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In linear perturbation theory, a static perturber in the vicinity of a Schwarzschild black hole (BH) enhances [suppresses] the Gauss-Bonnet (GB) curvature invariant, $\mathcal{R}_{\rm GB}$, in the high [low] tide regions. By analysing exact solutions of the vacuum Einstein field equations describing one or two BHs immersed in a multipolar gravitational field, which is locally free of pathologies, including conical singularities, we study the corresponding non-linear tides on a fiducial BH, in full General Relativity (GR). We show that the tidal field due to a far away, or close by, static BH creates high/low tides that can deviate not only quantitatively but also qualitatively from the weak field/Newtonian pattern. Remarkably, the suppression in low tide regions never makes $\mathcal{R}_{\rm GB}$ negative on the BH, even though the horizon Gaussian curvature may become negative; but $\mathcal{R}_{\rm GB}$ can vanish in a measure zero set, a feature qualitatively recovered in a Newtonian analogue model. Thus, purely gravitational, static, tidal interactions in GR, no matter how strong, cannot induce GB$^-$ scalarization. We also show that a close by BH produces noticeable asymmetric tides on another (fiducial) BH., Comment: 13 pages, 13 figures

The most accurate model to describe the gravitational interaction is the well-known theory of General Relativity. Several observational evidences corroborate the legitimacy of the theory compared to the older Newtonian gravity. General Relativity furthermore predicts the existence of gravitational waves, i.e. spacetime ripples produced by accelerated masses. Thanks to a connected network of interferometers called LIGO/Virgo, gravitational waves from the coalescence of massive and compact astrophysical bodies have been measured directly. These recent observations paved the way to a completely new route to test the gravitational interaction. The possibility of using gravitational waves to obtain a deeper understanding of open problems within General Relativity motivates the work developed in this thesis. Each part is essentially devoted to challenging the current model of gravitation, sometimes including yet undiscovered new matter fields, and other times modifying the theoretical framework of General Relativity. In the first part of this manuscript, I discuss the astrophysical consequences of the presence of scalar fields permeating galaxies. A detailed picture of the interaction of massive black holes and scalar dark matter structures is provided. The second part is dedicated to the analysis of the generation and propagation of gravitational waves. As an example, I examine the close limit approximation as a promising tool to investigate the collision of extreme compact objects. The last part of this thesis instead focuses on unstable mechanisms around black holes and stars (scalarization and vectorization), in two alternative models of gravitation., 224 pages, PhD Thesis

The close limit approximation of binary black hole is a powerful method to study gravitational-wave emission from highly non-linear geometries. In this work, we use it as a tool to model black hole spacetimes in theories of gravity with a new fundamental scalar degree of freedom. As an example, we consider Einstein-scalar-Gauss-Bonnet gravity, which admits as solution the Schwarzschild geometry as well as black holes with scalar hair. Accordingly, we find scalar perturbations growing unbounded around binary systems. This "dynamical scalarization" process is easier to trigger (i.e. occurs at lower values of the coupling constant of the theory) than the corresponding process for isolated black holes. Our results and framework highlight the fundamental role of the interaction during the collision of compact objects. They also emphasize the importance of having waveforms for black hole binaries in alternative theories, in order to consistently perform tests beyond General Relativity., 8 pages, 2 figures. Comments are welcome

© 2019 IOP Publishing Ltd. The grand challenges of contemporary fundamental physics-dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem-all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on 'Black holes, Gravitational waves and Fundamental Physics'.

The grand challenges of contemporary fundamental physics dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions.The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature.The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress., European Union (EU); European Cooperation in Science and Technology (COST); Polish National Science Center (NCN); Carl Tryggers Foundation; Science & Technology Facilities Council (STFC); European Union's H2020 ERC Consolidator Grant 'Matter and strong-field gravity: New frontiers in Einstein's theory'; European Research Council (ERC); Horizon 2020; Science & Technology Facilities Council (STFC; Ministry of Education and Science of the Republic of Serbia; Foundation for Polish Science; Austrian Science Fund (FWF); Polish National Center of Science (NCN); European Research Council (ERC); Hungarian National Research, Development, and Innovation Office; Swiss National Science Foundation (SNSF); European Union's H2020 ERC; H2020-MSCA-RISE-2015 Grant; National Science Foundation (NSF); PRACE; Simons Foundation; Ministry of Economy, Industry and Competitiveness of Spain; Slovenian Research Agency - Slovenia; EU H2020 under ERC; Spanish MINECO; Generalitat Valenciana; NASA by the Chandra X-ray Center; National Aeronautics & Space Administration (NASA); Scientific and Technological Research Council of Turkey (TÜBİTAK); H2020-MSCA-RISE-2017 Grant; Scientific and Technological Research Council of Turkey (TÜBİTAK); National Science Centre of Poland - European Union; Deutscher Akademischer Austausch Dienst (DAAD); GWAVES of ARIS-GRNET(Athens); Royal Society of London; Research Grant; Scientific and Technological Research Council of Turkey (TÜBİTAK)