After going through a graduate degree, my preference is for the latter as the math you learn is applicable in lots of other areas, i.e. things like differential geometry, real analysis, functional analysis. But for an undergraduate degree, you probably want something that builds on physical reasoning. Hartle mostly takes that approach, but also includes more mathematical material that you could expand on. Plus a nice treatment of gravitational waves.

]]>I’ve heard of those guys…

]]>Anyway, a good complement might be Schutz’s other book, “Geometrical Methods of Mathematical Physics”. It has a better introduction to differential geometry than the GR book, so students struggling through the math might like the companion. It’s also great because it comes with other applications of differential geometry to physics, in particular, Schutz’s discussion of thermodynamics is briliant and students might appreciate that the math goes beyond GR in terms of utility.

As for a physics complement, I would suggest Norbert Dragon’s “Geometry of Special Relativity”. The first two chapters do SR in the same fashion as one learns Euclidean Geometry in school, no coordinates, just diagrams, now suitably interpreted to be clocks in addition to rulers. It’s a great way to seeing the solution to various paradoxes, instead of just calculating them away.

The GR version of having a geometric centered discussion would be Geroch’s Lecture notes on General Relativity, recently printed in book form. Lots of diagrams and clear exposition of the underlying geometry of curved spacetimes.

Lastly, the best discussion of the physical interpretation of the Einstein equations is arguably John Baez’s “The Meaning of Einstein Equations”, a short pdf you can find on his website. The idea here is to show that Ricci curvature has a very straightforward interpretation as the second derivative of a volume element, divided by that same volume element (to first order), something that surprisingly rarely appears in GR textbooks.

I hope this is helpful

]]>Schutz was indeed the book recommended for experimental postgrad students learning GR here. I think this level is comparable to final year bachelor TP students so you are possibly in safe hands.

A final name would be Hartle, which is recommended for the final-year bachelor course here on gravitational waves. If it works for bachelor students in the Netherlands it may work in Ireland. Unfortunately I can say nothing about the content of the book however.

These are by no means exotic choices in the world of GR textbooks but I thought I would throw in the names I know 🙂

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