Classical General relativity
While classical general relativity, and in particular the topic of exact solutions of the Einstein field equations, is by now an old and venerable subject that has been picked over by hundreds of physicists and mathematicians, there are still surprises left and useful information to be extracted.
In particular, classical general relativity is a good place to find advanced undergraduate projects and topics appropriate for Master's theses.
For instance, over the last few years there have been some significant developments in the field of exact solutions for static fluid spheres. Based on a new "algorithmic" approach one first explicitly writes down the most general metric for a static spherically symmetric perfect fluid spacetime in terms of an arbitrary "generating function". Only after this is accomplished, and the perfect fluid constraint is satisfied, does one attempt to constrain the generating function by imposing additional physics requirements (such as positivity of energy and pressure).
On a related front, it is also possible to use the classic TOV equation to derive numerous bounds on the structure of aribitrary static fluid spheres.
Petarpa Boonserm's Master of Science thesis
has focused on two main issues:
- The strategic use of coordinate conditions to simplify Einstein's equations.
- Transformations that map solutions of Einstein's equations into new solutions.
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Some references on perfect fluid spheres
For further information on perfect fluid spheres see:
- Shahinur Rahman and Matt Visser, Spacetime geometry of static fluid spheres. e-Print arXiv: gr-qc/0103065, Classical and Quantum Gravity 19 (2002) 935--952;
- Damien Martin and Matt Visser, Algorithmic construction of static perfect fluid spheres. e-Print arXiv: gr-qc/0306109, Physical Review D69 (2004) 104028.
- Damien Martin and Matt Visser, Bounds on the interior geometry and pressure profile of static fluid spheres. e-Print arXiv: gr-qc/0306038, Classical and Quantum Gravity 20 (2003) 3699-3716.