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One proper time event inside OJ287 black hole



 
 
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  #1  
Old May 19th 20, 05:57 PM posted to sci.astro
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Default One proper time event inside OJ287 black hole

I have found analytic solution for proper time dependence of particle motion inside supermassive central back hole of OJ287 binary black hole system. I try descibe this proper time event: 1. particle goes inside Schwarzhild radius 54.18829002*10^9 km of black hole. 2. Proper time event: r=5.43*10^9 km to r=2.70*10^9 km particle moves in proper time. If we take proper time=0 when r=5.43*10^9 km it moves to 560891.1323 years PAST. When r=2.70*10^9 km particle moves instantneously to proper time=0,from which it continues moving instantaneously in proper time to FUTRE proper time 52920..23677 years. When particle moves from r=2.70*10^9 km to r=8.0*10^9 km, proper time decreases again to proper time=0.This ends this proper time event. I tried to describe it from plotting of analytic solution. I used Weinberg book 1972 definitions. Does this make any sense? Best Regards, Hannu Poropudas, Finland.
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  #2  
Old May 21st 20, 07:49 AM posted to sci.astro
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Default One proper time event inside OJ287 black hole

I give this complicated primitive function here (Maple 9 used): Analytic solution (Weinberg S. Gravitation and Cosmology, 1972, General Relativity definitions used from this book). Defintion areas: u=1.843608337*10^(-15), 0r=5.424145573*10^(-14) cm, u=1/r,0=P=Pi. u:=P-(-8.905287066*10^(-19)*cos(P)+3.686326146*10^(-15)) / (-cos(P) +1); ta:=P-0.14273426*10^18*arctan(19556.51583*(0.4000000000 *10^15-1506485618*sin(P)^2)^(1/2)*sin(P)/(-0.2000000000*10^15+753242809*sin(P)^2))-0.1021331259*10^48*(0.4000000000*10^15-1506485618*sin(P)^2)^(1/2)*sin(P)/((-0.2000000000*10^15+753242809*sin(P)^2)*(0.37747221 28*10^26+0.1443670077*10^35*(0.4000000000*10^15-1506485618*sin(P)^2)*sin(P)^2/(-0.2000000000*10^15+753242809*sin(P)^2)^2))+0.19991 51856*10^(-30)*((-0.2000000000*10^15+753242809*sin(P)^2)*(-1+sin(P)^2))^(1/2)*(0.3908757305*10^66*(1-sin(P)^2)^(1/2)*(0.4000000000*10^15-1506485618*sin(P)^2)^(1/2)*EllipticF(sin(P),0.1940673606*10^(-2))*sin(P)^2+0.6697771796*10^73*(1-sin(P)^2)^(1/2)*(0.4000000000*10^15-1506485618*sin(P)^2)^(1/2)*EllipticF(sin(P),0.1940673606*10^(-2))+0.2468340123*10^75*sin(P)+0.9296297238*10^69*s in(P)^5-0.2468349419*10^75*sin(P)^3+0.1234170061*10^68*(1-sin(P)^2)^(1/2)*(0.4000000000*10^15-1506485618*sin(P)^2)(1/2)*EllipticE(sin(P),0.1940673606*10^(-2)*sin(P)^2+0.211478707*10^75*(1-sin(P)^2)^(1/2)*(0.4000000000*10^15-1506485618*sin(P)^2)^(1/2)*EllipticE(sin(P),0.1940673606*10^(-2))-0..1273248266*10^68*(1-sin(P)^2)^(1/2)*(0.4000000000*10^15-1506485618*sin(P)^2)^(1/2)*EllipticPi(sin(P),-0.5835906962*10^(-7),0.1940673606*10^(-2))*sin(P)^2-0.2181748740*10^75*(1-sin(P)^2)^(1/2)*(0.4000000000*10^15-1506485618*sin(P)^2)^(1/2)*EllipticPi(sin(P),-0.5835906962*10^(-7),0.1940673606*10^(-2)))/((0.2000000000*10^15+753242809*sin(P)^4-0.2000007532*10^15*sin(P)^2)^(1/2)*(0.2202892715*10^19*sin(P)^2+0.3774722128*10^26 )*cos(P)*(0.4000000000*10^15-1506485618*sin(P)^2)^(1/2));
  #3  
Old May 21st 20, 10:52 AM posted to sci.astro
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Default One proper time event inside OJ287 black hole

Plot commands for Maple 9 program: plot([1/u(P),ta(P),P=0..Pi]); and plot([u(P), log10(ta(P), P=0..Pi]); Best Regards Hannu Poropudas, Finland.
  #4  
Old May 22nd 20, 12:46 PM posted to sci.astro
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Default One proper time event inside OJ287 black hole

