# gst: apropos of prolate- oblate spheroid transition, the chaotic behavior of a spinless entity around a black hole.

AA << investigate the long-term orbital dynamics of spinless extended bodies in Schwarzschild geometry, and show that periodic deviations from spherical symmetry in the shape of a test body may trigger the onset of chaos. (AA) do this by applying Dixon's formalism at quadrupolar order to a nearly spherical body whose shape oscillates between a prolate and an oblate spheroid. The late-time chaotic behavior is then verified by applying Melnikov's method. >>️

Ricardo A. Mosna, Fernanda F. Rodrigues, Ronaldo S. S. Vieira. Chaotic dynamics of a spinless axisymmetric extended body around a Schwarzschild black hole. arXiv: 2207.04341v1 [gr-qc]. Jul 9, 2022. 

https://arxiv.org/abs/2207.04341

Phys. Rev. D 106, 024016 (2022). 

https://doi.org/10.1103/PhysRevD.106.024016

Also - Oblate and Prolate Spheroid.  

<< The shape of the earth is that of a round ball or sphere slightly flattened at two opposite sides. Such a body is termed a spheroid. There are two kinds of spheroids-oblate and prolate; the former as the shape of an orange, the latter that of a lemon.  >>️

Oblate and Prolate Spheroid.  

https://etc.usf.edu/clipart/30500/30587/spheroid_30587.htm

img    https://etc.usf.edu/clipart/30500/30587/spheroid_30587_sm.gif

Also

keyword 'transition' in FonT: 

https://flashontrack.blogspot.com/search?q=transition

keyword 'transizione' | 'transition' in Notes (quasi-stochastic poetry): 

https://inkpi.blogspot.com/search?q=transizione

https://inkpi.blogspot.com/search?q=transition

Keywords: gst, spheroid, behavior, chaos, transition, black hole