori Nagatani [ / - . / Back ]
17
[ BallisticAction , BallisticPicture ]
Exterior Structures of Black Holes
P.30/62
Equations of Motion for {yµ } and φ
EoM for particles: (= Energy Cons. Law)
Ei = Yi |φ(yi )| γi F(yi )
EoM for scalar field:
−4φ =
−
1 ∂V
4 ∂φ
−
1 ∂|φ|
2 ∂φ
Yi (3)
∑ γi δ (x − yi (t))
i
Put All Particle Trajectories {yi } with {Ei }
2
Veff (φ) = V (φ) + φ F
∑
i
Yi2 (3)
δ (x − yi (t))
Ei
Particle Index: i ⇒ Species Index: f
Yukinori Nagatani [ / - . / Back ]
[ BallisticAction ]
Exterior Structures of Black Holes
P.31/62
By using Differential Particle #-Density: dE × N f (E; x)
Veff (φ) = V (φ) + φ2 F
∑ Y f2
f
dE
N f (E; x)
E
Z
Around a BH with Temperature TBH and Radius rBH ,
N f (E; x) is produced by the Hawking Radiation:
1 gf
4 (2π)3
dE N f =
2
fTBH (E) 4πE dE × F
fTBH (E) :=
1
eE/TBH ±1
−1
r
BH 2
r
F.D. or B.E.
Approx. Backreaction is Ignored.
Yukinori Nagatani [ / - . / Back ]
18
[ OverView3 ]
Exterior Structures of Black Holes
P.32/62
Effective Potential around a BH
Veff (φ, r) =
2
A ≡
e.g.
1
768π
∑
f
SM A2 '
Yukinori Nagatani [ / - . / Back ]
g̃ f Y f2 ,
1
200 ,
2
A
µ2 4
2
2
−µ + 2 φ + 2 φ
r
v
g̃ f =
n g
f
1
2gf
( f : boson)
( f : fermion)
SU(5) GUT A2 '
[ BallisticAction , BallisticPicture ]
1
60
Exterior Structures of Black Holes
P.33/62
Distribution of the Effective Potential
V
V
φ
V
V
φ
φ
φ
φmin
v/ 2
r
r
DW
BH
Characteristic Radius of Wall: rDW ≡ A/µ
Condition for Wall Formation: rDW > rBH
∗ ≡ µ ' µ
TBH > TBH
4πA
∗ ' 100 GeV,
∗ ' 1016 GeV
e.g.
SM TBH
GUT TBH
Yukinori Nagatani [ / - . / Back ]
19
[ BallisticAction , BallisticPicture ]
Exterior Structures of Black Holes
P.34/62
Profile of the Wall
Equation for Higgs vev:
∆φ(r) =
Numerical Solutions:
1
A2 = 0.01
A2 = 0.1
/ (v/ 2 )
0.8
A2
=
1
0.6
0.4
=1
0
φ (r)
1 ∂
4 ∂φ Veff (φ, r)
φ min(r)
A2
0.2
: minimizes potential at each r
0
0
Yukinori Nagatani [ / - . / Back ]
0.5
1
1.5
2
r/rDW
[ BallisticAction , BallisticPicture ]
2.5
3
3.5
Exterior Structures of Black Holes
P.35/62
Contributions to the Profile:
Hawking Pressure ∝ F ∆p
Potential Energy
Wall Tension
Yukinori Nagatani [ / - . / Back ]
20
∝ +1/r 2
∝ ∂rV /S ∝ −const.
∝ ∂r S /S ∝ −1/r
[ BallisticAction , BallisticPicture ]
Exterior Structures of Black Holes
P.36/62
Spontaneous Charge-up of BH
as an application of the Dynamical Wall
Assumptions
1. C-violated Theory: Chiral Charge Assignment
2. CP-broken Phase in the Wall : ∆θCP
⇒ (Hyper) Charge Reflection Asymmetry on the Wall
Yukinori Nagatani [ / - . / Back ]
[ NumSol , OverView1 ]
Exterior Structures of Black Holes
P.37/62
Dynamical Wall
CP
BH
Broken
Phase
0
=
Y
Y=0
/
Non−Neutral
Reflection
Asymmetry
Net Charge Flow
⇒ Charge Transportation into the Black Hole
⇒ Spontaneous Charge-up of the Black Hole
Yukinori Nagatani [ / - . / Back ]
21
[ NumSol , OverView1 ]
Exterior Structures of Black Holes
P.38/62
Charge Transportation Rate into BH
Charge Transportation Rate:
dQ
= σBH ×Cfcs FQ
dt
σBH : Absorption Cross Section for the B.H.
