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Stellar-mass black holes (3 M⊙≲MBH≲150 M⊙) are the natural product of the evolution of heavy stars (Mstar≳20 M⊙). In our Galaxy, we expect that 108–109 stellar-mass black holes have been formed from the gravitational collapse of heavy stars, but currently we know fewer than 100 objects. We also know of ∼100 stellar-mass black holes in other galaxies, most of them discovered by gravitational wave observatories in the past 10 years. The detection of black holes is indeed extremely challenging and possible only in very special cases. This article is a short review on the physics and astrophysics of stellar-mass black holes, including Galactic and extragalactic black holes in X-ray binaries, black holes in astrometric binaries, isolated black holes, and black holes in compact binaries. The article also addresses some important open issues and introduces the idea of a possible interstellar mission to the closest black hole.

Wormholes are hypothetical topologically-non-trivial structures of spacetime. From the theoretical point of view, the possibility of their existence is challenging but cannot be ruled out. This article is a compact and non-exhaustive review of past and current efforts to search for astrophysical wormholes in the Universe.

This is a tutorial on the strong gravity effects (motion of massive and massless particles in a curved spacetime, evaluation of redshift factors, estimate of physical quantities in different reference frames, etc.) necessary to calculate the electromagnetic spectra of geometrically thin and optically thick accretion disks around black holes. The presentation is intentionally pedagogical, and most calculations are reported step by step. In the disk–corona model, the spectrum of a source has three components: a thermal component from the disk, a Comptonized component from the corona, and a reflection component from the disk. This tutorial reviews only the strong gravity effects, which can be decoupled from the physical processes involving the interaction between matter and radiation. The formulas presented here are valid for stationary, axisymmetric, asymptotically flat, circular spacetimes, so they can be potentially used for a large class of black hole solutions.

Relativistic reflection features are commonly observed in the X-ray spectra of accreting black holes. In the presence of high quality data and with the correct astrophysical model, X-ray reflection spectroscopy can be quite a powerful tool to probe the strong gravity region, study the morphology of the accreting matter, measure black hole spins, and possibly test Einstein’s theory of general relativity in the strong field regime. In the last decade, there has been significant progress in the development of the analysis of these features, thanks to more sophisticated astrophysical models and new observational facilities. Here we review the state-of-the-art in relativistic reflection modeling, listing assumptions and simplifications that may affect, at some level, the final measurements and may be investigated better in the future. We review black hole spin measurements and the most recent efforts to use X-ray reflection spectroscopy for testing fundamental physics.

We consider electromagnetic fields and charged particle dynamics around non-singular black holes in conformal gravity immersed in an external, asymptotically uniform magnetic field. First, we obtain analytic solutions of the electromagnetic field equation around rotating non-singular black holes in conformal gravity. We show that the radial components of the electric and magnetic fields increase with the increase of the parameters L and N of the black hole solution. Second, we study the dynamics of charged particles. We show that the increase of the values of the parameters L and N and of magnetic field causes a decrease in the radius of the innermost stable circular orbits (ISCO) and the magnetic coupling parameter can mimic the effect of conformal gravity giving the same ISCO radius up to ω B ≤ 0.07 when N = 3 .

We study the motion of test particles and photons in the vicinity of the (2+1)-dimensional Gauss–Bonnet (GB) BTZ black hole. We find that the presence of the coupling constant serves as an attractive gravitational charge, shifting the innermost stable circular orbits outward with respect to the one for this theory in four dimensions. Further, we consider the gravitational lensing, to test the GB gravity in (2+1) dimensions and show that the presence of the GB parameter causes the bending angle to first increase with the increase in the inverse of the closest approach distance, u0, reaching a peak value for a specific u0∗, and then decreasing to zero. We also show that the increase in the value of the GB parameter decreases the bending angle, and the increase in the absolute value of the negative cosmological constant produces an opposite effect on this angle.

We present a dynamical toy model for an expanding universe inside a black hole. The model is built by matching a spherically symmetric collapsing matter cloud to an expanding Friedmann–Robertson–Walker universe through a phase transition that occurs in the quantum-gravity dominated region, here modeled with semi-classical corrections at high density. The matching is performed on a space-like hyper-surface identified by the co-moving time at which quantum–gravity induced effects halt collapse. The purpose of the model is to suggest a possible reconciliation between the observation that black holes are well described by the classical solutions and the fact that the theoretical resolution of space–time singularities leads to a bounce for the collapsing matter.

We consider a class of space-times given by a stationary extension of the Zipoy–Voorhees metric that was found by Halilsoy. We show that the solutions do not describe rotating sources but must be interpreted, similarly to the NUT case, as deformed sources endowed with a gravitomagnetic charge. We show that the Halilsoy family is directly linked to the NUT space-time, which can be obtained in the limit of vanishing deformations. We investigate the motion of test particles and photons in this class of space-times, in particular the innermost stable circular orbits and photon capture radius. Finally we show that this class of solutions possesses a sub-manifold where closed time-like curves are allowed.

The gravitational field around an astrophysical black hole (BH) is thought to be described by the Kerr spacetime, which is a solution of the Einstein equation. Signatures of binary black hole (BBH) coalescence in gravitational waves (GW) follow the Kerr spacetime as the theoretical foundation. Hence, any possible deviations from the Kerr spacetime around BHs serve as a test of the nature of gravity in the strong-field regime and of the predictions of General Relativity. In our study, we perform a theory-agnostic test of the Kerr hypothesis using BBH inspirals from the third Gravitational-wave Transient Catalog (GWTC-3). Considering the Johannsen metric, we compute the leading-order deviation to the emitted GW in the frequency domain. Our results provide constraints on two deformation parameters ( α 13 and ϵ 3 ) and demonstrate the degeneracy between these two non-Kerr parameters.

The study of black hole shadows provides a powerful tool for testing the predictions of general relativity and exploring deviations from the standard Kerr metric in the strong gravitational field regime. Here, we investigate the shadow properties of axisymmetric gravitational compact objects using a coordinate-independent formalism. We analyze black hole shadows in various spacetime geometries, including the Kerr, Taub-NUT, γ , and Kaluza-Klein metrics, to identify distinctive features that can be used to constrain black hole parameters. To achieve a more robust characterization, we employ both Legendre and Fourier expansions, demonstrating that the Fourier approach may offer better coordinate independence and facilitate cross-model comparisons. Finally, we develop a machine learning framework based on neural networks trained on synthetic shadow data, enabling precise parameter estimation from observational results. Using data from observational astronomical facilities such as the Event Horizon Telescope (EHT), Keck, and the Very Large Telescope Interferometer (VLTI), we provide constraints on black hole parameters derived from shadow observations. Our findings highlight the potential of coordinate-independent techniques and machine learning for advancing black hole astrophysics and testing fundamental physics beyond general relativity.