For mathematical completeness I must say that +, - ta(P) both signs ara analytic solutions. That logaritmic plot is such that it shows only positive side of this parametric representation of proper time. If you want to find negative part in plotting you must use plottings with abs(ta(P). That last logarithmic plotting command shows log10(ta(P)) axis curve beteen 28 to 16 and u(P)=1/r(P) axis between 0.5*10^(-15) to 3.15*10^(-13). Strong oscillation is in proper time between 20.4 and 16, u(P) is between 10^(-3) and 3.15*10^(-13). Mathematically this is due those three elliptic integrals (1., 2., and 3. kinds). Their shape is triangular if you plot them separately. 0.5*10(-15) corresponds 20*10^9 km. 3.15*10^(-13) corresponds 3.17*10^7 km. I have used ln instead log10, so in my e^28 corresponds to 45830 years, e^20.4 corresponds to 23 years, e^19 corresponds to 5.7 years, e^16 corresponds to 103 days. Largest proper time oscillation seems to be 5.4 years. Oscillation happens from 100 million km to 32 million km. Best Regards Hannu Poropudas. I think thst this analytic solution could be IMPORTANT!
  #5  
Old June 1st 20, 02:56 PM posted to sci.astro
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Default One proper time event inside OJ287 black hole

I notice that ta has typo error. I have written this long formula by hand with my mobile phone. I try to post ta again when I get proper internet connection which I did not have when I posted these. Our libraries are all closed their internet connection which I have used before due this coronavirus pandemia. Sorry that typo error. Hannu
  #6  
Old June 1st 20, 03:20 PM posted to sci.astro
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Default One proper time event inside OJ287 black hole

On Monday, June 1, 2020 at 4:56:29 PM UTC+3, wrote:
I notice that ta has typo error. I have written this long formula by hand with my mobile phone. I try to post ta again when I get proper internet connection which I did not have when I posted these. Our libraries are all closed their internet connection which I have used before due this coronavirus pandemia. Sorry that typo error. Hannu


CORRECT ONE:

# I give this complicated primitive function here (Maple 9 used): Analytic solution (Weinberg S. Gravitation and Cosmology, 1972, General Relativity definitions used from this book).

# Defintion areas: u=1.843608337*10^(-15), 0r=5.424145573*10^(-14) cm, u=1/r,0=P=Pi.


ta := P- 0.14273426e18*arctan(19556.51583*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*sin(P)/(-0.2000000000e15+753242809*sin(P)^2))-0.1021331259e48*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*sin(P)/((-0.2000000000e15+753242809*sin(P)^2)*(0.3774722128e 26+0.1443670077e35*(0.4000000000e15-1506485618*sin(P)^2)*sin(P)^2/(-0.2000000000e15+753242809*sin(P)^2)^2))+0.19991518 56e-30*((-0.2000000000e15+753242809*sin(P)^2)*(-1+sin(P)^2))^(1/2)*(0.3908757305e66*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*EllipticF(sin(P), 0.1940673606e-2)*sin(P)^2+0.6697771796e73*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*EllipticF(sin(P), 0.1940673606e-2)+0.2468340123e75*sin(P)+0.9296297238e69*sin(P)^5-0.2468349419e75*sin(P)^3+0.1234170061e68*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*EllipticE(sin(P), 0.1940673606e-2)*sin(P)^2+0.2114787075e75*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*EllipticE(sin(P), 0.1940673606e-2)-0.1273248266e68*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*EllipticPi(sin(P), -0.5835906962e-7, 0.1940673606e-2)*sin(P)^2-0.2181748740e75*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*EllipticPi(sin(P), -0.5835906962e-7, 0.1940673606e-2))/((0.2000000000e15+753242809*sin(P)^4-0.2000007532e15*sin(P)^2)^(1/2)*(0.2202892715e19*sin(P)^2+0.3774722128e26)*cos( P)*(0.4000000000e15-1506485618*sin(P)^2)^(1/2));

u:=P-(-8.905287066*10^(-19)*cos(P)+3.686326146*10^(-15)) / (-cos(P) +1);


  #7  
Old June 6th 20, 06:56 AM posted to sci.astro
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Default One proper time event inside OJ287 black hole

I have thought that could there be something wrong when I used OJ287 pendulum orbit E and J in case of proper time general relativity equation? I try to investigate this more closely. Best Regards, Hannu Poropudas
  #8  
Old June 6th 20, 08:29 AM posted to sci.astro
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Default One proper time event inside OJ287 black hole

E and J are same in all cases. So their values are right. I remind that Weinberg S 1972 book has these formulae for E and J for bounded orbit wrong. Correct formulae are found in my old articles in sci.physics.relativity. Hannu
  #9  
Old June 6th 20, 02:36 PM posted to sci.astro
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Default One proper time event inside OJ287 black hole

