There is no royal road to science, and only those who do not dread the fatiguing climb of its steep paths have a chance of gaining its luminous summits.

— Karl Marx, Capital, Vol. 1: A Critical Analysis of Capitalist Production

Numerical relativity and Self Force

My research primarily revolves around employing numerical relativity techniques to accurately model binaries exhibiting intermediate to extreme mass ratios, such as IMRIs (Intermediate Mass Ratio Inspirals) or EMRIs (Extreme Mass Ratio Inspirals). Specifically, I am engaged in developing a modified version of the effective source method that enables precise numerical calculations of the gravitational self force.

Spherical Summation by Parts Operators

In spherical symmetry the treatment of the origin is a major headache when it comes to numerical calculations, since it’s singular. But the singularity is only a mere coordinate singularity. In the literature a 2nd order SBP operator exists but generalizing to higher order is highly non trivial. Recently, there is a shift of the numerical relativity community towards using spherical coordinates. The techniques we develop can be also applied to the hyperboloidal slicing method, to get higher order SBP operators that treat the singularities at future null infinity.