So here I'm begging for your suggestions. Thanks.
What is your level of preparation? and what are you looking to learn?
Do you have access to online journals?
My level of preparation is something like a desaster i would say. I haven't heard any lectures on general relativity. I just read some chapters in Malcolm Ludvigsen's general relativity and Carroll's spacetime and geometry, mainly the introductory parts on geometry and einstein's equation. They say some words about the diagrams but i would feel more comfortable with a somewhat more serious introduction. As far as i understood it, there exists something similar in electrodynamics. And about that I did have lectures. But my memory is already overwritten i guess...
Online journals... hm... i don't like that. I prefer books.
Concerning the connection to electrodynamics, you might be thinking of conformal mapping diagrams... which do share some similarities with the conformal diagrams of Penrose.
Here is a not-so-technical reference: https://www.amazon.com/Cosmic-Frontiers-General-Relativity/dp/0316483419
Hawking & Ellis "Large Scale Structure of Spacetime" is certainly one reference.
In addition, there are sections by Penrose in Battelle Rencontres 1967 and Les Houches 1963 (http://relativity.livingreviews.org/refdb/record/3976)... and here is a journal article, available online, http://prola.aps.org/abstract/PRL/v10/i2/p66_1
D'Inverno's text http://www.oup.com/us/catalog/general/subject/Physics/Relativity/?view=usa&sf=toc&ci=9780198596868 might be useful.
Here are some other possibly useful references (online): http://relativity.livingreviews.org/Articles/lrr-2004-1/
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