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’.

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A deep survey of the Large Magellanic Cloud at ∼ 0.1−100 TeV photon energies with the Cherenkov Telescope Array is planned. We assess the detection prospects based on a model for the emission of the galaxy, comprising the four known TeV emitters, mock populations of sources, and interstellar emission on galactic scales. We also assess the detectability of 30 Doradus and SN 1987A, and the constraints that can be derived on the nature of dark matter. The survey will allow for fine spectral studies of N 157B, N 132D, LMC P3, and 30 Doradus C, and half a dozen other sources should be revealed, mainly pulsar-powered objects. The remnant from SN 1987A could be detected if it produces cosmic-ray nuclei with a flat power-law spectrum at high energies, or with a steeper index 2.3 − 2.4 pending a flux increase by a factor > 3 − 4 over ∼ 2015 − 2035. Large-scale interstellar emission remains mostly out of reach of the survey if its > 10 GeV spectrum has a soft photon index ∼ 2.7, but degree-scale 0.1 − 10 TeV pion-decay emission could be detected if the cosmic-ray spectrum hardens above >100 GeV. The 30 Doradus star-forming region is detectable if acceleration efficiency is on the order of 1 − 10% of the mechanical luminosity and diffusion is suppressed by two orders of magnitude within < 100 pc. Finally, the survey could probe the canonical velocity-averaged cross section for self-annihilation of weakly interacting massive particles for cuspy Navarro-Frenk-White profiles.

A new measurement of a spatially extended gamma-ray signal from the center of the Andromeda galaxy (M31) has been recently published by the Fermi-LAT collaboration, reporting that the emission broadly resembles the so-called Galactic center excess (GCE) of the Milky Way (MW). Steadily, the weight of the evidence is accumulating on a millisecond pulsar (MSPs) origin for the GCE. These elements prompt us to compare the mentioned observations with what is, perhaps, the simplest model for an MSP population, solely obtained by rescaling of the MSP luminosity function determined in the local MW disk via the respective stellar mass of the systems. Remarkably, we find that without free fitting parameters, this model can account for both the energetics and the morphology of the GCE within uncertainties. For M31, the estimated luminosity due to primordial MSPs is expected to contribute only about a quarter of the detected emission, although a stronger contribution cannot be excluded given the large uncertainties. If correct, the model predicts that the M31 disk emission due to MSPs is not far below the present upper bound. We also discuss additional refinements of this simple model. Using the correlation between globular cluster gamma-ray luminosity and stellar encounter rate, we gauge the dynamical MSP formation in the bulge. This component is expected to contribute to the GCE only at a level 5%, but it could affect the signal's morphology. We also comment on limitations of our model as well as on future perspectives for improved diagnostics.

The Andromeda (M31) and Triangulum (M33) galaxies are the closest Local Group galaxies to the Milky Way, being only 785 and 870 kpc away. These two galaxies provide an independent view of high-energy processes that are often obscured in our own Galaxy, including possible signals of dark matter (DM) particle interactions. The Fermi Large Area Telescope (Fermi-LAT) preliminary eight year list of sources includes both M31, which is detected as extended with a size of about 0.4 • , and M33, which is detected as a point-like source. The spatial morphology of M31 γ-ray emission could trace a population of unresolved sources and energetic particles originating in sources not related to massive star formation. Alternatively, the γ-ray emission could also be an indication of annihilation or decay of DM particles. We investigate these two possibilities using almost 10 years of data from the Fermi LAT. An interpretation that involves only a DM γ-ray emission is in tension with the current limits from other searches, such as those targeting Milky Way dwarf spheroidal galaxies. When we include a template of astrophysical emission, tuned on γ-ray data or from observations of these galaxies in other wavelengths, we do not find any significant evidence for a DM contribution and we set limits for the annihilation cross section that probe the thermal cross section for DM masses up to a few tens of GeV in the bb and τ + τ − channels. For models where the DM substructures have masses above 10 −6 solar masses our limits probe the DM interpretation of the Fermi LAT Galactic center excess. We provide also the lower limit for the DM decay time assuming the same spatial models of the DM distribution in M31 and M33.