GR BH BH 2015.10.10 BH at 2015.09.07 NICT 2015.05.26 Typeset by FoilTEX 1
BH BH BH BH Typeset by FoilTEX 2
1. BH 1.1 1 Typeset by FoilTEX 3
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
3 Step 1 K inertia b K rest w.r.t. star star b Typeset by FoilTEX 5
Step 2 K free fall K b = K b K-system star Typeset by FoilTEX 6
Step 3 star free fall for a long time Typeset by FoilTEX 7
1.3 3 2 1 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
2 A star K free fall = light light K-system (free fall system) Typeset by FoilTEX 9
Abell1689 Typeset by FoilTEX 10
Typeset by FoilTEX 11
1.4 2 2 Typeset by FoilTEX 12
( paper ) ( sphere ) 4 2 180 Typeset by FoilTEX 13
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
1.6 BH BH light cone 1.1 ct x light { ct y x Typeset by FoilTEX 15
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
BH BH BH BH BH BH light BH BH BH Typeset by FoilTEX 17
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
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
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
1.7 BH OK Typeset by FoilTEX 21
OK OK Typeset by FoilTEX 22
OK BH BH Typeset by FoilTEX 23
BH BH (A) BH (B) BH (A) BH (B) BH Typeset by FoilTEX 24
1 BH Typeset by FoilTEX 25
2. BH BH 2.1 BH BH BH BH Typeset by FoilTEX 26
BH BH 3 M : J : Q : Q = 0 Typeset by FoilTEX 27
BH Einstein Schwarzschild BH r BH = 2m, m = GM c 2 [cm] BH 0 Typeset by FoilTEX 28
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
Kerr BH BH a = 0.8 m Typeset by FoilTEX 30
2.2 BH BH BH BH M a ( a := J Mc ) BH BH 0 a < m = GM c 2 Typeset by FoilTEX 31
2.3 BH BH VLBI { Typeset by FoilTEX 32
2.4 BH BH source W 0 earth W 1 W 0 0 W 1 1 Typeset by FoilTEX 33
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
2.5 Gouy phase shift E 0 W 0 1 0.8 0.6 0.4 0.2-0.5 0 0.5 oscillation of observed wave at ONE telescope E 1 Hilbert Trans. of W E 0 0.4 0 t obs t obs t obs t obs -1.0-0.5 0.2-0.2 E 1 W 1 0.5 1.0 Zenginoglu &Galley PRD86(2012)064030, YouTube -2-4 4 2 source BH 10 W 1 W 0 20 earth Typeset by FoilTEX 35
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
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
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
3 M : BH a : BH ν 1 /ν 0 : (= T 0 /T 1 ) BH BH M, a Typeset by FoilTEX 39
W 0 W 1 Gouy Phase Shift intensity (photon no.) W 0 an example W1 source ν Typeset by FoilTEX 40
2.7 Step1: A, B Step2: B Hilbert E obs Step3: A B 2 3 1 0.8 0.6 0.4 0.2 0.2-0.2 E original data (A) W 0 W 1 t obs 1 2 3 strong corelation W 0 W 1 1 2 3 t obs modulated data (B) W 0, W 1 t obs, E obs, ν 1 /ν 0 VLBI Typeset by FoilTEX 41
3. 3.1 ( t obs, E obs, ν 1 /ν 0 ) E obs = F obs (1) F obs (0) Specific Flux Typeset by FoilTEX 42
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
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
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
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) 0.7 1.3 Typeset by FoilTEX 46
W 0 W 1 Gaussian Power law Planckian (θ obs, ϕ obs ) E obs Mathematica file Typeset by FoilTEX 47
3.3 VLBI W 0, W 1 { BH W1 W 0 source u s BH Typeset by FoilTEX 48
4. BH M, a BH BH ( t obs, F 1 /F 0, ν 1 /ν 0 ) Typeset by FoilTEX 49