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The Event Horizon Telescope (EHT) Collaboration recently published the first images of the supermassive black holes in the cores of the Messier 87 and Milky Way galaxies. These observations have provided a new means to study supermassive black holes and probe physical processes occurring in the strong-field regime. We review the prospects of future observations and theoretical studies of supermassive black hole systems with the next-generation Event Horizon Telescope (ngEHT), which will greatly enhance the capabilities of the existing EHT array. These enhancements will open up several previously inaccessible avenues of investigation, thereby providing important new insights into the properties of supermassive black holes and their environments. This review describes the current state of knowledge for five key science cases, summarising the unique challenges and opportunities for fundamental physics investigations that the ngEHT will enable., Comment: To be submitted to journal. Comments are welcome

Merging supermassive black hole binaries is expected as a consequence of galaxy mergers, yet the detailed evolution path and underlying merging mechanisms of these binaries are still subject to large theoretical uncertainties. In this work, we propose to combine the (future) gravitational wave measurements of supermassive black hole binary merger events with the galaxy merger rate distributions from galaxy surveys/cosmological simulations, to infer the delay time of binary mergers, as a function of binary mass. The delay time encodes key information about binary evolution, which can be used to test the predictions of various evolution models. With a Mock data set of supermassive black hole binary merger events, we discuss how to infer the distribution of delay time with hierarchical Bayesian inference and test evolution models with the Bayesian model selection method. The astrophysical model uncertainties are also considered in the hierarchical Bayesian inference and Bayesian model selection., Comment: Published in MNRAS

Radiation encephalopathy (REP) is the most common complication for nasopharyngeal carcinoma (NPC) radiotherapy. It is highly desirable to assist clinicians in optimizing the NPC radiotherapy regimen to reduce radiotherapy-induced temporal lobe injury (RTLI) according to the probability of REP onset. To the best of our knowledge, it is the first exploration of predicting radiotherapy-induced REP by jointly exploiting image and non-image data in NPC radiotherapy regimen. We cast REP prediction as a survival analysis task and evaluate the predictive accuracy in terms of the concordance index (CI). We design a deep multimodal survival network (MSN) with two feature extractors to learn discriminative features from multimodal data. One feature extractor imposes feature selection on non-image data, and the other learns visual features from images. Because the priorly balanced CI (BCI) loss function directly maximizing the CI is sensitive to uneven sampling per batch. Hence, we propose a novel weighted CI (WCI) loss function to leverage all REP samples effectively by assigning their different weights with a dual average operation. We further introduce a temperature hyper-parameter for our WCI to sharpen the risk difference of sample pairs to help model convergence. We extensively evaluate our WCI on a private dataset to demonstrate its favourability against its counterparts. The experimental results also show multimodal data of NPC radiotherapy can bring more gains for REP risk prediction., Comment: 11 pages, 3 figures, MICCAI2022

In this work, we study how to infer the orbit of a supermassive black hole binary (SMBHB) by time-dependent measurements with Very Long Baseline Interferometry (VLBI), such as the Event Horizon Telescope (EHT). Assuming a point-like luminosity image model, we show that with multiple years of observations by EHT, it is possible to recover the SMBHB orbital parameters -- eccentricity, (rescaled) semi-major axis, orbital frequency, and orbital angles -- from their time-varying visibilities even if the binaries orbital period is a few times longer than the duration of observation. Together with the future gravitational wave detections of resolved sources of SMBHBs with Pulsar Timing Array, and/or the detections of optical-band light curves, we will be able to further measure the individual mass of the binary, and also determine the Hubble constant if the total mass of the binary is measured through the light curves of the two black holes or by alternative methods., Comment: 15 pages, 8 figures

In this letter we calculate the gravitational waves (GWs) emitted from a small binary (SB) by solving the Teukolsky equation in the background of a massive exotic compact object (ECO) which is phenomenologically described by a Schwarzschild geometry with a reflective boundary condition at its "would-be" horizon. The "continuous echo" waves propagating to infinity due to reflectivity of ECO at its "would-be" horizon provide an exquisite probe to the nature of the ECO's horizon., Comment: 6 pages, 3 figures; Detectability of the continuous echo added

