My research projects have spanned right from my undergraduate days until now.
In the long history of the study of stability of black holes, the last decade has been very exciting following the discovery of an instability of extreme black holes. A general understanding of the instability has emerged from a variety of techniques, whose domains of validity are largely non-overlapping. Due to the limited validity of these techniques, the cause of this instability has been elusive.
In search of a simple description of a possibly universal phenomenon, in this paper, we studied the instability in the simplest possible setting. Using some neat tricks and numerical analysis we were able to identify the cause of the instability to be a class of null geodesics (light rays) that orbit around the event horizon for arbitrarily long times.
I have also been interested in studying the implications of this instability to spacetime holography - the idea that gravitational theories are dual to field theories in one lower dimension. As a result, geometric phenomena that occur in a gravitational theory can be mapped onto phenomena on a quantum field theory.
In this paper, we asked whether this horizon instability has implications for strongly coupled field theory. Surprisingly, the answer seems to be no: this effect is definitely physical in the bulk and is tied to the emergence of conformal symmetry and an associated ‘semi-local quantum criticality’ (a phase transition at zero temperature), which has been intensively studied with the hope of describing condensed matter systems, but the field theory on the boundary itself does not see this effect buried deep in the bulk of the spacetime.
So far, the systems that have been studied with regards to this horizon instability all share the same near-horizon geometry, leading to an emergent symmetry which results in the instability. I am currently investigating an extremal horizon with a different near-horizon geometry - the D3 brane (the original system where the idea of holography emerged). Preliminary results indicate that the instability doesn’t exist in this system, leading us to believe that the emergent symmetries due to the near-horizon geometry is crucial for the instability.
Semi-local Quantum Criticality and the Instability of Extremal Planar Horizons (with Samuel Gralla and Peter Zimmerman) arXiv; journal
Horizon Instability of the Extremal BTZ Black Hole (with Samuel Gralla and Peter Zimmerman) arXiv; journal
Here are some of the talks I have given.
My research interests before I started my doctoral studies were primarily directed towards the foundations of quantum physics.
I was first introduced during a reading project to the EPR paper and Bell’s inequalities which seemed to me to be an extremely strong result that nature is non-local! Through some reading I came across the body of work that seemed to overcome a lot of the problems of ‘Copenhagen’ Quantum theory and described quantum physics with particles moving in trajectories while still recovering all known formalisms and results - Bohmian mechanics. So I went on to work with Dr. Detlef Duerr at Ludwig Maximilians Universitaet, Munich, Germany on my Master’s thesis on studying a way to describe time of arrival statistics in quantum theory. Conventional quantum theory does not allow the existence of a time operator because its canonical conjugate operator, the Hamiltonian, is a positive self-adjoint operator. However, we do observe phenomena such as the decay of a radioactive substance, emitting particles towards a detector, where we observe an arrival time distribution. Since conventional quantum theory doesn’t provide us a formalism to help us describe this phenomenon, we used Positive-Operator-Valued-Measures (POVMs) to describe the arrival time statistics in the context of Bohmian mechanics.
During my time in Munich, I got interested in various ideas in the foundations of quantum physics. For the latter part of my time there, realizing the problems with the ad-hoc procedure to remove infinities that appeared in Quantum Electrodynamics (renormalization) which still gave extremely accurate predictions about the nature of reality, I tried to look at what I could learn from Wheeler and Feynman’s attempt to come up with an underlying description of how a theory could look without needing this ad-hoc procedure of renormalization. The hope was to use the idea of advanced and retarded actions to somehow describe the Lamb shift in QED. Alas, I wasn’t able to make much progress (after all, geniuses like Feynman had difficulties in making progress in this direction). I still am extremely curious about how one could overcome the difficulties of renormalization in quantum field theories.
With the idea of learning about techniques in computing the self-force, I moved to Arizona to work with my now advisor Dr. Samuel Gralla I worked on studying Wheeler-Feynman Electrodynamics and