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Strong gravitational lensing of variable sources, such as quasars or supernovae, can be used to constrain cosmological parameters through a technique known as "time-delay cosmography''. Competitive constraints on the Hubble constant have been achieved with electromagnetic observations of lensed quasars and lensed supernovae. Gravitational wave (GW) astronomy may open up a new channel for time-delay cosmography with GW signal replacing the electromagnetic (EM) one. We highlight the similarities of using GW signals to be applied to time-delay cosmography compared to EM signal. We then discuss key differences between GW and EM signals and their resulting advantages and inconveniences from the angle of the current state-of-the-art using quasars and lensed supernovae for time-delay cosmography. We identify the astrometric precision requirement of the images as a key challenge to overcome and highlight the potentially significant impact that near-perfect time-delay measurements of lensed GWs can bring to the table., Comment: 9 pages, 2 figures, accepted to be published in Philosophical Transactions A

Labourie raised the question of determining the possible asymptotics for the growth rate of compact $k$-surfaces, counted according to energy, in negatively curved $3$-manifolds, indicating the possibility of a theory of thermodynamical formalism for this class of surfaces. Motivated by this question and by analogous results for the geodesic flow, we prove a number of results concerning the asymptotic behavior of high energy $k$-surfaces, especially in relation to the curvature of the ambient space. First, we determine a rigid upper bound for the growth rate of quasi-Fuchsian $k$-surfaces, counted according to energy, and with asymptotically round limit set, subject to a lower bound on the sectional curvature of the ambient space. We also study the marked energy spectrum for $k$-surfaces, proving a number of domination and rigidity theorems in this context. Finally, we show that the marked area and energy spectra for $k$-surfaces in $3$-dimensional manifolds of negative curvature are asymptotic if and only if the sectional curvature is constant., Comment: 27 pages

We study finite-type solutions of the elliptic sinh-Gordon equation along the strip $\Bbb{R}\times[0,L]$ with Durham conditions on each boundary component. We determine necessary rationality criteria for these conditions to be satisfied on both components. These rationality criteria are analogous to the necessary and sufficient criteria for finite-type solutions to be periodic. However, in contrast to the periodic case, they are not in themselves sufficient for Durham conditions to be satisfied on both boundary components: certain additional criteria must also be satisfied at 4 specific points of the spectral curve. Nevertheless, in the special case where the Durham conditions imposed on the two boundary components are complementary to one another in a sense that we will clarify, these rationality criteria are, indeed, sufficient. This study is a necessary preliminary for any general construction of finite-type solutions of the elliptic sinh-Gordon equation subject to Durham boundary conditions., Comment: 31 pages, 3 figures, 1 appendix

The Legacy Survey of Space and Time (LSST) at Vera C. Rubin Observatory is planned to begin in the Fall of 2025. The LSST survey cadence has been designed via a community-driven process regulated by the Survey Cadence Optimization Committee (SCOC), which recommended up to 3% of the observing time to carry out Target of Opportunity (ToO) observations. Experts from the scientific community, Rubin Observatory personnel, and members of the SCOC were brought together to deliver a recommendation for the implementation of the ToO program during a workshop held in March 2024. Four main science cases were identified: gravitational wave multi-messenger astronomy, high energy neutrinos, Galactic supernovae, and small potentially hazardous asteroids possible impactors. Additional science cases were identified and briefly addressed in the documents, including lensed or poorly localized gamma-ray bursts and twilight discoveries. Trigger prioritization, automated response, and detailed strategies were discussed for each science case. This document represents the outcome of the Rubin ToO 2024 workshop, with additional contributions from members of the Rubin Science Collaborations. The implementation of the selection criteria and strategies presented in this document has been endorsed in the SCOC Phase 3 Recommendations document (PSTN-056). Although the ToO program is still to be finalized, this document serves as a baseline plan for ToO observations with the Rubin Observatory.

We describe the structure of the singular sets of constant curvature, convex hypersurfaces in hyperbolic space for general convex curvature functions. We apply this result to the study of the ideal Plateau problem in hyperbolic space for such curvature functions., Comment: A brief review, by invitation, for a forthcoming volume in honour of Marcos Dajczer. 16 pages, 6 figures

Like many areas of astrophysics and cosmology, the Vera C. Rubin Observatory will be transformational for almost all the applications of strong lensing, thanks to the dramatic increase in the number of known strong lenses by two orders of magnitude or more and the readily available time-domain data for the lenses with transient sources. In this article, we provide an overview of the forecasted number of discovered lenses of different types and describe the primary science cases these large lens samples will enable. We provide an updated forecast on the joint constraint for the dark energy equation-of-state parameters, $w_0$ and $w_a$, from combining all strong lensing probes of dark energy. We update the previous forecast from the Rubin Observatory Dark Energy Science Collaboration's Science Review Document by adding two new crucial strong lensing samples: lensed Type Ia supernovae and single-deflector lenses with measured stellar kinematics. Finally, we describe the current and near-future activities and collaborative efforts within the strong lensing community in preparation for the arrival of the first real dataset from Rubin in early 2026., Comment: 12 pages, 2 figures. Invited review for the Royal Society meeting "Multi-messenger Gravitational Lensing", submitted to Philosophical Transactions A. This version: updated references

