I am fascinated by the dynamics of nonlinear systems. The dynamics of fluids such as air or water is described by nonlinear equations. These predict incredible phenomena such as rogue waves, or explain why hurricanes never split in two.
Black holes and gravitational waves are also described by nonlinear equations, the equations of General Relativity.
In my work, I focus on understanding better the nonlinear dynamics of the relaxation of black holes (BHs) to equilibrium, the dynamics of strongly gravitating fluids, and the connection between hydrodynamics and gravitational physics.

BH Spectroscopy

Viscous Stars

BHs and Fluids

Black holes relax to equilibrium emitting gravitational waves. This happens, for example, after two black holes merge, in the miliseconds after the remnant black hole first forms. This stage is called the ringdown.
BHs ringdown by emitting waves with particular tones. These tones only depend on the BH mass and its spin, which is incredibly useful, for example, to test General Relativity.
However the ringdown also contains higher harmonics, obtained by combining several tones. These are much weaker, but nonetheless will be detectable in the future.
The ratio between the children higher harmonic, and their parent tones, is a very interesting quantity. In a recent work, we showed by exciting and extracting these higher harmonics in perturbation theory, that this ratio depends only on the mass and spin of the BH, which can be predicted. This means, that once we detect these modes, we will have a novel way to test GR.
Another aspect of BH spectroscopy is that we can only extract the pure tones of the BH at late enough times, after the remnant BH has initially formed. This is a problem: at later times, the signal is weaker, and therefore extracting the tones accurately becomes more complicated.
One of the problems at extracting the tones at earlier times is that the BH is still growing: its mass and spin changing significantly.
In a recent work, we showed in a very simplified scenario, that one can model and extract the tones accurately even as the BH is changing its mass.

in collaboration with E. Berti, V. Cardoso, G. Carullo, D. Pereñiguez, J. Ripley
Some other wonderful people doing amazing work on these topics are B. Bucciotti, M. Cheung, T. May, S. Yi, H. Zhu.

A long time ago, W. Press conjectured that a material that is viscous enough could be used as a mirror or as a waveguide for gravitational waves. He dubbed this material Respondium. Although I am not the biggest fan of the name, I became very intrigued by this idea.
In the past year, I have been working towards extending the study of perturbations of stars to include viscosity. It turns out that there are several ways in which one can describe relativistic, dissipative hydrodynamics, so I have been learning a lot about fluids.
I do not have much to say publicly yet about this, but stay tuned: I am very excited about the results we are getting!

in collaboration with V. Boyanov, V. Cardoso and K. Kokkotas.

Einstein equations, once projected onto the horizon of a black hole, can be cast in a form which ressembles a lot the equations of fluid dynamics. This is the so-called membrane paradigm.
Upon a more careful inspection, it was shown that in fact those equations correspond to a Carrollian fluid, i.e., a hydrodynamic theory living on a Carrollian (instead of a Riemannian) geometry. Although this introduces some exotic construction, it is the most natural from the geometric point of view.
In my masters thesis I studied the dynamics of perturbations to the horizon of a BH, both from the gravitational and the fluid perspective. I believe there is much left to be understood between the connection of these two fields, and I am very excited to continue working on this.

in collaboration with L. Lehner (mostly), as well as P. Jai-akson, L. Freidel, and L. Ciambelli.

Publications

Here are some of my favourite papers. You can find a full list of my publications in Spires or in Google Scholar.

Codes

Together with G. Carullo and M. De Amicis we developed the Python package bayRing, which allows for simple Bayesian inference of ringdown numerical waveforms using several templates, including nonlinear modes. The repository VaidyaPT.jl is the companion of this paper, and allows to perform numerical evolution of gravitational perturbations on Vaidya spacetime, as well as to extract quasinormal modes, in pure Julia. I am a big fan and user of XAct, for analytical calculations, and GRChombo, for numerical relativity works.