Studying for a PhD in GR: Advice & Resources

[tommyj]

Hi all, wondering if I might have some advice. I would like to study for a PhD in GR. First things first

1. What would people recommend as a complete book on GR? By complete I mean one that serves as an intro then goes above and beyond, ideally no more than £20!

2. Does anyone have any institutions (in the UK) that they would recommend? I'm aware the GR bubble has burst somewhat.

3. Does anyone have any area of GR they would suggest as being a good area to go into? My favorite is black holes (I'm aware this is a bit vague...). I would be happy to go into either physics or math, but would prefer math (so theoretical physics if anything one imagines) but would also be interested in some numerics (I have seen some titles "Black Hole Accretion Disks" and one to do with orbits of a binary system of black holes, with app. to gravitational waves, a priori these seem really interesting!)

Heres my background; just graduated with an MSCi degree in mathematics from Imperial College London, first class. Taken courses in GR, SR and electromagnetism, geometry of curves and surfaces, manifolds, Riemannian geometry and alegbraic topology (might be useful). My masters project was on the riemannian positive mass theorem and the riemannian penrose inequality. I really enjoyed this, but it was more of a "heres the motivation from physics in the first chapter, rest is geometry" whereas for a PhD I would prefer GR to be the whole way through.

I both look forward and appreciate any help you can give, thanks Tom

note* i have looked into these things myself, I'm not being lazy! just would like to see what more experience and knowledgeable people think

 

[TonyG]

Hi Tom,

First of all, congratulations on graduating with a first class degree in mathematics from Imperial College London! That is quite an accomplishment and a great foundation for pursuing a PhD in GR.

To answer your questions:

1. For a complete book on GR, I would recommend "Gravitation" by Misner, Thorne, and Wheeler. It is a classic text that covers all aspects of GR, from the basics to advanced topics. It may be a little over your budget, but it is definitely worth the investment.

2. Some top institutions in the UK for studying GR are the University of Cambridge, the University of Oxford, and the University of Edinburgh. But there are many other universities that also have strong programs in GR, so it's worth researching and considering all your options.

3. Black holes are a fascinating and popular area in GR, so it's a great choice for a research topic. In terms of specific areas, you could look into numerical relativity, which is the study of solving Einstein's equations numerically to simulate black holes and other astrophysical phenomena. Another interesting area is gravitational waves, which have been a hot topic since their recent detection. You could also consider studying the thermodynamics of black holes or the dynamics of accretion disks.

Based on your background and interests, I think you would be a strong candidate for a PhD in GR. Your experience in geometry and topology will definitely be useful in this field. I would recommend reaching out to professors and researchers in the field to discuss your research interests and see if they have any openings for PhD students.

I hope this helps and best of luck in your pursuit of a PhD in GR! It's a challenging but rewarding field to study. Feel free to reach out if you have any other questions.