The geometrical configuration of the Einstein Telescope (ET) gravitational-wave observatory is one the most important design choices to be made for this future scientific facility. Two baseline configurations are currently being considered, a single triangle or 2 distant L-shaped detectors tilted by about $45^{\circ}$. In this document we present a study of the scientific performance of the ET baseline configurations in both stand-alone mode and in the presence of either an L-shaped Cosmic Explorer detector with 40-km long arms located in the United States or the existing LIGO-Virgo-KAGRA network. We also include in the study an alternative ET configuration, which is currently not being considered and consists of a triangle plus a distant L-shaped detector. We find that in stand-alone mode this alternative configuration performs significantly better than the other two in both the compact binary coalescence and stochastic gravitational wave background scientific cases. The differences in performance between the ET configurations are reduced in the presence of the considered, additional non-ET detectors. We also show that the impact of possible correlated noise in co-located detectors on the stochastic gravitational-wave background performance can be addressed with the addition of extra detectors. Finally, we study the impact on the ET scientific performance of the relative orientation of the future detectors in the network. We find that, while the configurations that include a triangular ET detector are basically insensitive to this orientation, a balanced compromise for the ET configuration consisting of two L-shaped detectors could be represented by a tilt angle between the two detectors of about $30^{\circ}$. less

Gravitational tail-of-tail corrections arise when radiation scatters twice from the mass-monopole field of its source. In the multipolar effective field theory, one of the two-loop topologies contributing to this process involves genuinely coupled loop momenta, preventing its evaluation through nested one-loop integrations. After tensor reduction, this nonfactorizing structure leads to a particularly challenging family of scalar integrals with unbounded numerator powers as the multipole rank increases. We derive exact closed-form expressions for the entire relevant integer numerator domain, valid in generic dimension and accommodating Feynman, retarded, and advanced prescriptions through consistent analytic continuation. Near $d=3+ε$, we also obtain explicit Laurent expansions through $O(ε)$, retaining the subleading information needed in higher-order radiative calculations. While these expansions determine the dimensional poles, identifying their ultraviolet (UV) or infrared (IR) origin requires a separate analysis of momentum regions. We carry out this analysis throughout the integral domain and apply it directly to the coupled tail-of-tail emission diagram for arbitrary electric and magnetic multipoles. In this way, we independently determine the UV and IR residues, and explicitly verify that the complete infrared pole structure, including both double and simple poles, agrees with the exponentiation of the one-loop gravitational tail. The UV residues, calculated directly from hard-momentum regions, reproduce the established multipole anomalous dimensions when combined with the known contributions of the remaining diagrams. less

The spin-induced quadrupole moment (SIQM) of a compact object provides a direct null test of the Kerr hypothesis. Most existing gravitational-wave tests of SIQM assume quasi-circular binaries, although dynamical formation channels can produce measurable eccentricity that may persist in the sensitive band of third-generation (3G) detectors. We extend the symmetric SIQM test to eccentric, aligned-spin binaries using a post-Newtonian spinning-eccentric phasing model, and forecast its measurability with Cosmic Explorer (CE) and Einstein Telescope (ET). Single-event Fisher-matrix forecasts show that the impact of eccentricity on SIQM measurement precision depends on the binary parameters and detector configuration, rather than uniformly degrading the measurement. A population study with a truncated eccentric expansion indicates that ET's additional low-frequency eccentric cycles tighten $Δκ_s$ by roughly a factor of two relative to CE (median $0.11$ to $0.12$ versus $0.20$ to $0.23$); the absolute values are indicative only. We further show that quasi-circular template banks can lose significant effectualness for moderately eccentric signals, motivating the development of eccentric-spin template families. Accounting for eccentricity is therefore important both for SIQM measurements and for avoiding systematic losses in searches, and it strengthens tests of the nature of compact objects with 3G gravitational-wave detectors. less

