BH BH BH BH Typeset by FoilTEX 2
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- ぜんすけ さわい
- 5 years ago
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1 GR BH BH BH at NICT Typeset by FoilTEX 1
2 BH BH BH BH Typeset by FoilTEX 2
3 1. BH Typeset by FoilTEX 3
4 1.2 2 A B A B t = 0 A: m a [kg] B: m b [kg] t = t f star free fall x x x t = t f t = 0 : Typeset by FoilTEX 4
5 3 Step 1 K inertia b K rest w.r.t. star star b Typeset by FoilTEX 5
6 Step 2 K free fall K b = K b K-system star Typeset by FoilTEX 6
7 Step 3 star free fall for a long time Typeset by FoilTEX 7
8 A v a = A A A light A A-system ( if v a = constant ) K Inertia light A A-system ( v a increases ) accelerate! A = v a [m/s] light Typeset by FoilTEX 8
9 2 A star K free fall = light light K-system (free fall system) Typeset by FoilTEX 9
10 Abell1689 Typeset by FoilTEX 10
11 Typeset by FoilTEX 11
12 Typeset by FoilTEX 12
13 ( paper ) ( sphere ) Typeset by FoilTEX 13
14 1.5 Einstein R(P) G c 4 ρ(p) L 1 R 1 < R 2 < R 3 P 2 R(P) 1 P 1 L 2 L(P) 2 L 3 P 3 ρ(p) P [erg/cm 3 ] R(P) P [1/cm 2 ] G/c 4 [cm/erg] L(P) ct P x. =. ct P x Typeset by FoilTEX 14
15 1.6 BH BH light cone 1.1 ct x light { ct y x Typeset by FoilTEX 15
16 BH BH horizon L BH = 2GM c 2 Black hole Singularity: ρ = ct light cone BH lights core of a star M [kg] L BH BH x Typeset by FoilTEX 16
17 BH BH BH BH BH BH light BH BH BH Typeset by FoilTEX 17
18 BH Schwarzschild BH r(λ) ( ) dr(λ) 2 ( L 2 c 2 ) ( + dλ r 2 (µc 2 ) 2 1 r ) BH r { µ 0 µ µ = 0 E L = E 2 λ Typeset by FoilTEX 18
19 BH E, L BH µ 0 { µ = 0 potential µ = 0 µ = 0 3_ 2 r BH 3 r BH BH BH r Typeset by FoilTEX 19
20 L = 0 Singularity O ct Black Hole (Trapped Region) R BH gravity Light Cone r ct Singularity O Grav. Doppler Light Cone Trapped Region (Black Hole) R BH world sheet of a wave source r Typeset by FoilTEX 20
21 1.7 BH OK Typeset by FoilTEX 21
22 OK OK Typeset by FoilTEX 22
23 OK BH BH Typeset by FoilTEX 23
24 BH BH (A) BH (B) BH (A) BH (B) BH Typeset by FoilTEX 24
25 1 BH Typeset by FoilTEX 25
26 2. BH BH 2.1 BH BH BH BH Typeset by FoilTEX 26
27 BH BH 3 M : J : Q : Q = 0 Typeset by FoilTEX 27
28 BH Einstein Schwarzschild BH r BH = 2m, m = GM c 2 [cm] BH 0 Typeset by FoilTEX 28
29 BH Einstein Kerr BH r BH = m + m 2 a 2, a = J Mc [cm] BH BH 0 a < m r erg = m + m 2 a 2 cos 2 θ θ BH r < r erg BH Typeset by FoilTEX 29
30 Kerr BH BH a = 0.8 m Typeset by FoilTEX 30
31 2.2 BH BH BH BH M a ( a := J Mc ) BH BH 0 a < m = GM c 2 Typeset by FoilTEX 31
32 2.3 BH BH VLBI { Typeset by FoilTEX 32
33 2.4 BH BH source W 0 earth W 1 W 0 0 W 1 1 Typeset by FoilTEX 33
