Multioutput regression of noisy time series using convolutional neural networks with applications to gravitational waves

In this thesis I implement a deep learning algorithm to perform a multioutput regression. The dataset is a collection of one dimensional time series arrays, corresponding to simulated gravitational waveforms emitted by a black hole binary, and labelled by the masses of the two black holes. In addition, white Gaussian noise is added to the arrays, to simulate a signal detection in the presence of noise. A convolutional neural network is trained to infer the output labels in the presence of noise, and the resulting model generalizes over many order of magnitudes in the noise level. From the results I argue that the hidden layers of the model succesfully denoise the signals before the inference step. The entire code is implemeted in the form of a Python module, and the neural network is written in PyTorch. The training of the network is speeded up using a single GPU, and I report about efforts to improve the scaling of the training time with respect to the size of the training sample

Black holes beyond general relativity: theoretical and phenomenological developments.

In four dimensions, general relativity is the only viable theory of gravity satisfying the requirements of diffeoinvariance and strong equivalence principle. Despite this aesthetic appeal, there are theoretical and experimental reasons to extend gravity beyond GR. The most promising tests and bounds are expected to come from strong gravity observations. The past few years have seen the rise of gravitational wave astronomy, which has paved the way for strong gravity observations. Future GW observations from the mergers of compact objects will be able to constrain much better possible deviations from GR. Therefore, an extensive study of compact objects in modified theories of gravitation goes in parallel with these experimental efforts. In this PhD Thesis we concentrate on black holes. Black holes act as testbeds for modifications of gravity in several ways. While in GR they are extremely simple objects, in modified theories their properties can be more complex, and in particular they can have hair. The presence of hair changes the geometry felt by test fields and it modifies the generation of GW signals. Moreover, black holes are the systems in which the presence of singularities is predicted by classical gravity with the highest level of confidence: this is not only true in GR, but also in most of the modified gravity theories formulated in classical terms as effective field theories. Singularities are regarded as classical artifacts to be cured by quantum gravity effects. Therefore, considering mechanisms of singularity resolutions is a theoretical arena to study the form of these effects. The Thesis presents theoretical contributions to all these aspects of black hole physics. The work is organized following three main topics: black holes with universal horizons, hairy black holes in Einstein-Maxwell-dilaton theory and regular black holes. These models originate from various motivations: black holes with universal horizons are found in modified gravity theories which break local Lorentz symmetry; Einstein-Maxwell-dilaton black holes originate in string theory and in lower dimensional compactifications, but they also serve as proxies for black holes in theories propagating additional degrees of freedom; regular black holes are motivated by the efforts to understand how quantum gravity solves the classical singularities. In each of the above cases, we present results which appear to be relevant for the follow up research in their respective fields. We also emphasize that, besides the contextual significance of our results, we also developed thechniques for addressing the respective problems, which can be useful well beyond the specific cases considered in this Thesis

Scalar charge of black holes in Einstein-Maxwell-dilaton theory

We show that the monopole scalar charge of black holes in Einstein--Maxwell--dilaton theory is proportional to the electric potential at the event horizon, with a proportionality factor given by (minus) the scalar coupling constant. We also show that the scalar charge, in the weak electric charge limit, does not depend on the black hole spin. This result can be very useful to circumvent spin degeneracy issues when testing the theory against gravitational waves observations.Comment: v2: 6 pages, corrected typos, references adde

Quasinormal modes of weakly charged Einstein-Maxwell-dilaton black holes

Einstein-Maxwell-dilaton theory is an interesting and well-motivated theoretical laboratory to explore the impact of new fundamental degrees of freedom in the context of testing the no-hair conjecture, due to the existence of hairy black hole solutions together with the propagation of scalar, vector and tensor modes. In this paper we compute the quasinormal mode spectrum of static and slowly rotating black holes for generic values of the dilaton coupling, within a weak electric charge approximation. Our results suggest that these spacetimes are stable for generic values of the dilaton coupling and the black hole charge. We also show that while gravitational modes are only weakly affected by the coupling with the dilaton, the spectrum of electromagnetic modes exhibits a more pronounced dilaton-dependent breaking of isospectrality between the axial and polar sectors. We further show that the gravitational quasinormal modes are well approximated by the properties of unstable null circular geodesics in those spacetimes, while the treatment of electromagnetic and scalar modes can be simplified by a suitably modified Dudley-Finley scheme for the perturbed equations.Comment: 20 pages, 11 figures; v2: references added; v3: Matches published versio