Tidal Love numbers characterize the conservative response of compact objects to external perturbations and provide a powerful probe of their nature. While the static Love numbers of Schwarzschild, Kerr, and Reissner--Nordström black holes remarkably vanish, the tidal response of a generic Kerr--Newman black hole has remained unexplored due to the intrinsic coupling between gravitational and electromagnetic perturbations. Exploiting a recent breakthrough in the separability of these perturbations, we analytically determine the static tidal response of the most general stationary black hole in four-dimensional Einstein--Maxwell theory. For arbitrary multipole order, charge, and spin, we show that the entire matrix of conservative Love numbers vanishes, including the mixed gravito-electromagnetic couplings. We also compute the nonvanishing static dissipative response induced by frame dragging. less

In this work, using nonlinear electrodynamics (NLED) as a source in the field equations of extended scalar-tensor-Gauss-Bonnet (E-STGB) gravity, a novel type of static and spherically symmetric spacetime is found. We show that this novel type of spacetime can be used to explain the rotation curves and gravitational lensing of spiral galaxies. The NLED model used to derive our solution, in the weak and strong field limits, reduces to Maxwell electrodynamics. Furthermore, for a wide range of parameter values where our solution describes the gravitational field of a spiral galaxy, the NLED model satisfies the null and weak energy conditions. Hence, our results suggest that the extended scalar-tensor-Gauss-Bonnet gravity minimally coupled to nonlinear electrodynamics (E-STGB-NLED) provides a viable alternative to explain flat rotation curves of spiral galaxies without invoking dark matter. less

The discrete geometry on an $n$-dimensional simplicial manifold are studied, in order to incorporate torsion into Regge calculus. In each simplex, the edge vectors are assigned to the edges to encode the information of their lengths and directions. In addition, the holonomies along the curves across the interfaces of two adjacent simplices are represented by the internal gauge group elements. The torsion manifests itself as the difference between an edge vector on an interface belonging to one simplex and the parallel transported edge vector, via the holonomy, of the same edge but belonging to the adjacent simplex. The simplicial Einstein--Cartan actions are then constructed as functions of the edge vectors and holonomies in three and four dimensions with Euclidean and Lorentzian signatures, respectively. It is shown that they return to the corresponding Regge actions for the torsion-free cases. The variations of the 4-dimensional discrete action with respect to the edge vectors and holonomies, respectively, give two equations of motion. It is shown that the former is consistent with the corresponding equation in the continuum theory, and the torsion-free holonomies satisfy the latter equation as in the continuous case. Thus, the resulting theory on the simplicial manifold can be regarded as a discrete analogue of Einstein--Cartan theory. less

We present the results of \textbf{MADGRAV}, a deep-learning-based search for high-mass compact binary coalescences, applied to the data collected by the LIGO interferometers during the third observing run and during the first and second part of the fourth observing run. The \textbf{MADGRAV} pipeline consists of a series of sequential convolutional neural networks that perform anomaly detection, glitch classification, coherence testing, and signal ranking. Data from the Hanford and Livingston LIGO detectors are studied (both individually and in coherence) by way of 1 second Q-transform windows. Of the candidates that survive every stage of the pipeline, 48 reach the significance threshold, and we report 47 gravitational wave detections characterised by a false alarm rate below $1\,{\rm yr}^{-1}$ with a probability of astrophysical origin $p_{\rm astro}>0.9$. Of the 47 detections, 44 are shared with the minimally modelled coherent WaveBurst search. The observed total source-frame masses, extracted from official gravitational wave transient catalogues, are in the $14-236 M_{\odot}$ range with a median of $69 M_{\odot}$, and a median SNR of 16. We note that the recovered fraction of confident detections rises with mass: for LIGO detectors network SNR $>10$ the pipeline recovers $8.1\%$ of confident catalog events below $30 M_{\odot}$, $39.8\%$ between $30$ and $100 M_{\odot}$, and $53.3\%$ above $100 M_{\odot}$, corresponding to $33.3\%$, $45.5\%$ and $53.3\%$ of the events detected by coherent WaveBurst in the same bins. These results suggest that anomaly detection pipelines can serve as an independent detection channel complementary to matched filtering in the high-mass high-SNR regime. less

