On September 14th 2015 the first gravitational wave was detected from a compact binary coalescence [1]. The landmark detection provides the unique opportunity to test gravity in the strong-field regime and possibly look for deviations from Einstein's celebrated theory of gravity [2]. While electromagnetic observations have provided strong evidence of the astrophysical reality of black holes, only gravitational waves can provide a final proof of their existence.
On the theoretical side, several families of exotic compact objects (ECOs) have been conceived in order to overcome some paradoxes associated with black holes [3]. ECOs can mimic the features of black holes by means of electromagnetic observations, however their characteristic frequencies, the so-called quasi-normal modes (QNMs), in gravitational wave signals differ dramatically from those of black holes [4]. Thus, from the measurement of the QNMs of the remnant of a binary merger, we can infer the nature of the compact object.
The first gravitational wave event GW150914 is consistent with a black hole remnant [2]. However recent studies report evidence for signatures of an ECO [5] and a debate about the nature of the remnant is currently underway [6].
The approaches adopted so far in the modelling of the waveform emitted by ECOs are phenomenological and not necessarily related to the physical properties of the remnant. The scope of the proposed project is the derivation of an accurate template bank based on a robust theoretical framework. A correspondence with the physics of the compact object is crucial in order to perform a discrimination between black holes and ECOs in future detections.
[1] Abbott et al., PRL 116, 061102 (2016)
[2] Abbott et al., PRL 116, 221101 (2016)
[3] Giudice et al., JCAP 1610, 001 (2016)
[4] Cardoso et al., PRL 116, 171101 (2016)
[5] Abedi et al., PRD 96, 082004 (2017)
[6] Westerweck et al., PRD 97, 124037 (2018)
After the first detection, GWs are one of the most promising channels for the study of General Relativity in strong field regime. General Relativity can be tested through gravitational waveforms by exploiting the main characteristic features of the signals.
Currently, the most stringent constraints on the deviations of General Relativity come from the analysis of the inspiral phase of a GW signal [2]. During this stage, the phase evolution of the signal can be traced accurately due to the presence of many cycles in the GW. For this reason, it is possible to measure deviations from the phase evolution of the signal predicted by General Relativity. Or alternatively, it is possible to derive modified dispersion relations for a propagating GW by analysing the relative phase mismatch among different frequencies. Usually, this work is based phenomenological models which add a perturbation term to the phase of the GW signal, without assuming any particular alternative model of gravity. The tests have produced scientifically interesting results and put constraints on several alternative theories of gravity.
The aim of this project is to develop a viable way of testing General Relativity through the final stage of a GW signal: the ringdown, from which we can infer, as explained, the nature of the remnant of a merger. Unfortunately, the ringdown phase of a GW signal is typically very short, thus it is not possible to gather the necessary cycles that allow to constrain a general phase mismatch from the data. The only possible method which allows to maximize the recovered signal to noise ratio, and hence the phase measurement of the GW signal, is the matched filtering technique that cross-correlate the data with a GW template. The higher is the cross-correlation between the template and the data, the higher is the phase match between the two. In fact, a slightly non-matching phase will drastically reduce the cross-correlation, whereas a good matching phase enhances the cross-correlation exponentially. Matched filtering techniques are the optimal methods for physical model selection. However, no complete and self-consistent model for GW echoes is currently in literature and this kind of searches are usually reduced to general wavelets or parametric solutions.
This project is devoted to the derivation of a complete and physically-driven description of the GW waveform for alternative objects, allowing for a deeper understating of LIGO and VIRGO data. The goal will be reached by improving the weak points of the models currently used. In particular, this project will be characterized by the following innovative milestones:
i) The project aims at analytical templates, in order to get rid of the necessity of launching numerical simulations. The latter are usually computationally expensive and suffer from numerical singularities which can create divergencies in the computation of the waveforms.
ii) The project will provide a physically driven parametrization of compact objects, which will remove redundant or ambiguous parametrization currently in literature. In fact, the number of parameters plays a fundamental role in Bayesian analysis: the larger is the number of unnecessary parameters, the higher is the penalty analysis factor for model selection. Hence, it is important to model waveform parameters which are connected to the physics of the object, in order to perform a direct physical model selection in case of a detection.
iii) The project will produce fast and general waveforms, which will allow us to study the detectability of these signals with current and future experiments.
iv) The project will establish an open data science center where users can download and compute waveforms. Given the increasing interest in GW astronomy, it is important to give access to gravitational waveform generators. The latter will be user-friendly and ready to use for scientific production.
The milestones previously described are designed to optimize the scientific impact of this work, given the current wide interest in tests of General Relativity through gravitational wave astronomy.