Diagnostic tests which can detect pre-clinical or sub-clinical infection, are one of the most powerful tools in our armoury of weapons to control infectious diseases. Considerable effort has been therefore paid to improving diagnostic testing for human, plant and animal diseases, including strategies for targeting the use of diagnostic tests towards individuals who are more likely to be infected. Here, we follow other recent proposals to further refine this concept, by using machine learning to assess the situational risk under which a diagnostic test is applied to augment its interpretation . We develop this to predict the occurrence of breakdowns of cattle herds due to bovine tuberculosis, exploiting the availability of exceptionally detailed testing records. We show that, without compromising test specificity, test sensitivity can be improved so that the proportion of infected herds detected by the skin test, improves by over 16 percentage points. While many risk factors are associated with increased risk of becoming infected, of note are several factors which suggest that, in some herds there is a higher risk of infection going undetected, including effects that are correlated to the veterinary practice conducting the test, and number of livestock moved off the herd.

The Wide-field Spectroscopic Telescope (WST) is proposed as a new facility dedicated to the efficient delivery of spectroscopic surveys. This white paper summarises the initial concept as well as the corresponding science cases. WST will feature simultaneous operation of a large field-of-view (3 sq. degree), a high multiplex (20,000) multi-object spectrograph (MOS) and a giant 3x3 sq. arcmin integral field spectrograph (IFS). In scientific capability these requirements place WST far ahead of existing and planned facilities. Given the current investment in deep imaging surveys and noting the diagnostic power of spectroscopy, WST will fill a crucial gap in astronomical capability and work synergistically with future ground and space-based facilities. This white paper shows that WST can address outstanding scientific questions in the areas of cosmology; galaxy assembly, evolution, and enrichment, including our own Milky Way; origin of stars and planets; time domain and multi-messenger astrophysics. WST's uniquely rich dataset will deliver unforeseen discoveries in many of these areas. The WST Science Team (already including more than 500 scientists worldwide) is open to the all astronomical community. To register in the WST Science Team please visit https://www.wstelescope.com/for-scientists/participate, Comment: 194 pages, 66 figures. Comments are welcome (wstelescope@gmail.com)

We use Clifford algebras to construct a unified formalism for studying constant extrinsic curvature immersed surfaces in riemannian and semi-riemannian $3$-manifolds in terms of immersed bilegendrian surfaces in their unitary bundles. As an application, we provide full classifications of both complete and compact immersed bilegendrian surfaces in the unit tangent bundle $\text{U}\Bbb{S}^3$ of the $3$-sphere., Comment: 36 pages. Dedicated to Fran\c{c}ois Labourie on the occasion of his 60th birthday

We provide a full classification of complete maximal $p$-dimensional spacelike submanifolds in the pseudo-hyperbolic space $\mathbf{H}^{p,q}$, and we study its applications to Teichm\"uller theory and to the theory of Anosov representations of hyperbolic groups in $\mathsf{PO}(p,q+1)$., Comment: 60 pages

We combine the Planck-SZ2 galaxy cluster catalogue with near-infrared photometry of galaxies from the VISTA Hemisphere Survey to identify candidate brightest cluster galaxies (BCGs) in 306 massive clusters in the Southern skies at redshifts of $z>0.1$. We find that 91% of these clusters have at least one candidate BCG within the 95% confidence interval on the cluster centers quoted by the Planck collaboration, providing reassurance that our analyses are statistically compatible, and find 92% to be reasonable candidates following a manual inspection. We make our catalog publicly available to assist colleagues interested in multi-wavelength studies of cluster cores, and the search for gravitationally lensed explosive transients in upcoming surveys including the Legacy Survey of Space and Time by the Vera C. Rubin Observatory., Comment: Published in RNAAS in March 2023. 3 pages, 1 figure

We study the space of Hopf differentials of almost fuchsian minimal immersions of compact Riemann surfaces. We show that the extrinsic curvature of the immersion at any given point is a concave function of the Hopf differential. As a consequence, we show that the set of all such Hopf differentials is a convex subset of the space of holomorphic quadratic differentials of the surface. In addition, we address the non-equivariant case, and obtain lower and upper bounds for the size of this set.

