surfing the internet to look for good books and have stumbled on this one, just scanning few pages i can already say this is a good book, may come handy for pre-requisite refresher topics
Introduction to Differential Geometry
https://link.springer.com/book/10.1007/978-3-662-64340-2
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/
Are you thinking about this or are you ghosting me?
@timely_pace
Are these equations extensible to a 3+1 spacetime?