(just posting today, an mwfsat day, what has been done yesterday, a tthsun day), here, adhering to what is analogous to Kaluza's cylinder hypothesis
https://foxtrotpaparomeo.wordpress.com/2023/01/11/11012023rough-draftstatic-solutions-to-einsteins-field-equations-in-11-space-time/
Are these equations extensible to a 3+1 spacetime?
Are you thinking about this or are you ghosting me?
polishing it with some corrections, i might exceed five pages
https://foxtrotpaparomeo.wordpress.com/2023/03/20/20032023rough-draftstatic-solutions-to-einsteins-field-equations-in-11-space-time/