34 W 0 W 1 BH t obs E obs = E 1 E 0 BH M a BH source W 1 W 0 earth Typeset by FoilTEX 34
35 2.5 Gouy phase shift E 0 W oscillation of observed wave at ONE telescope E 1 Hilbert Trans. of W E t obs t obs t obs t obs E 1 W Zenginoglu &Galley PRD86(2012)064030, YouTube source BH 10 W 1 W 0 20 earth Typeset by FoilTEX 35
36 Gouy Phase Shift (GPS) (caustic) 1 Fourier π/2 Fourier +π/2 Hilbert caustic BH caustic (ex. non-rot. BH) For each beam [cross section] = 0 Typeset by FoilTEX 36
37 F obs E obs 2 E obs F obs (t obs ) GPS W 0 W 1 t obs 2 3 Hilbert GPS BH Typeset by FoilTEX 37
38 2.6 E obs Oscillation of observed wave at ONE telescope Τ 0 (ex. line emission) E Τ 1 obs W 0 W 1 t obs t obs { t obs, E obs BH T 0 T 1 Typeset by FoilTEX 38
39 3 M : BH a : BH ν 1 /ν 0 : (= T 0 /T 1 ) BH BH M, a Typeset by FoilTEX 39
40 W 0 W 1 Gouy Phase Shift intensity (photon no.) W 0 an example W1 source ν Typeset by FoilTEX 40
41 2.7 Step1: A, B Step2: B Hilbert E obs Step3: A B E original data (A) W 0 W 1 t obs strong corelation W 0 W t obs modulated data (B) W 0, W 1 t obs, E obs, ν 1 /ν 0 VLBI Typeset by FoilTEX 41
42 ( t obs, E obs, ν 1 /ν 0 ) E obs = F obs (1) F obs (0) Specific Flux Typeset by FoilTEX 42
43 Specific Flux [erg/s cm 2 Hz] F obs (ν obs ) = I obs (ν obs ) Ω obs = I(ν) ( νobs ν s = ν s (ν obs ) ν s ) 3Is (ν s ) Ω obs Specific Intensity I(ν) [erg/s cm 2 Hz ste-rad] ν 3 = const. Ω obs 1 ν 2 obs Typeset by FoilTEX 43
44 3.2 BH (M, a) M = 1, a = 0.8 obs. φ φ=0 BH θ = 0.7π 2.2 r BH source v s = φ ZAMO W 0 W 1 v s Typeset by FoilTEX 44
45 図 A 光線 これらの光線は 遠方に居る同一観測者に届く しかし 到着時刻がずれて 観測強度も異なる Caustic point on the light orbit 光源がバースト的に発光 赤線はエルゴ領域の赤道 光線ではない
46 φ obs F 1 /F 0 ν 1 /ν 0 φ obs φ obs 0 2π t obs /M F 1 /F 0 ν 1 /ν 0 O(0.1) Typeset by FoilTEX 46
47 W 0 W 1 Gaussian Power law Planckian (θ obs, ϕ obs ) E obs Mathematica file Typeset by FoilTEX 47
48 3.3 VLBI W 0, W 1 { BH W1 W 0 source u s BH Typeset by FoilTEX 48
49 4. BH M, a BH BH ( t obs, F 1 /F 0, ν 1 /ν 0 ) Typeset by FoilTEX 49
B 1 B.1.......................... 1 B.1.1................. 1 B.1.2................. 2 B.2........................... 5 B.2.1.......................... 5 B.2.2.................. 6 B.2.3..................
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2.6 2.6.1 mẍ + γẋ + ω 0 x) = ee 2.118) e iωt Pω) = χω)e = ex = e2 Eω) m ω0 2 ω2 iωγ 2.119) Z N ϵω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j 2.120) Z ω ω j γ j f j f j f j sum j f j = Z 2.120 ω ω j, γ ϵω) ϵ
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