Cfcs
: Focusing Factor by Spherical Reflection
Charge flux at the wall
Z structure:
FQ =
∑
f ∈Fermions
E>m f
dE N f (E; rDW ) ∆Q f ∆R f (E)
∆Q f ≡ Q fL − Q fR
∆R f (E) ≡ R fR → fL (E) − R f¯R → f¯L (E)
Yukinori Nagatani [ / - . / Back ]
[ NumSol , OverView3 ]
Exterior Structures of Black Holes
P.39/62
The ref. asym. ∆R f depends on
(
CPv-Phase: ∆θCP
Wall Profile
and is calculated numerically.
The charge flux is rewritten into:
FQ = ∑ g f ∆Q f m3f ∆R (m f , TBH )
f
Assume CP-broken Phase Profile:
h
hφ(r)i = f (r) × exp i ∆θCP 1 −
Yukinori Nagatani [ / - . / Back ]
[ NumSol , OverView3 ]
f (r)
f (∞)
i
Exterior Structures of Black Holes
P.40/62
e.g.) Numerical Results for ∆θCP = π and m f = µ:
-1
∆R(mf , TBH)
10
A2 = 0.1
-2
10
-3
A2 = 0.01
-4
A2 = 0.00
10
1
10
-5
10
-6
10
-1
10
Yukinori Nagatani [ / - . / Back ]
0
10
[ EffPot , NumSol ]
1
10
TBH / µ
2
10
Exterior Structures of Black Holes
P.41/62
22
The Total Charge Transported into a BH
of the Hawking temperature TBH < µ, in its lifetime:
Q =
Z τBH
2
m
∆θ
dQ
pl
CP
' 10−5 ×
dt
dt
π µ2
g f ∆Q f Y f
∑ g∗
f
GUT: µ ' 1016 GeV Q ' O(1) × ∆Q ∆θCP
SM:
µ ' 100 GeV
Q ' 1025 × ∆θCP Hyper Charge
In the SM, the top quark (gtop = 3, ∆Qtop = 1/2, Ytop ' 1)
mainly contributes.
Even for highly suppression of the KM-phase in the SM:
∆θCP ∼ 10−19 , this can be significant.
Yukinori Nagatani [ / - . / Back ]
[ ParameterTable ]
Exterior Structures of Black Holes
P.42/62
Spontaneous Charge-up of Black Hole
⇒
Extremal Black Hole?
Charged Remnant of BH??
after Hawking Radiation.
vs.
Schwinger Pair Production,
Spontaneous charge loss of BH.
Yukinori Nagatani [ / - . / Back ]
[ ParameterTable ]
Exterior Structures of Black Holes
P.43/62
23
Electroweak Baryogenesis
proposed by Cohen Kaplan Nelson (1990).
This can explain the baryon number in the universe:
B/S ' 10−10 .
Sakharov’s 3 Criteria for Baryogenesis
p ppp pp ppp ppp
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
p
1. ppBaryon
: Sphaleron Process in the SM
p
pp
pp pp
: The SM is Chiral Theory
2. pC
p
p
p p pp
pppp pppp : Extension of the SM:
ppCP
Assume more than 2 Higgs Doublets
3. Non-Equilibrium :
Assume EW Phase Trans. is 1st order.
Yukinori Nagatani [ / - . / Back ]
[ BHSakharov ]
Exterior Structures of Black Holes
P.44/62
Scenario of the Electroweak Baryogenesis
Big Bang
Universe Expansion
Symmetric Phase
T > TW
T = TW
Broken Phase
Domain Wall
Broken Phase
Yukinori Nagatani [ / - . / Back ]
[ BHBG ]
T < TW
Exterior Structures of Black Holes
P.45/62
Our Scenario of the Universe
Assumption
(i) Formation of Black Holes with mass:
mBH ∼ mpl (mpl /TW )2/3 ' Some100 kg
at least density: ΩBH ∼ 10−10
after inflation: tuniv ' 10−33 sec ⇑ Horizon Mass
(ii) CPv Phase in Wall : ∆θCP ∼ O(1)
The assumption (i) results the Black Hole Dominant
Universe at tuniv ∼ τBH ∼ 10−12 sec.