Orthogonal gauge fixing of first order gravity

We consider the first order connection formulation of 4D general relativity in the "orthogonal" gauge. We show how the partial gauge fixing of the phase space canonical coordinates leads to the appearance of second class constraints in the theory. We employ the gauge unfixing procedure in order to successfully complete the Dirac treatment of the system. While equivalent to the inversion of the Dirac matrix, the gauge unfixing allows us to work directly with the reduced phase space and the ordinary Poisson bracket. At the same time, we explicitly derive the new set of residual first class constraints preserving the partial gauge fixing, which are linear combinations of the original constraints, and these turn out to contain nonlinear terms. While providing an explicit example of how to consistently recast general relativity in a given partial gauge, the main motivation of this classical analysis is the application of the Quantum Reduced Loop Gravity program to a Schwarzschild black hole geometry.Comment: 14 pages; 'radial gauge' replaced with 'orthogonal gauge' to avoid confusion with previous literature, on which we comment on more extensively. Published versio

The cosmic variance of testing general relativity with gravitational-wave catalogs

Combining multiple gravitational-wave observations allows for stringent tests of general relativity, targeting effects that would otherwise be undetectable using single-event analyses. We show that the finite size of the observed catalog induces a significant source of variance. If not appropriately accounted for, general relativity can be excluded with arbitrarily large credibility even if it is the underlying theory of gravity. This effect is generic and entirely analogous to the so-called "cosmic variance" of cosmology: in essence, we only have one catalog that contains all the events. We show that the cosmic variance holds for arbitrarily large catalogs and cannot be suppressed by selecting "golden" observations with large signal-to-noise ratios. We present a mitigation strategy based on bootstrapping (i.e. resampling with repetition) that allows assigning uncertainties to one's credibility on the targeted test. We demonstrate our findings using both toy models and real gravitational-wave data. In particular, we quantify the impact of the cosmic variance on the ringdown properties of black holes using the latest LIGO/Virgo catalog.Comment: 6 pages, 2 figure

Bayesian parameter estimation on boson-star binary signals with a coherent inspiral template and spin-dependent quadrupolar corrections

Compact boson star binaries are hypothetical sources for ground-based and space gravitational-wave detectors. Their signal would be a messenger for novel fundamental fields and could shed light on the dark matter. In this work, we further develop our analysis in Phys. Rev. D 102, 083002 (2020), aimed at constraining the properties of these objects with future observations. We use a coherent waveform template for the inspiral stage of boson star binaries with large quartic self interactions, including tidal deformability and the nonlinear dependence of the quadrupole moments on the spin in terms of the fundamental couplings of the scalar field theory. Performing a Bayesian analysis, we investigate the ability of a third-generation gravitational-wave detector such as the Einstein Telescope to distinguish these exotic sources from black holes and infer constraints on the fundamental couplings of the model

Landscape of stellar-mass black-hole spectroscopy with third-generation gravitational-wave detectors

Gravitational-wave black-hole spectroscopy provides a unique opportunity to test the strong-field regime of gravity and the nature of the final object formed in the aftermath of a merger. Here we investigate the prospects for black-hole spectroscopy with third-generation gravitational-wave detectors, in particular the Einstein Telescope in different configurations, possibly in combination with Cosmic Explorer. Using a state-of-the-art population model for stellar-origin binary black holes informed by LIGO-Virgo-KAGRA data, we compute the average number of expected events for precision black-hole spectroscopy using a Fisher-matrix analysis. We find that Einstein Telescope will measure two independent quasinormal modes within ${\cal O}(1)\%$ (resp. ${\cal O}(10)\%$) relative uncertainty for at least ${\cal O}(1)$ (resp. ${\cal O}(500)$) events per year, with similar performances in the case of a single triangular configuration or two L-shaped detectors with same arm length. A 15-km arm-length configuration would improve rates by roughly a factor of two relative to a 10-km arm-length configuration. When operating in synergy with Cosmic Explorer the rates will improve significantly, reaching few-percent accuracy for ${\cal O}(100)$ events per year.Comment: 13 pages, 9 figure

Sensitivity of Neutron Star Observations to Three-nucleon Forces

Astrophysical observations of neutron stars have been widely used to infer the properties of the nuclear matter equation of state. Beside being a source of information on average properties of dense matter, however, the data provided by electromagnetic and gravitational wave (GW) facilities are reaching the accuracy needed to constrain, for the first time, nuclear dynamics in dense matter. In this work we assess the sensitivity of current and future neutron star observations to directly infer the strength of repulsive three-nucleon forces, which are key to determine the stiffness of the equation of state. Using a Bayesian approach we focus on the constraints that can be derived on three-body interactions from binary neutron star mergers observed by second and third-generation of gravitational wave interferometers. We consider both single and multiple observations. For current detectors at design sensitivity the analysis suggests that only low mass systems, with large signal-to-noise ratios (SNR), allow to reliably constrain the three-body forces. However, our results show that a single observation with a third-generation interferometer, such as the Einstein Telescope or Cosmic Explorer, will constrain the strength of the repulsive three-body potential with exquisite accuracy, turning third-generation GW detectors into new laboratories to study the nucleon dynamics.Comment: Minor changes to improve the discussion of the results. Technical details added to extend the equation of state descriptio