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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