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Asymptotically flat spacetimes have been studied in five separate regions: future/past timelike infinity$i^{\pm }$, future/past null infinity, and spatial infinityi⁰. We formulate assumptions and definitions such that the five infinities share a single Bondi–Metzner–Sachs (BMS) group of asymptotic symmetries and associated charges. We show how individual ingoing/outgoing massive bodies may be ascribed initial/final BMS charges and derive global conservation laws stating that the change in total charge is balanced by the corresponding radiative flux. This framework provides a foundation for the study of asymptotically flat spacetimes containing ingoing and outgoing massive bodies, i.e. for generalized gravitational scattering. Among the new implications are rigorous definitions for quantities like initial/final spin, scattering angle, and impact parameter in multi-body spacetimes, without the use of any preferred background structure.

 

The 2017 Event Horizon Telescope (EHT) observations of M87* detected a ring-shaped feature ∼40 μas in diameter, consistent with the event horizon scale of a black hole of the expected mass. The thickness of this ring, however, proved difficult to measure, despite being an important parameter for constraining the observational appearance. In the first paper of this series, we asked whether the width of the ring was sensitive to the choice of likelihood function used to compare observed closure phases and closure amplitudes to model predictions. In this paper, we investigate whether the ring width is robust to changes in the model itself. We construct a more realistic geometric model with two new features: an adjustable radial falloff in brightness, and a secondary ‘photon ring’ component in addition to the primary annulus. This thin, secondary ring is predicted by gravitational lensing for any black hole with an optically thin accretion flow. Analysing the data using the new model, we find that the primary annulus remains narrow (fractional width ≤ 0.25) even with the added model freedom. This provides further evidence in favour of a narrow ring for the true sky appearance of M87*, a surprising feature that, if confirmed, would demand theoretical explanation. Comparing the Bayesian evidence for models with and without a secondary ring, we find no evidence for the presence of a lensed photon ring in the 2017 observations. However, the techniques we introduce may prove useful for future observations with a larger and more sensitive array.

 

Event Horizon Telescope (EHT) observations of the core of the galaxy M87 suggest an observational appearance dominated by a ring of approximately 40 $\mu$as in diameter. The thickness of the ring is less certain: imaging efforts constrained it to be less than half the diameter (consistent with an imaging resolution of 20 $\mu$as), while visibility-domain modelling suggested a variety of fractional widths, including as low as $10{{\ \rm per\ cent}}$ on some days. The fractional width is very interesting as it has the potential to discriminate between different astrophysical scenarios for the source; in fact, the 10–$20{{\ \rm per\ cent}}$ range is so narrow as to be in tension with theoretical expectations. In the first of a series of papers on the width of the observed ring, we reproduce a subset of EHT visibility-domain modelling results and we explore whether alternative data analysis methods might favour thicker rings. We point out that the closure phase (and closure amplitude) likelihood function is not independent of residual station gain amplitudes, even at high signal-to-noise, and explore two approximations of practical interest: one standard in the field (and employed by the EHT collaboration), and a new one that we propose. Analysing the public data, we find that the new likelihood approximation prefers somewhat thicker rings, more in line with theoretical expectations. Further analysis is needed, however, to determine which approximation is better for the EHT data.

 

Context. High-frequency very-long-baseline interferometry (VLBI) observations can now resolve the event-horizon-scale emission from sources in the immediate vicinity of nearby supermassive black holes. Future space-VLBI observations will access highly lensed features of black hole images – photon rings – that will provide particularly sharp probes of strong-field gravity. Aims. Focusing on the particular case of the supermassive black hole M 87*, our goal is to explore a wide variety of accretion flows onto a Kerr black hole and to understand their corresponding images and visibilities. We are particularly interested in the visibility on baselines to space, which encodes the photon ring shape and whose measurement could provide a stringent test of the Kerr hypothesis. Methods. We developed a fully analytical model of stationary, axisymmetric accretion flows with a variable disk thickness and a matter four-velocity that can smoothly interpolate between purely azimuthal rotation and purely radial infall. To determine the observational appearance of such flows, we numerically integrated the general-relativistic radiative transfer equation in the Kerr spacetime, taking care to include the effects of thermal synchrotron emission and absorption. We then Fourier transformed the resulting images and analyzed their visibility amplitudes along the directions parallel and orthogonal to the black hole spin projected on the observer sky. Results. Our images generically display a wedding cake structure composed of discrete, narrow photon rings ( n  = 1, 2, …) stacked on top of broader primary emission that surrounds a central brightness depression of model-dependent size. At 230 GHz, the n  = 1 ring is always visible, but the n  = 2 ring is sometimes suppressed due to absorption. At 345 GHz, the medium is optically thinner and the n  = 2 ring displays clear signatures in both the image and visibility domains. We also examine the thermal synchrotron emissivity in the equatorial plane and show that it exhibits an exponential dependence on the radius for the preferred M 87* parameters. Conclusions. The black hole shadow is a model-dependent phenomenon – even for diffuse, optically thin sources – and should not be regarded as a generic prediction of general relativity. Observations at 345 GHz are promising for future space-VLBI measurements of the photon ring shape, since at this frequency the signal of the n  = 2 ring persists despite the disk thickness and nonzero absorption featured in our models. Future work is needed to investigate whether this conclusion holds in a larger variety of reasonable models. 

Abstract We revisit the old problem of the self-force on a particle moving in a weak-field spacetime in the context of renewed interest in two-body gravitational scattering. We analytically calculate the scalar, electromagnetic, and gravitational self-force on a particle moving on a straight-line trajectory at a large distance from a Newtonian star, and use these results to find the associated correction to its motion. In the gravitational case we must also include the matter-mediated force, which acts at the same perturbative order as the gravitational self-force. We further augment the gravitational results with geodesic calculations at second order in the central body mass to determine the full, explicit solution to the two-body gravitational scattering problem at second post-Minkowskian order (2PM). We calculate the momentum transfer (which reproduces Westpfahl’s old result), the change in mechanical angular momentum (which matches the radiative flux recently computed by Damour), and the change in mechanical mass moment (the time-space components of the angular momentum tensor), which has not previously appeared. Besides the new 2PM results of explicit trajectories and all conserved quantities, this work clarifies the role of gravitational self-force in PM scattering theory and provides a foundation for higher-order calculations.