What other formalisms exist to solve the general relativity equations and their observables (such as energy, momentum and angular momentum of gravitational waves), in addition to the Cartan structure equations formalism, Killing equations, Lie algebras, Newman-Penrose formalism, and spinorial formalism, and what are their characteristics, advantages and disadvantages, including the advantages and disadvantages of these five formalisms mentioned (since I know their characteristics more or less)? And where can I consult them?
what about the formalism of https://en.wikipedia.org/wiki/Abhay_Ashtekar
Abhay Vasant Ashtekar (born 5 July 1949) is an Indian theoretical physicist. He is the Eberly Professor of Physics and the Director of the Institute for Gravitational Physics and Geometry at Pennsylvania State University. As the creator of Ashtekar variables, he is one of the founders of loop quantum gravity and its subfield loop quantum cosmology.[2] He has also written a number of descriptions of loop quantum gravity that are accessible to non-physicists. In 1999, Ashtekar and his colleagues were able to calculate the entropy for a black hole, matching a legendary 1974 prediction by Hawking.[3] Oxford mathematical physicist Roger Penrose has described Ashtekar's approach to quantum gravity as "The most important of all the attempts at 'quantizing' general relativity."[4] Ashtekar was elected as Member to National Academy of Sciences in May 2016.[5]
Thank you very much for the reference my very dear Professor Bobadilla. I will search the Wikipedia reference books and articles online. In fact, I want to attend a congress of loop quantum gravitaty, which is the main rival theory of string theory. Although there are some researchers who try to unify the loop quantum gravity with string theory, and I think they have written articles about it. But there are also many detractors who say that they cannot be unified, that they are two different and incompatible theories and that only one alternative is possibly correct. I do not close and contemplate both possibilities. In fact I have many string theory books that I plan to read later, and an introductory book on loop quantum gravitaty for beginners, to do so in future research on both theories and see if I can unify in search of my ultimate goal of a theory of everything version 1.0. Since the true scientist must have many girlfriends and not marry any idea, contrary to the moral norm. Soon I will send you a bibliography about all it, for now I send you a video of the Bhagavad Gita, which is something the Dr. mentioned studies.
https://www.youtube.com/watch?v=lkDposKHDQU
¡Saludos estimado profesor y amigo maestro!
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