Our understanding of space and time is probed to its depths by black holes. These objects, which appear as a natural consequence of general relativity, provide a powerful analytical tool able to examine macroscopic and microscopic properties of the universe. This introductory article presents in a pictorial way the basic concepts of black hole's theory, as well as a description of the astronomical sites where black holes are suspected to lie, namely binary X-ray sources and galactic nuclei.

Aspects of primordial black holes, i.e. black holes formed in the early Universe, are reviewed. Special emphasis is put on their formation, their role as dark matter candidates and their manifold signatures, particularly through gravitational waves.

The past 10 years have witnessed a change of perspective in the way astrophysicists think about massive black holes (MBHs), which are now considered to have a major role in the evolution of galaxies. This appreciation was driven by the realization that black holes of millions solar masses and above reside in the center of most galaxies, including the Milky Way. MBHs also powered active galactic nuclei known to exist just a few hundred million years after the Big Bang. Here, I summarize the current ideas on the evolution of MBHs through cosmic history, from their formation about 13 billion years ago to their growth within their host galaxies.

The detection of gravitational waves (GWs) from binary black hole (BBH) coalescences by the LIGO-Virgo-KAGRA (LVK) Collaboration has raised fundamental questions about the genesis of these events. In this chapter, we explore the possibility that PBHs, proposed candidates for dark matter, may serve as the progenitors of the BBHs observed by LVK. Employing a Bayesian analysis, we constrain the PBH model using the LVK third GW Transient Catalog (GWTC-3), revealing that stellar-mass PBHs cannot dominate cold dark matter. Considering a mixed population of astrophysical black holes (ABHs) and PBHs, we determine that approximately $1/4$ of the detectable events in the GWTC-3 can be attributed to PBH binaries. We also forecast detectable event rate distributions for PBH and ABH binaries by the third-generation ground-based GW detectors, such as the Einstein Telescope, offering a potential avenue to distinguish PBHs from ABHs based on their distinct redshift evolutions.

This paper reviews the role of black holes in the context of fundamental physics. After recalling some basic results stemming from Planckian string calculations, I present three examples of how stringy effects can improve the curvature singularity of classical black hole geometries.

Modified Newtonian potentials have been proposed for the description of relativistic effects acting on particles and fluids in permanent orbital motion around black holes. Here we further discuss spherically symmetric potentials like the one proposed by Artemova, Bjornson & Novikov (1996, Astrophysical Journal, 461, 565), and we illustrate their virtues by studying the acceleration along circular trajectories. We compare the results with exact expressions in the spacetime of a rotating (Kerr) black hole.

I review the evolution of binary supermassive black holes and focus on the stellar-dynamical mechanisms that may help to overcome the final-parsec problem - the possible stalling of the binary at a separation much larger than is required for an efficient gravitational wave emission. Recent N-body simulations have suggested that a departure from spherical symmetry in the nucleus of the galaxy may keep the rate of interaction of stars with the binary at a high enough level so that the binary continues to shrink rather rapidly. However, a major problem of all these simulations is that they do not probe the regime where collisionless effects are dominant - in other words, the number of particles in the simulation is still not sufficient to reach the asymptotic behaviour of the system. I present a novel Monte Carlo method for simulating both collisional and collisionless evolution of non-spherical stellar systems, and apply it for the problem of binary supermassive black hole evolution. I show that in triaxial galaxies the final-parsec problem is largely non-existent, while in the axisymmetric case it seems to still exist in the limit of purely collisionless regime relevant for real galaxies, but disappears in the N-body simulations where the feasible values of N are still too low to get rid of collisional effects.

Models predicting the existence of extra spatial dimensions offer compelling and novel solutions to outstanding problems of the Standard Model. In such models, our universe exists on a 4 dimensional brane embedded in a larger dimensional space time. By allowing gravity to propagate in the bulk the gravitational coupling could be comparable with the other gauge interactions thus removing the hierarchy problem. The phenomenology of these models could have dramatic observable effects at the LHC includingthe production and decay of gravitons and mini black holes. In this note we summarize feasibility studies for the discovery of strong gravitational interactions at the LHC.

This thesis is entirely devoted to black hole physics as a natural arena to study quantum gravity related questions. The five main Chapters present the results already published in arXiv:1512.04566 [gr-qc], arXiv:1604.07222 [gr-qc], arXiv:1707.00479 [gr-qc], arXiv:1807.02041 [gr-qc], arXiv:1811.03667 [gr-qc]. A main introductory Section, together with the Sections introducing each of the two parts of the manuscript compose the \emph{fil rouge} of the thesis, and are not published elsewhere. They contain reviews (together with my personal view) on the information paradox (Part 1) and the thermodynamics of spacetime (Part 2).

Radio-interferometry (RI) observes the sky at unprecedented angular resolutions, enabling the study of several far-away galactic objects such as galaxies and black holes. In RI, an array of antennas probes cosmic signals coming from the observed region of the sky. The covariance matrix of the vector gathering all these antenna measurements offers, by leveraging the Van Cittert-Zernike theorem, an incomplete and noisy Fourier sensing of the image of interest. The number of noisy Fourier measurements -- or visibilities -- scales as $\mathcal O(Q^2B)$ for $Q$ antennas and $B$ short-time integration (STI) intervals. We address the challenges posed by this vast volume of data, which is anticipated to increase significantly with the advent of large antenna arrays, by proposing a compressive sensing technique applied directly at the level of the antenna measurements. First, this paper shows that beamforming -- a common technique of dephasing antenna signals -- usually used to focus some region of the sky, is equivalent to sensing a rank-one projection (ROP) of the signal covariance matrix. We build upon our recent work arXiv:2306.12698v3 [eess.IV] to propose a compressive sensing scheme relying on random beamforming, trading the $Q^2$-dependence of the data size for a smaller number $P$ ROPs. We provide image recovery guarantees for sparse image reconstruction. Secondly, the data size is made independent of $B$ by applying $M$ Bernoulli modulations of the ROP vectors obtained for the STI. The resulting sample complexities, theoretically derived in a simpler case without modulations and numerically obtained in phase transition diagrams, are shown to scale as $\mathcal O(K)$ where $K$ is the image sparsity. This illustrates the potential of the approach.