Definition area: 0r=0.5424145573*10^14 cm. (correction, wrong minus sign was typo error, sorry about that). Who could imagine what kind time travel solution this is, but fortunately inside thus supermassive black hole's event horizon? Best Regards, Hannu Poropudas
  #10  
Old June 8th 20, 10:47 AM posted to sci.astro
Hannu Poropudas[_2_]
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Default One proper time event inside OJ287 black hole

On Saturday, June 6, 2020 at 4:36:08 PM UTC+3, wrote:
Definition area: 0r=0.5424145573*10^14 cm. (correction, wrong minus sign was typo error, sorry about that). Who could imagine what kind time travel solution this is, but fortunately inside thus supermassive black hole's event horizon? Best Regards, Hannu Poropudas


I found to this proper time corresponding coordinate time analytic solution:

# OJ 287 Coordinate time t dependence of r H.P. 07.06.2020
# MG := 0.2709414501*10^15;
# E := 1.015569493;
# J := -1.731669280*10^16;
# Definition areas: 0 = P = Pi, u = 0.1843608337e-14, u = 1/r,
# 0 r = 5.424145573*10^14 cm, (c.g.s units and c = 1)
t := P- 0.2709414538e15*arctanh(249.8793613*(0.8000000000e 15+188610932..2*sin(P))/(-0.1505032022e30*(sin(P)+0.6259964581e-1)^2+0.1884289432e29*sin(P)+0.3996140492e35)^(1/2))-0.2709414538e15*arctanh(249.8793613*(0.8000000000e 15-188610932.2*sin(P))/(-0.1505032022e30*(sin(P)-0.6259964581e-1)^2-0.1884289432e29*sin(P)+0.3996140492e35)^(1/2))+0.14597870e18*arctan(19556.51583*(0.4000000000 e15-1506485618*sin(P)^2)^(1/2)*sin(P)/(-0.2000000000e15+753242809*sin(P)^2))-0.1013472108e48*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*sin(P)/((-0.2000000000e15+753242809*sin(P)^2)*(0.3774722128e 26+0.1443670077e35*(0.4000000000e15-1506485618*sin(P)^2)*sin(P)^2/(-0.2000000000e15+753242809*sin(P)^2)^2))+0.13417302 34e-82*((-0.2000000000e15+753242809*sin(P)^2)*(-1+sin(P)^2))^(1/2)*(0.1155543602e119*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*EllipticF(sin(P), 0.1940673606e-2)*sin(P)^2+0.1980058301e126*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*EllipticF(sin(P), 0.1940673606e-2)+0.1418433905e118*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618.*sin(P)^2)^(1/2)*EllipticPi(sin(P), 255.1856495, 0..1940673606e-2)*sin(P)^2+0.2430528646e125*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*EllipticPi(sin(P), 255.1856495, 0.1940673606e-2)-0.1940237723e120*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618.*sin(P)^2)^(1/2)*EllipticPi(sin(P), -0.5835906962e-7, 0.1940673606e-2)*sin(P)^2-0.3324654996e127*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*EllipticPi(sin(P), -0.5835906962e-7, 0.1940673606e-2)+0.3649478065e127*sin(P)+0.1374471555e122*sin(P) ^5-0.3649491810e127*sin(P)^3+0.1824739033e120*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618*sin(P)^2)^(1/2)*EllipticE(sin(P), 0.1940673606e-2)*sin(P)^2+0.3126744557e127*(1-sin(P)^2)^(1/2)*(0.4000000000e15-1506485618.*sin(P)^2)^(1/2)*EllipticE(sin(P), 0.1940673606e-2))/((0.2000000000e15+753242809*sin(P)^4-0.2000007532e15*sin(P)^2)^(1/2)*(0.2202892715e19*sin(P)^2+0.3774722128e26)*cos( P)*(0.4000000000e15-1506485618*sin(P)^2)^(1/2));

u := P - (-0.8905287066e-18*cos(P)+0.3686326146e-14)/(-cos(P)+1);

plot([1/u(P),t(P),P=0..Pi]);
# log = ln
plot([u(P),log(t(P)),P=0..Pi]);


This Maple 9 program can be used by copy-paste due is command mark of Maple 9.

This is also OPEN QUESTION, because this analytic solution is also inside super massive black hole's event horizon of the OJ287 binary black hole system. This solution is primitive function (integration constant=0).

Let us try to figure out what these two analytic solutions tries to tell
us about inside event horizon motion of particle (proper time solution and this coordinate time solution dependence of radial distance r ?

Best Regards,

Hannu Poropudas
Finland
 




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