Most of my publications are concerned with the hyperboloidal method, which is a technique to follow light to infinity using suitable coordinates for numerical computations. Originally motivated by gravitational waves, explorations of this technique led me to many other topics such as black hole perturbation theory, numerical methods, and PDE analysis.


  • Devised a practical method that solves the outer boundary problem and the radiation extraction problem in numerical calculations of wave equations [1].
  • Introduced horizon-penetrating, hyperboloidal coordinates in black-hole perturbation theory [2], [3] and performed the first numerical computations with such coordinates [4], [5], [6].
  • Computed caustic echoes from a black hole (with Chad Galley) [7]. Such echoes in the X-ray regime have recently been observed astronomically.
  • Demonstrated an efficiency gain of 5,000 in the computation of gravitational waves at null infinity using hyperboloidal compactification on the background of a rotating black hole (with Gaurav Khanna) [8].
  • Contributed to the Simulating-eXtreme-Spacetimes Collaboration. Two of my papers as part of that collaboration [9], [10] have been cited by the first detection of gravitational waves that led to the 2017 Nobel Prize in Physics.

See also Google Scholar and the Astrophysics Data System for a list of my publications.


  • My main research target was hyperboloidal compactification for Einstein equations. I made some progress on this as part of my Ph.D. thesis. But after publishing a paper describing how one could do this in principle, all my efforts failed. The topic is now an active area of research, with David Hilditch and Alex Vañó-Viñuales leading the effort.
  • My thesis was about global numerical computations using the generalized conformal Einstein equations. I was fascinated by the Weyl connection and the related conformal Gauss gauge. In that gauge, I made the first global calculation of Schwarzschild spacetime and even computed gravitational radiation around spatial infinity in 3D. But I never published a single refereed paper about these topics because I eventually convinced myself that spatial infinity was irrelevant for radiation. Today, I consider this a missed opportunity (although I still think that spatial infinity is not that relevant from an astrophysical perspective).
  • After years of uncertainty and semi-forced relocations, I gave up scientific research due to personal reasons at the end of 2013, less than two years before the discovery of gravitational waves. I don’t believe that you should “never give up,” especially when the price for not giving up is paid by the ones you love. But the choice is never easy because you end up giving up a part of your identity.
Hyperboloidal method for frequency-domain self-force calculations
Template banks for binary black hole searches with numerical relativity waveforms
Stability of nonspinning effective-one-body model in approximating two-body dynamics and gravitational-wave emission
Self-force via Green functions and worldline integration
Intermediate behavior of Kerr tails
Effective-one-body model for black-hole binaries with generic mass ratios and spins
Catalog of 174 binary black hole simulations for gravitational wave astronomy
Quasinormal modes of nearly extremal Kerr spacetimes: spectrum bifurcation and power-law ringdown
Intermediate behavior of Kerr Black Hole tails
Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration
Spacelike matching to null infinity
Hyperboloidal data and evolution