S-stars in the Galactic Center are excellent testbeds of various general relativistic effects. While previous works focus on modeling their orbital motion around Sgr A*--the supermassive black hole in the Galactic Center--here we explore the possibility of using the rotation of S-stars to test the de Sitter precession predicted by general relativity. We show that by reorienting the rotation axes of S-stars, de Sitter precession will change the apparent width of the absorption lines in the stellar spectra. Our numerical simulations suggest that the newly discovered S4714 and S62 are best suited for such a test because of their small pericenter distances relative to Sgr A*. Depending on the initial inclination of the star, the line width would vary by as much as $20-76\,{\rm km\,s^{-1}}$ within a period of $20-40$ years. Such a variation is comparable to the current detection limit. Since the precession rate is sensitive to the orbital eccentricity and stellar quadrupole structure, monitoring the rotation of S-stars could also help us better constrain the orbital elements of the S-stars and their internal structures., Comment: 5 pages, 3 figures. Comments welcome!

The binary black holes (BBHs) formed near the supermassive black holes (SMBHs) in the galactic nuclei would undergo eccentricity excitation due to the gravitational perturbations from the SMBH and therefore merger more efficiently. In this paper, we study the coupling of the three body 1st post-Newtonian (PN) effects with the spin effects from the SMBH in the hierarchical triple system. We extend previous work by including the coupling between the de Sitter precession and the Lense-Thirring precession from the SMBH spin. This coupling includes both the precessions of the inner orbit angular momentum and the Runge-Lenz vector around the outer orbit angular momentum in a general reference frame. We find the change of the (maximal) eccentricity in the neighboring Kozai-Lidov cycles due to spin effects is detectable by LISA in the future. Our general argument on the coupling of the three body 1PN effects in three body systems could be extended to any other situation as long as the outer orbital plane evolves., Comment: 10 pages, 3 figures, accepted by Physical Review D

Ordinary differential equations have been used to model dynamical systems in a broad range. Model checking for parametric ordinary differential equations is a necessary step to check whether the assumed models are plausible. In this paper we introduce three test statistics for their different purposes. We first give a trajectory matching-based test for the whole system. To further identify which component function(s) would be wrongly modelled, we introduce two test statistics that are based on integral matching and gradient matching respectively. We investigate the asymptotic properties of the three test statistics under the null, global and local alternative hypothesis. To achieve these purposes, we also investigate the asymptotic properties of nonlinear least squares estimation and two-step collocation estimation under both the null and alternatives. The results about the estimations are also new in the literature. To examine the performances of the tests, we conduct several numerical simulations. A real data example about immune cell kinetics and trafficking for influenza infection is analyzed for illustration.

Recent theoretical studies suggest that stellar-mass binary black holes (BBHs) would merge more efficiently due to the Kozai-Lidov mechanism if these binaries form in the vicinity of supermassive black holes (SMBHs). Since SMBHs are likely rotating rapidly, we continue our earlier study on the generalization of the Kozai-Lidov formalism to include the spin of the SMBH and study the evolution of a nearby BBH. We find that the eccentricity and orbital inclination of the BBH is significantly affected, because the spin (i) forces the orbital plane of the center-of-mass of the BBH around the SMBH to precess (the Lense-Thirring effect) and (ii) imposes an additional gravitomagnetic force on the BBH. As a result, the merger time of the BBH could be significantly different. We calculate the waveform from the BBH in one representative example and study its detectability by a milli-Hertz GW detector, such as the Laser Interferometer Space Antenna (LISA). We find that the signal is distinguishable from that in the case without spin. Our results imply that the BBHs in the LISA band could potentially be used to probe the spin of the SMBHs in galaxy centers., Comment: 8 pages, 9 figures, comments welcome

The leading order effect of the spin of a distant supermassive black hole (SMBH) on the orbit of compact binary revolving around it appears at the 1.5 post Newtonian (PN) expansion through coupling with the inner and outer orbital angular momenta, and makes an oscillating characteristic contribution to the secular evolution of the compact binary eccentricity over a long time scale compared to the Kozai-Lidov dynamics caused by a non-spinning SMBH., Comment: 5 pages, 2 figures