General Relativity: Flamm's Paraboloid...

[Orion1]

[math]\text{General Relativity: Flamm's Paraboloid}[/math]
[math]\text{The exterior Schwarzschild metric space-time curvature solutions for a radius greater than the Schwarzschild radius } (r > r_{s})[/math]
[math]\text{can be visualized as mathematical parametrics. There is an additional Euclidean z-axis metric polar dimension w,}[/math]
[math]\text{which has no physical reality and is not part of space-time.}[/math]

[math]\color{blue}{ \text{Any discussions and/or peer reviews about this specific topic thread?}}[/math]

[math]\color{blue}{\text{"I think of the horizon at midnight, the sky and sea blurring together." - Sophie Hardcastle}}[/math]
 

 

 

Edited March 14, 2022 by Orion1

[Orion1]

Any discussions and/or peer reviews about this specific topic thread?

"I think of the horizon at midnight, the sky and sea blurring together." - Sophie Hardcastle

 

 

 

Edited March 14, 2022 by Orion1

[studiot]

Why have you got 2 threads on this one subject ?

[Orion1]

Any discussions and/or peer reviews about this specific topic thread?

"I think of the horizon at midnight, the sky and sea blurring together." - Sophie Hardcastle

Reference:
Wikipedia - Schwarzschild metric - Flamm's paraboloid: (ref. 1)
https://en.wikipedia.org/wiki/Schwarzschild_metric#Flamm's_paraboloid
Wikipedia - Schwarzschild radius: (ref. 2)
https://en.wikipedia.org/wiki/Schwarzschild_radius
Wikipedia - Schwarzschild metric: (ref. 3)
https://en.wikipedia.org/wiki/Schwarzschild_metric
Wikipedia - Boyer-Lindquist coordinates - Line element: (ref. 4)
https://en.wikipedia.org/wiki/Boyer-Lindquist_coordinates#Line_element
Science Forums - General Relativity: Four Exterior Metric Solutions - Orion1: (ref. 5)
https://www.scienceforums.net/topic/126549-general-relativity-four-exterior-metric-solutions/
Wikipedia - Photon sphere: (ref. 6)
https://en.wikipedia.org/wiki/Photon_sphere
Wikipedia - Astrophysical jet: (ref. 7)
https://en.wikipedia.org/wiki/Astrophysical_jet
Wikipedia - Accretion disk: (ref. 8)
https://en.wikipedia.org/wiki/Accretion_disk
Wikipedia - Black hole - Innermost stable circular orbit: (ref. 9)
https://en.wikipedia.org/wiki/Black_hole#Innermost_stable_circular_orbit_(ISCO)
 

Mathematica 7 - General Relativity - Flamm's Paraboloid source code notebook attachment:

General Relativity - Flamm's Paraboloid.nb

Mathematica 7 - General Relativity - Schwarzschild Black Hole Toy Model source code notebook attachment:

General Relativity - Schwarzschild Black Hole Toy Model.nb

33 minutes ago, studiot said:

Why have you got 2 threads on this one subject ?

Please merge the threads if there is a protocol violation.

 

 

Edited March 14, 2022 by Orion1