In [17], Labourie initiated the study of the dynamical properties of the space of $k$-surfaces, that is, suitably complete immersed surfaces of constant extrinsic curvature in $3$-dimensional manifolds, which he presented as a higher-dimensional analogue of the geodesic flow when the ambient manifold is negatively curved. In this paper, following the recent work [5] of Calegari--Marques--Neves, we study the asymptotic counting of surface subgroups in terms of areas of $k$-surfaces. We determine a lower bound, and we prove rigidity when this bound is achieved. Our work differs from that of [5] in two key respects. Firstly, we work with all quasi-Fuchsian subgroups as opposed to merely asymptotically Fuchsian ones. Secondly, as the proof of rigidity in [5] breaks down in the present case, we require a different approach. Following ideas outlined by Labourie in [19], we prove rigidity by solving a general foliated Plateau problem in Cartan--Hadamard manifolds. To this end, we build on Labourie's theory of $k$-surface dynamics, and propose a number of new constructions, conjectures and questions., Comment: 46 Pages, 8 Figures, Mostly cosmetic revisions, PDF Only

A black hole can launch a powerful relativistic jet after it tidally disrupts a star. If this jet fortuitously aligns with our line of sight, the overall brightness is Doppler boosted by several orders of magnitude. Consequently, such on-axis relativistic tidal disruption events (TDEs) have the potential to unveil cosmological (redshift $z>$1) quiescent black holes and are ideal test beds to understand the radiative mechanisms operating in super-Eddington jets. Here, we present multi-wavelength (X-ray, UV, optical, and radio) observations of the optically discovered transient \target at $z=1.193$. Its unusual X-ray properties, including a peak observed luminosity of $\gtrsim$10$^{48}$ erg s$^{-1}$, systematic variability on timescales as short as 1000 seconds, and overall duration lasting more than 30 days in the rest-frame are traits associated with relativistic TDEs. The X-ray to radio spectral energy distributions spanning 5-50 days after discovery can be explained as synchrotron emission from a relativistic jet (radio), synchrotron self-Compton (X-rays), and thermal emission similar to that seen in low-redshift TDEs (UV/optical). Our modeling implies a beamed, highly relativistic jet akin to blazars but requires extreme matter-domination, i.e, high ratio of electron-to-magnetic field energy densities in the jet, and challenges our theoretical understanding of jets., Comment: To appear in Nature Astronomy on 30th November 2022. Also see here for an animation explaining the result: https://youtu.be/MQHdSbxuznY

In the study of immersed surfaces of constant positive extrinsic curvature in space-forms, it is natural to substitute completeness for a weaker property, which we here call quasicompleteness. We determine the global geometry of such surfaces under the hypotheses of quasicompleteness. In particular, we show that, for $k>\text{Max}(0,-c)$, the only quasicomplete immersed surfaces of constant extrinsic curvature equal to $k$ in the $3$-dimensional space-form of constant sectional curvature equal to $c$ are the geodesic spheres. Together with earlier work of the author, this completes the classification of quasicomplete immersed surfaces of constant positive extrinsic curvature in $3$-dimensional space-forms., Comment: 1 Figure

In [15] Labourie develops a theory of immersed surfaces of prescribed extrinsic curvature which has since found widespread applications in hyperbolic geometry, general relativity, Teichm\"uller theory, and so on. In this chapter, we present a quaternionic reformulation of these ideas. This yields simpler proofs of the main results whilst pointing towards the higher-dimensional generalisation studied by the author in [25]., Comment: Requested chapter for forthcoming book. Some new results and simpler proofs of existing results

Cross-referencing a watchlist of galaxy groups and clusters with transient detections from real-time streams of wide-field survey data is a promising method for discovering gravitationally lensed explosive transients including supernovae, kilonovae, gravitational waves and gamma-ray bursts in the next ten years. However, currently there exists no catalogue of objects with both sufficient angular extent and depth to adequately perform such a search. In this study, we develop a cluster-finding method capable of creating an all-sky list of galaxy group- and cluster-scale objects out to $z\simeq1$ based on their lens-plane properties and using only existing data from wide-field infrared surveys such as VHS and UHS, and all-sky \textit{WISE} data. In testing this method, we recover 91 per cent of a sample containing known and candidate lensing objects with Einstein radii of $\theta_E \geq 5\arcsec$. We also search the surrounding regions of this test sample for other groups and clusters using our method and verify the existence of any significant findings by visual inspection, deriving estimates of the false positive rate that are as low as 6 per cent. The method is also tested on simulated Rubin data from their DP0 programme, which yields complementary results of a good recovery rate of $\gtrsim 80$ per cent for $M_{200}\geq7\times10^{13}$M$_\odot$ clusters and with no false positives produced in our test region. Importantly, our method is positioned to create a watchlist in advance of Rubin's LSST, as it utilises only existing data, therefore enabling the discovery of lensed transients early within the survey's lifetime., Comment: 11 pages, 9 figures. Published, MNRAS

