Spring 2002

The dynamics of black hole formation is one of the unsolved problems of modern physics. This owes to both the unsolvability of two-body problems in Einstein's theory of General Relativity and the auantum nature of certain black hole processes. With Antal Jevicki, I examined an exactly solvable model of black hole formation in 2 + 1 dimensions in order to predict qualitative features of black hole formation in higher dimensional spaces.

In particular, we found no exponential supression or enhancement of the process. This is different from the result predicted by models that assume a test particle falling in an effective black hole background. We believe the reason for the difference is that the total energy of the system is the mass of the created black hole, so models that assume a small mass test particle ignore the fact that the test mass kinetic energy must contribute to the mass of the black hole. This changes the diverege of the momentum near the effective horizon from a linear to a logarthymic diverges, so the classical action is finite as opposed to infinite, therefore the semi-classical transition amplitude does not have an exponential suppression.

I was an APS Apker Award finalist for this research.

• Dynamics of black hole formation in an exactly solvable model.
  Antal Jevicki and Jesse Thaler.
  Phys. Rev. D66 024041, hep-th/0203172.

Summer 2001

During the summer of 2001, I worked with Prof. Antal Jevicki on Matrix Models. In particular, Group Theory and Lie Algebra is necessary to develop the language of Symmetry that seems to be essential for a description of the fundamental microscopic structure of the universe.

For most of the summer, I learned about the fundamentals of Group Theory and Lie Alegbra. I gave three presentations as part of my study: the first covered classical and quantum mechanics on the SU(2) symmetry group; the second covered the characters and representations of SU(N) with a followup presentation on the equivalence between the characters of a group and the eigenstates of the group Hamiltonian; and the third covered the relationship between Matrix Models and Integrable Systems (i.e. systems with a conserved quantity for each degree of freedom).

Then, I studied the relationship between Matrix Models and Supersymmetry. Roughly speaking, supersymmetric systems are systems that are invariant under an exchange of bosons (force carriers) and fermions (matter particles). The structure of supersymmetric systems is closely connected to a study of Clifford Algebras, and these algebras impose limits on the kinds of systems that can exhibit supersymmetry.

This work was sponsored by an Undergraduate Teaching and Research Assistantship (UTRA) at Brown University.