The Illinois Relativity Group is committed to excellence in research, education and mentoring. Graduate students in the group will have a primary adviser (Professor Shapiro, Professor Witek, or Professor Yunes) and they are expected to collaborate with other graduate students and postdoctoral researchers in the astrophysics, gravitation and cosmology group. The primary adviser mentors the student to help her/him develop professional research skills, technical writing skills and oral presentation skills. The research topics graduate students work on can be found in our research section.
Policy for Prospective Graduate Students
Graduate students interested in becoming members of the Illinois Relativity Group must demonstrate a mastery of physics and, in particular, of general relativity and gravitation. Typically, the student should
- excel in the first year graduate courses that she/he may be taking,
- pass the Physics PhD qualifying exam (written version), and
- complete a small research project with their adviser of choice.
Graduate students should take the core general relativity (GR) courses Physics 515 and Physics 516 and all other special topics seminars in General Relativity that are offered from time to time. Students should also take the course on the physics of compact objects, Physics 541, and on cosmology, Physics 598C0S.
After becoming members of the relativity group, students will be allowed to obtain a Ph.D. in gravitational research. As all other graduate students, gravity students must submit a Ph.D. dissertation in compliance with departmental and graduate school rules. The dissertation must be based on research carried out by the graduate student during her/his tenure at Illinois. Relativity students are recommended to complete at least 4 papers to be published in refereed scientific publications. Moreover, the relativity group encourages the dissemination of scientific results at conferences and workshops. Students will be required to present her/his results in at least 2 conferences or workshops before completion of their Ph.D. Venues for such presentations include the APS April Meeting, the Midwest Gravity Meeting, the International Conference on General Relativity and Gravitation, the Amaldi Meeting, or other special workshops or invited talks at accredited universities.
Core and Recommended Courses
Core Courses for Gravity Students
Graduate students in the Physics Department are normally required to take 2 of the following core courses, which include
- PHYS 580: Quantum Mechanics I — Operators, state vectors, and the formal structure of quantum theory.
- PHYS 581: Quantum Mechanics II — Spin and identical particles, simple many-particle systems and elements of second-quantization theory.
- PHYS 505: Electromagnetism — Review of Maxwell's equations; relativistic formulation of the electromagnetic field and the motion of charged particles.
- PHYS 504: Statistical Physics — Single-particle distribution functions; classical and quantum mechanical systems, Boltzmann equation, virial theorem, and equations of state for gases.
- PHYS 508: Mathematical Methods A — Core techniques of mathematical physics widely used in the physical sciences.
- PHYS 509: Mathematical Methods B — Complex variables; group theory in classical and quantum systems; tensors in physics; differential forms and their applications in mechanics; electromagnetism.
- PHYS 540: Astrophysics — Basic physical concepts and principles, the key observational evidence, and illustrative calculations.
Graduate students interested in research on gravitation should consider taking some subset of courses listed above in consultation with their adviser. For a list of all graduate courses offered, please refer to https://physics.illinois.edu/academics/courses/.
Required Courses for Gravity Students
In addition to these core Physics Department courses, graduate students interested in gravitation should take the following courses:
- PHYS 515: General Relativity I — Tensor calculus, differential geometry, and an introduction to Einstein's theory of gravity.
- PHYS 516: General Relativity II — Black hole theory, the 3+1 formulation of Einstein's theory, black hole perturbation theory and extreme mass-ratio inspirals.
- PHYS 541: Physics of Compact Objects — neutron star and black hole theory and astrophysics.
- PHYS 598COS: Cosmology — basic cosmological theory and perturbations.
- PHYS XXX: Special topics: Numerical Relativity — initial data problem, evolution schemes, wave extraction.
- PHYS XXX: Special topics: Post-Newtonian Theory — dynamics of inspiraling compact objects binary.
Recommended Courses for Gravity Students
Finally, students interested in gravitation should also consider taking the following related courses:
- PHYS 598CPA — Computational Physics and Astrophysics computational modeling and numerical methods.
- PHYS 575: Particle Physics I — elementary particle theory, q.e.d and q.c.d
- PHYS 582: General Field Theory — introduction to quantum field theory
- PHYS 585: Advanced Field Theory — quantization and Feynman path integral approach.
- PHYS 598ADS: ADS/QFT Correspondance — ADS/CFT and other dualities.
Several courses offered in the Astronomy Department may be of interest to students as well, including courses on radiative transfer, stellar structure, stellar dynamics, etc.