Research

My PhD research focuses on high-accuracy numerical methods for black hole perturbation theory, with applications to gravitational wave physics, extreme mass ratio inspirals (EMRIs), and horizon-scale phenomena in extremal black holes.

Research Highlights

1. Discontinuous Galerkin methods for singular-source Teukolsky evolutions

Figure: Convergence of the numerical flux $\dot{E}$ in Teukolsky simulation to a reference value from Black Hole Perturbation toolkit (BHPT) for circular orbits.

EMRIs are key targets for LISA and require accurate time-domain solutions of the Teukolsky equation. I develop discontinuous Galerkin (DG) methods that directly handle distributional particle sources, avoiding narrow-Gaussian regularization errors and improving convergence near the source.

Related links: Coming soon

2. Radiation outer boundary conditions for long-time stable simulations

Figure: Schematic showing the boundary-kernel workflow in time-domain and frequency-domain.

Long-duration simulations on finite domains are often contaminated by spurious reflections and late-time artifacts under standard outgoing boundary conditions. I investigate exact radiation boundary kernels and hyperboloidal-inspired strategies for the Bardeen–Press equation to enable stable long-time evolution and accurate asymptotic waveform recovery.

Figure: Impact of correct boundary conditions on the simulation. Clean late time power-law decay of solution

Related links: Paper · ICERM poster

3. Horizon hair as a potential observable of extremal black holes

While classical no-hair results characterize stationary black holes by mass, spin, and charge, extremal Kerr geometries exhibit conserved horizon quantities for specific perturbations. I study how these scalar/gravitational hair signatures can propagate into measurable waveform features and distinguish extremal from sub-extremal systems.

Related links: Paper · Talk slides

Last updated: August 2026