Lorentz-Einstein equation and Sturm Liouville Theory

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The discussion centers on the exploration of the Lorentz-Einstein equation (LEE) and its potential representation as a second-order differential equation through a change of basis. The participant, Blackforest, inquires whether it is valid to analyze this new formulation using Sturm Liouville Theory. The equation is defined in terms of the volumetric density of matter (ρ), the 4-speed vector (u), and the Lorentz force ([F].j), where [F] is the strength field tensor and j is the Lorentz current. The conversation highlights the intersection of advanced mathematical theories and their applications in physics.

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member 11137
I first want to excuse me if it is the wrong place to post my question and if it is forbidden to ask such question on this forum because I know that personal research are not specially wellcome here. I don't want to disturb; I just want to learn more.
The question is: does it make sense to developp an essay in which I would try to recognize a set of four differential equations in observing the Lorentz-Einstein equation (LEE)? With other words does it make sense to look for a change of basis that would allow to read this LEE as a diff equ of second order ? And if I find one of these basis where it seems to be possible, is it correct to analyze the new formulation of the LEE with the Sturm Liouville Theory ?
One year ago I discovered the Connectivity Theory and I remarked that this latter obtain similar mathematical results than my approach, but through other ways.
Thank you for constructive remarks. Blackforest
 
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What do you call "the Lorentz-Einstein equation"?

Seratend.
 
On the left hand: ro. Du/ds where ro is the volumetric density of matter, u is the 4-speed vector, D the total derivative along the path s; on the right hand: [F].j the Lorentz force where [F] is the strenght field tensor and j the Lorentz current. Sorry I don't work with Latex or similar useful program (I will try to learn).
 

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