We search for gravitational wave (GW) events from LIGO-Virgo's third run that may have been affected by gravitational lensing. Gravitational lensing delays the arrival of GWs, and alters their amplitude -- thus biasing the inferred progenitor masses. This would provide a physically well-understood interpretation of GW detections in the ''mass gap'' between neutron stars and black holes, as gravitationally lensed binary neutron star (BNS) mergers. We selected three GW detections in LIGO-Virgo's third run for which the probability of at least one of the constituent compact objects being in the mass gap was reported as high with low latency -- i.e. candidate lensed BNS mergers. Our observations of powerful strong lensing clusters located adjacent to the peak of their sky localisation error maps reached a sensitivity $\rm AB\simeq25.5$ in the $z'$-band with the GMOS instruments on the Gemini telescopes, and detected no candidate lensed optical counterparts. We combine recent kilonova lightcurve models with recent predictions of the lensed BNS population and the properties of the objects that we followed up to show that realistic optical counterparts were detectable in our observations. Further detailed analysis of two of the candidates suggests that they are a plausible pair of images of the same low-mass binary black hole merger, lensed by a local galaxy or small group of galaxies. This further underlines that access to accurate mass information with low latency would improve the efficiency of candidate lensed BNS selection., Comment: Accepted for publication on MNRAS

Secure confirmation that a gravitational wave (GW) has been gravitationally lensed would bring together these two pillars of General Relativity for the first time. This breakthrough is challenging for many reasons, including: GW sky localization uncertainties dwarf the angular scale of gravitational lensing, the mass and structure of gravitational lenses is diverse, the mass function of stellar remnant compact objects is not yet well constrained, and GW detectors do not operate continuously. We introduce a new approach that is agnostic to the mass and structure of the lenses, compare the efficiency of different methods for lensed GW discovery, and explore detection of lensed kilonova counterparts as a direct method for localising candidates. Our main conclusions are: (1) lensed neutron star mergers (NS-NS) are magnified into the "mass gap" between NS and black holes, therefore selecting candidates from public GW alerts with high mass gap probability is efficient, (2) the rate of detectable lensed NS-NS will approach one per year in the mid-2020s, (3) the arrival time difference between lensed NS-NS images is $1\,\rm sec\lesssim\Delta t\lesssim1\,year$, and thus well-matched to the operations of GW detectors and optical telescopes, (4) lensed kilonova counterparts are faint at peak (e.g.\ $r_{\rm AB}\simeq24-26$ in the mid-2020s), fade quickly ($d<2\,\rm days$), and are detectable with target of opportunity observations with large wide-field telescopes. For example, just $\lesssim0.25$ per cent of Vera C.\ Rubin Observatory's observing time will be sufficient to follow up one well-localized candidate per year. Our predictions also provide a physically well-defined basis for exploring electromagnetically the exciting new "mass gap" discovery space., Comment: Accepted by MNRAS. 20 pages, 10 figures

This report is the result of a joint discussion between the Rubin and Euclid scientific communities. The work presented in this report was focused on designing and recommending an initial set of Derived Data products (DDPs) that could realize the science goals enabled by joint processing. All interested Rubin and Euclid data rights holders were invited to contribute via an online discussion forum and a series of virtual meetings. Strong interest in enhancing science with joint DDPs emerged from across a wide range of astrophysical domains: Solar System, the Galaxy, the Local Volume, from the nearby to the primaeval Universe, and cosmology., Comment: Report of the Rubin-Euclid Derived Data Products Working Group, 78 pages, 11 figures

We present the Strong Lensing Science Collaboration's (SLSC) recommended observing targets for the science verification and science validation phases of commissioning. Our recommendations have been developed in collaboration with the Dark Energy Science Collaboration (DESC) Strong Lensing Topical Team. In summary, our key recommendations are as follows: (1) Prioritize fields that span the full range of declination observable from Cerro Pachon during the engineering focused Science Verification phase of commissioning, before concentrating on equatorial fields for the Science Validation surveys. (2) Observe quadruply lensed quasars as the ultimate test of the Active Optics system towards the end of the Science Verification phase of commissioning. These systems are the strongest tests known for delivered image quality. (3) Prioritize science validation survey fields (both single deep pointings and wide fields) that have been searched thoroughly by precursor surveys for strong lenses. (4) The optimal wide (~100 degree^2) science validation field would include the CFHT-LS W4 field, and overlap with the SDSS Stripe 82, DES-SN, KIDS and HSC-SSP fields. (5) The optimal single pointing science validation fields are the XMM-LSS and COSMOS Deep Drilling Fields, the equatorial Hubble Frontier Fields galaxy clusters, and strongly lensed quasars with measured time delays that are well-matched to commissioning timescales., Comment: 8 pages, 1 figure