A new breakthrough in gravitational wave physics is behind the corner: with design sensitivities interferometers and next generation detectors, previously unreached areas of the Universe will be explored with unmatched precision in the next years. An equally important step forward is expected from the theoretical side, as new opportunities to test Einstein's theory of gravity will be available.
The late-time signal, called ringdown, emitted by the coalescence of two compact objects carries all the fundamental features of the ultimate description of gravity, so far partially concealed due to experimental limitations in the signal-to-noise ratio. In the ringdown phase, the remnant of the binary system is a highly perturbed black hole that relaxes to equilibrium through peculiar oscillations, called quasinormal modes (QNMs). If these modes are found to be dependent on other parameters besides the mass and the spin of the black hole, it will be a clear sign of General Relativity (GR) breaking down. With the imminent technological advancement, it will be possible to verify this possibility and assess the nature of GR deviations comparing ringdown observations with theoretical predictions in modified theories of gravity.
As the ringdown signal is observed with more and more accuracy, is of utmost importance to find the QNMs emitted by black holes in alternative theories of gravity. With this project I plan to lead the way towards this goal, considering a specific theory as a case study: Einstein-dilaton Gauss-Bonnet (EdGB), which is arguably the simplest theory modifying GR in the large curvature regime. I will develop a method to compute the QNMs of slowly rotating EdGB Black Holes and I will show how to use these results as direct tests of GR with current and future observations. Finally, I will generalize this framework to easily adapt it to other theories, in order to provide a first catalogue of quasinormal mode spectra in modified theories of gravity.
Although the most stringent constraints on deviations from General Relativity (GR) come from the inspiral part of the gravitational wave (GW) signal, the ringdown physics era is behind the corner, as detectors with increasing sensitivity, different frequency windows and a wide range of targets will allow us to have almost daily GW observations with unprecedentedly high signal-to-noise ratio. This incredible experimental effort must be accompanied by an equally challenging progress on the theory side of gravitational wave physics.
In order to get closer to the complete understanding of gravity and the universe, we need to understand how Einstein's theory can be overcome and improved, since we know it is not the ultimate description of gravity for all scales and energies. Studying the ringdown observables, such as the quasinormal modes (QNMs), could provide "smoking guns" for new physics.
Until now, only theory-agnostic test of GR are performed on the currently available data, since theoretical knowledge of QNM spectrums of modified gravity theories is missing. Therefore, is of utmost importance to provide the community with theoretical predictions of the QNM spectrum for rotating black holes (BHs) in modified theories of gravity. So far, there has not been many attempts in this direction, due to the difficulty of the task: one must first analyze stationary BH solutions in the specific theory, then linearize the extremely involved perturbed field equations around the background given by those solutions.
Although laborious, with a deep knowledge of BH perturbation theory and familiarity with differential equation manipulation and integration, this is far from impossible.
By studying the QNMs of slowly rotating BHs in Eintein-dilaton Gauss-Bonnet gravity, taken as a case study, I will contribute to give a first reliable estimate of the characteristic oscillation modes of non-GR BHs. Given the generality of the approach, many other theories that consists of dynamical modifications to GR can be studied in this way, with the ultimate goal of having a rich collection of QNM spectra for alternative theories of gravity.
Following the steps of this proposal, the following milestones will be reached:
I) QNM spectrum of slowly rotating Einstein-dilaton Gauss-Bonnet Black Holes
II) Direct tests of GR with current available ringdown data and statistical infrastructure to perform model selection analysis using QNMs in modified gravity theories
III) An adaptable framework to compute the QNM spectrum in other theories of gravity.
At the end of this project, new and long awaited predictions for the QNM spectrum of rotating BHs in different alternative theories of gravity will be available to the scientific community and new constraints on modifications of Einstein's theory in the strong-field regime will finally be achieved.