Yukinori Nagatani [ / - . / Back ]
[ BHSakharov ]
Exterior Structures of Black Holes
P.46/62
Our Scenario of the Universe
Big Bang
Universe Expansion
Inflation
Black Hole
BH Dominant
T < TW
Broken Phase
Broken Phase
Age of Univ.
BH Lifetime
ReHeating by BH
Domain Wall
Radiation Dominant
T < TW
Broken Phase
Yukinori Nagatani [ / - . / Back ]
[ EWBG ]
Exterior Structures of Black Holes
P.47/62
Baryon Entropy Ratio in the Scenario
BH Mass
−→ BH Life Time ≡ Age of Univ.
(Einstein Eq.) ↓
↓
Energy Density of BH
←−
||
BH # Density
Energy Density of Rad.
⇓
CP
↓
↓
ReHeating Temp. of Univ.
Baryon # Density
Entropy Density
−→
−→
Baryon-Entropy Ratio in the Universe
b/s ' 10−9 ×
Yukinori Nagatani [ / - . / Back ]
∆θ TReHeat
π
TW
[ BaryonProduct ]
Exterior Structures of Black Holes
P.48/62
Results of the Scenario
mBH
⇒ TReHeat
⇒
b/s
∼
'
<
∼
∼
mpl (mpl /TW )2/3
270 ∼ 400 kg
100 GeV
10−10
This Satisfies the Restrictions:
(1) No Wash out:
TReHeat < TW
(2) Nucleosynthesis: TReHeat > 10 MeV & b/s ' 10−10
(3) Stationary Thermalized Wall Condition:
76 kg < mBH < 4600 kg
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.49/62
Formation of B.H.
−33
sec
10
Evapolation
of B.H.
−10
t
BH−
.
Blac
10
k Ho
Dom
sec
.
les
Graviton
Matter
Dom.
3
Tbg
B.H.Remnants
Baryon Number
m.
Do
n−
tio
dia
Ra
Energy Density of Universe
t
m
Do
n−
tio
dia
Ra
Density History of the Universe
End of Inflation
t
10 year
Now10
t 10 year
Matt
er−D
3K CMB, νBG
0~2
10
11~14.6
10
o
Dark minan
t
Bary Matter
on M
atter
10
10
4.6 150eV
10
Graviton BG
Scale of Universe
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.50/62
Cold Dark Matter
Assumption
After the end of evaporation of the black holes,
any black hole left a Remnant with a Planck mass.
⇒ The BH Remnants behave as Cold Dark Matter.
Mass of Baryon and Dark Matter produced by a BH:
MB = B mNuc ' 10−11 × mBH '
mDM = α mpl
Yukinori Nagatani [ / - . / Back ]
[ BaryonProduct ]
3µg
' 20µg
Exterior Structures of Black Holes
P.51/62
Density Ratio of Dark Matter and Baryon in the Univ.:
ρDM /ρB = mDM /MB
' 20 · 1011 × (TW /mpl )2/3 ' 10
c.f.) According to the recent observations:
ΩB ' 0.04
ΩDM ' 0.3
(BBN, CMB, · · ·)
(CMB, IaSN, · · ·)
Our model can explain both the baryon number
and the dark matter in the universe.
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.52/62
Remnants number density near the Earth:
nDMnear = ρDMnear /mDM ' (1/35 km)3
Remnants flux on the Ground:
FDMnear = nDMnear × vDM ' 0.2/m2 year

 ρ
−3
DMnear = 0.3 GeV/cm ,
 vDM ' 260 km/ sec
The detectability of the DM is depending on properties
of the BH remnant.
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.53/62
24
Does the BH Remnant exist?
If it does, what is it??
Will be solved by Quantum Gravity or String Theory.
• Zel’dovich 1984
Uncertainty Principle: ∆mBH × ∆rBH > h̄/2
⇒ mBH > mpl
⇒ Hawking Radiation stops at mBH ' mpl .
