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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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