What General Relativity Project Should I Undertake to Enhance My Knowledge?

[aashay]

I am new to General relativity and want to master it. Can you suggest some problem or a project on which I can work in summer holidays or so that will enable me to enhance my knowledge of general relativity and its applications?I have the basic knowledge of GR and am pretty familiar with the mathematics of it.

 

[haushofer]

You could try to derive different solutions, like the Schwarzschild solution or Reissner-Nordstrom solution, and do an analysis of the spacetime (consider geodesics, causal structure, etc.) Also, cosmological solutions like the Robertson-Walker metric provide a nice way to acquint yourself with different solutions.

Another nice "project" is to become acquinted with the Hilbert action, and derive the Einstein equations via a variational principle (and see how the equations are changed if you add higher order or extra derivative terms).

It depends a bit on the level you've already acquired :)

 

[bcrowell]

I've had a lot of fun playing around with computer algebra systems to find solutions to the Einstein field equations in the form of series. There are some examples in this book: http://www.lightandmatter.com/genrel/ See section 6.2.4 and ch. 9, problem 2.

 

[aashay]

I have already done the derivation of Einstein's equations from variational principle and have also done the Schwarzschild solutions. I will see the other solutions.

 

[Mentz114]

How about the kinetic decomposition of congruences ? I have nearly completed a package of routines that enable this to be done easily in Maxima, if you don't have gr-tensor for Maple.