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jpmferreira

- 6

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So far I have had an undergraduate introductory course on GR, two courses in Cosmology (which was the topic of my master's thesis), a master's course on Black Holes & Gravitational Waves and a very introductory course to Numerical Relativity.

What is motivating this thread is my concern of not being able to understand GR well enough to be able to have new ideas and be able to proof the results that I'm after, which is crucial given that I wish to remain in academia.

This is true for both for its mathematical structure and its physical interpretation.

Therefore, I'm after references which do not neglect the mathematical foundations of GR, but also shouldn't introduce it in an excessively abstract way, while discussing the physics behind it.

I asked a professor of mine and he recommended me the book "Modern Geometry - Methods and Applications: Part I" for the studies of the mathematical foundations of GR.

With respect to GR itself, I was pointed towards Sean Carrol's lecture notes on GR.

On Numerical Relativity, I remember briefly looking at Alcubierre's booking on the 3+1 decomposition, which felt like skipped a couple of steps in the demonstrations.

Do you find these references suitable for my studies?

Are there any others I should consider?

I don't believe I have the time to read through the whole thing before starting my PhD, so I'll keep them close during my project.

Thank you in advance!