• Aharonov Casher Nussinov 1987,
Banks Dabholker Douglas Loughlin 1992, · · ·:
Information goes to a remnant
⇒ Very long-lived remnant with a mass O(mpl )
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.54/62
• Gibbons Maeda 1988, Torii Maeda 1994
Reissner-Nordström B.H. goes to extremal.
⇒ Hawking Radiation stops at mBH ' O(mpl ).
..
.
Our Result:
A neutral BH can evolve into a charged BH.
Discussion:
The BH Remnant may be a few-charged extremal BH
with mpl ?
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.55/62
Black Atom as Dark Matter
If the remnant has electric charge Z,
it captures opposite charged particles
and forms atomic structure.
Z > 0 The remnant captures electrons,
and forms the ExBH(+) − e− atom.
◦
Ratom ∼ αem /me ∼ 1 A
The flux of them as the Dark Matter is excluded
by the experiments. [MICA, OYA, · · ·]
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.56/62
Z < 0 The remnant captures protons,
and forms the ExBH(−) − p+ atom
Ratom ∼ αem /m p ∼ (7 MeV)−1
p+
p+
BH
Yukinori Nagatani [ / - . / Back ]
−
Radius is 1/2000 of
ordinary atom.
p+
Not excluded by
the experiments.
Ratom
⇒ Black Atom
Exterior Structures of Black Holes
P.57/62
Ionization Energy of the Black Atoms:
Eion ' α2 m p /2 ∼ 25 keV
c.f.) the ordinary atomic ionization energy ∼ 13.6 eV
DM velocity: vDM ∼ 300 km/ sec
Kinetic Energy of Nucleus into the Black Atom:
EN ' Nm p v2DM /2 ∼ 0.5 N keV
The nucleon heavier than N ' 50 can ionize the Black
Atoms.
We can detect by experiment ??
The Underground elements:
16 O
8
27
40
56
(50%), 28
14 Si (25%), 13 Al (8%), 26 Fe (5%), 20 Ca (3%), · · ·
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.58/62
Lifetime of the Black Atom
If the central remnant captures the protons,
the remnant may decay like the positronium-decay.
2 .
The capture crosssection to ExBH: σ = 16πrBH
A very rough estimation of the lifetime:
h
i−1
m2pl
1
1
τ = πR3 σv p
= 32(Zα)4 m3
p
10 year
τ >
10
∼
age of univ.
⇒
⇔
Z <
∼ 8
The Black Atoms can be source of
the Ultra High Energy Cosmic Ray?
Yukinori Nagatani [ / - . / Back ]
Exterior Structures of Black Holes
P.59/62
Cosmological Graviton Background
0.2
Epeak= 2.82 TBH
c.f.) Planck
Spectrum
0.1
Graviton
Spectrum
Epeak= 3.93 TBH
Strength of Graviton
The black holes also radiate gravitons with Eg ∼ TBH .
0
0
2
4
6
8
10
Eg / TBH
12
14
16
18
Our model predicts the Cosmological Graviton BG:
Energy Density : ρg = ρCMB /82.2
Peak Energy :
Epeak = 120 ∼ 280 eV
Yukinori Nagatani [ / - . / Back ]
[ History , ParameterTable ]
Exterior Structures of Black Holes
P.60/62
Summary
1. Spherical Domain Wall Formation by BH
Thermal
Dynamical
2. Baryogenesis by BH
Electroweak
GUT
×
(BH&SM&CP)
3. Spontaneous Charge-up of BH (BH&SM/GUT&CP)
4. Cosmological Model by the BH dominant scenario
Baryogenesis
Dark Matter
Graviton BG: Eg ∼ 150 eV, ρg ' ρCMB /82
Yukinori Nagatani [ / - . / Back ]
[ History ]
Exterior Structures of Black Holes
P.61/62
Works to Do
• Origin of the CP-Broken Phase
• Origin of the Black Holes
◦ Inflation
[Yokoyama ’97] [Kawasaki et al ’98]
◦ 1st Order Phase Transition
• Remnant of the Black Hole
Charged BH? Weak? Electric? GUT?
⇒ Planck-massive Extremal BH?
⇒ Charged Heavy Dark Matter?
Yukinori Nagatani [ / - . / Back ]
[ History ]
Exterior Structures of Black Holes
P.62/62