We construct the complete spectrum of gravitational total-transmission modes (TTMs) of Kerr black holes and find four globally continuous families, $n_\infty=1,2,3,4$. Compared with the three-family classification of Cook and Lu [Phys. Rev. D 107, 044043 (2023)], our global continuation separates complex conjugation at fixed $m$ from the mirror symmetry connecting the $m$ and $-m$ spectra, yielding a uniform four-family classification without additional symmetry-unrelated roots. The $n_\infty=3$ family approaches the Schwarzschild algebraically special frequency, whereas the $n_\infty=1,2,$ and $4$ families diverge as $ω\propto a^{-4/3}$ along lower-half-plane directions $-150^\circ$, $-90^\circ$, and $-30^\circ$. High-precision data up to $\ell=32$ recover the Cook--Lu small-spin asymptotics and show how the divergent branches are embedded in the global four-family spectrum. The spherical-limit polar labeling and large-$|aω|$ angular ordering are related in a family-dependent manner. For axisymmetric perturbations, we show that the $n_\infty=2$ and $n_\infty=3$ branches coalesce at exceptional points and subsequently evolve toward distinct small-spin limits, rather than exhibiting the overtone-multiplet splitting proposed by Cook and Lu. Finally, we identify a previously unreported anomalous proximity between the $n_\infty=3$ TTM family and the unconventional Kerr quasinormal-mode sequence, with separations reaching order $10^{-8}$ while remaining numerically well resolved. less

We investigate generalized projective symmetry and its breaking in four-dimensional parity-even metric-affine gravity, considering an action linear in curvature and at most quadratic in torsion and nonmetricity. We derive the action of the generalized projective transformation on the irreducible components of the affine geometry and determine the coupling relations defining the axial, metric-trace, and fully projectively invariant theories. Complete invariance reduces the $12$ gravitational coefficients to a five-parameter family and generates four vectorial Noether identities for the connection equations. Projective invariance makes the connection operator singular, thus we develop a symmetry-adapted method for solving its vacuum field equations. We then analyze couplings to Dirac, electromagnetic, and complex Klein-Gordon fields. Locally exact axial-projective transformations correspond to chiral rotations for massless fermions at the classical level, while a combination of covectors acts as an Abelian connection linking a locally exact vector-projective representative to scalar $U(1)$ symmetry. Standard Maxwell theory is independent of the affine connection, whereas a torsion-dependent Maxwell-like extension can preserve both electromagnetic and projective invariance through compensating Stückelberg fields. Exact gravitational projective invariance makes the corresponding connection directions nondynamical and forces matter currents sourcing them to vanish. Controlled explicit breaking lifts these zero modes and converts them into auxiliary fields. Thus, projective symmetry provides a unified principle for identifying affine gauge modes, constraining matter couplings, and relating symmetry breaking in the gravitational sector to effective matter interactions. less

We show that the space of vacuum initial data sets on a closed manifold often has many non-trivial homotopy groups. The starting point is a result of the second named author, which constructs non-trivial elements in the homotopy groups of the space of initial data sets satisfying the strict dominant energy condition, together with a later result in joint work with Bernd Ammann showing that these elements often persist when the strictness assumption is dropped. In this work, we use a parametrized version of the conformal method to show that these elements may also be represented by maps into the space of vacuum initial data sets. This requires two results that may be of independent interest: metrics admitting conformal Killing vectors can be removed from the space of metrics without changing its weak homotopy type, and over the remaining metrics the York decomposition can be carried out in families, the TT-tensors forming a trivial Hilbert bundle. To our knowledge, this is the first result on the global topology of this space. less