Interests: general relativity, quantum fields and strings, geometric analysis
Contact me: nikhil.chakraborty@stonybrook.edu
Advisor: Marcus Khuri
Introduction to quantum field theory, momentum space Feynman rules (supplement). Mostly basic perturbation theory with scalars and no gauge symmetry. Main source: Peskin and Schroeder.
Hawking radiation on a Vaidya spacetime. This derivation does not discuss the universality of the radiation spectrum -- it just provides a specific example. Source: this paper; I just wrote out the calculations in some more detail.
A couple of non-standard derivations of ADM energy. One derivation is based on conservation of energy, the other is based on asymptotic time translation symmetry.
Spacetime positive mass thoerem and the Jang equation. My attempt at presenting the seminal Schoen-Yau paper where they established the spacetime positive mass theorem by extending the Riemannian one. One starts with initial data (M, g, k). The Jang equation, if solved, gives a hypersurface as a graph in M x R whose mean curvature is the trace of k. Apparent horizons obstruct existence of such a surface, but you can perturb the Jang equation, solve it, then send the perturbation to 0 and get a smooth hypersurface with apparent horizons. You can then conformally close the apparent horizons and do a conformal transformation so the hypersurface has 0 scalar curvature. Provided you've done the process with asymptotics that match those of M, you can invoke the Riemannian positive mass theorem to get the result.
Calabi-Yau compactification of the heterotic string. If we take the heterotic string, compactify 6 of the dimensions, then demand N=1 supersymmetry of the 4-dimensional effective field theory, we learn that the 6 internal dimensions must be a Calabi-Yau manifold. The moduli of the 4D effective field theory (which come from the 10-dimensional equations of motion and the topology of the Calabi-Yau manifold) are discussed. Getting the Standard Model gauge group out of either of the heterotic strings is not discussed.