In the early 60's, a series of papers by Bondi, Metzner and Sachs [1,2] were dedicated to the analysis of the asymptotic structure of an arbitrary metric. Targeting gravitational waves, they chose a specific gauge of the metric such that radially outgoing radiation can be easily described using frame fields.
Due to recent progress in gravitational wave physics, interest in the community in the asymptotic behaviour of metrics has risen again. One particularly intriguing and to that day unsolved problem is the derivation of asymptotic symmetries for metrics that are not only asymptotically Minkowskian (as in [1,2]) but rather de Sitter or even FLRW like. Understanding the structure of the Killing fields in those space times could lead to interesting insights via their corresponding conserved quantities and fluxes. For asymptotically Minkowskian space times, these symmetries have been used to derive "balance laws" for gravitational waves [3,4] that can constrain and quantify the accuracy of gravitational wave form models (for instance [5]). Finding analogous "laws" for the asymptotically FLRW space time might result in even more advance wave forms and pave the way for high precision gravitaional wave tests. Together with a few colleagues, I am trying to understand the asymptotic symmetry structure of FLRW and derive meaningful symmetry relations that could be applied to gravitational wave physics.

Gravitational waves are not only produced by coalescing binaries but various other sources in the (early) universe [1,2]. Accumulated, all unresolved signals form a sort of stochastic background of gravitational wave strain that could potentially be detected by future space-based interferometers. Due to its multi-faced contributions the stochastic gravitational wave background is rich in phenomenological informations. This is especially interesting as one could technically probe beyond the CMB, into the dark ages of the universe when it was still opaque to electromagnetic radiation. This era has yet been hidden from us physicist but plays a fundamental role in our understanding of the universe. Thus, naturally, shedding light on these dark spots would be an amazing advancement for science.
Without a doubt, currently the LISA mission [3] is the most promising survey regarding the detection of the stochastic background. Even though it probes the right frequency band and has a comparably high signal-to-noise (SNR) ration, detecting such a signal is beyond challenging. In my group, we are currently investigating novel techniques and data extractions methods to approach the problem. Additionally, we analyse the modulation of the background signal by kinetic anisotropies due to the doppler motion of our galaxy [4] (similar to the CMB) to increase the SNR significantly

As mentioned before, the asymptotic structure of our model of space time lets us compute certain conserved currents and fluxes that pass through the boundary that is artificially added to account for very distant observers with respect to any source of radiation. The derivation of these flux laws however has only been made explicitly for General Relativity (GR) and no other theory of gravity. And even in GR the derivations lack of rigour or are using complicated mathematical structures to circumvent certain technical problems (see for instance [1])
Together with a Postdoc at ETH Zurich, I am currently working on a generalization of these flux laws derived from a simple identity that is based on the variation of the action on a manifold with a boundary. Here, it is important to consider the so called "corner terms" [2,3] that appear when a hypersurface orthogonal cannot be defined smoothly on the full manifold. We analyze these corner terms in order to get a complete description of the flux laws for every theory, also beyond GR.

Gravitational waveforms for compact binary coalescences (CBCs) are invaluable for detections by space- and ground-based gravitational wave interferometers. They are obtained by a combination of semi-analytical models and numerical simulations [1-4]. So far systematic errors arising from these procedures appear to be less than statistical ones. However, the significantly enhanced sensitivity of the new detectors that will become operational in the near future will require waveforms to be much more accurate. This task would be facilitated if one has a variety of cross-checks to evaluate accuracy, particularly in the regions of parameter space where numerical simulations are sparse.
Although there have been some suggestions of accuracy check (for instance [5]), there are still a lot of systematics to understand and to quantify. With the overall goal of identifying and eliminating the shortcomings of current waveform models, me and my colleagues are currently working on a multi-variable check of different waveform models. These check are of analytical as well as numerical nature and should provide a guideline for future waveform generations.

A century ago, Einstein formulated his elegant and elaborate theory of General Relativity (GR), which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious challenges of modern cosmology and of particle physics have motivated the exploration of further generalised theories of spacetime (see [1] for an extensive review). Naturally, these theories are tightly constraint by current observational data, however, around black holes, i.e. in the strong field limit, there is still room for new physics.
Because these strong gravity regimes are so interesting and not yet so much constrained, it is especially intriguing to study heavy objects such as black holes (or more general [2]) or neutron stars, or even more exotic objects such as fuzzballs [3,4], in modified theories of gravity. Currently, I am involved in a project concerning the modification of neutron star solutions by slight deviations of GR in $f(\mathbb{Q})$ gravity. This could be especially interesting as the modifications may influence the formation and hence the general statistics of observable neutron stars. Hence, deviations of GR with such implications could potentially be detected by simple telescopes.
On the other hand, it might as well be that quantum gravity effects dilute the horizon of a black hole (or whatever one would call such objects), leading to novel effects in gravitational waveform. An example for such would be the black hole echo effect [5]. In particular in the regimes of quantum gravity there is still a lot of room for theoretical work regarding the specifics of signals that might reach us from e.g. the string-theory analogy to a black hole, i.e. a fuzzball. I am excitingly following the literature in this domain up to date.

Although it is the last point on this page, for me it is one of the most puzzling but most exciting topic: the infrared triangle [1-4]. In a nutshell, the infrared triangle describes a conjectured connection between celestial amplitudes, the gravitational memory effect and the asymptotic symmetry group of the background manifold. Although there is an intuitive relation between celestial holography and the asymptotic symmetry if one is familiar with the concepts of AdS/CFT, the infrared triangle itself is only poorly understood.
With a background in gravitational wave physics, I am especially interested in the implications of celestial amplitudes [5] for the gravitational wave memory and asymptotic symmetries. In literature, celestial amplitudes are trending and new mathematical techniques are developed calculate and relate them to the symmetry structure. In the future, I plan to join the investigation from a cosmologist point of view and try to utilize insights gained form the infrared triangle for gravitational wave observations.