We propose a new strategy to probe nontensorial polarizations in the stochastic gravitational wave (GW) background. Averaging over polarization angles, we find that three-point correlations of the GW signal vanish for tensor and vector modes, while scalar modes generically leave a nonzero imprint. This property makes the GW bispectrum a distinctive and robust diagnostic of scalar polarizations predicted in theories beyond general relativity. We derive the corresponding response functions for ground-based interferometers, pulsar timing arrays, and astrometric observables, and we construct an optimal estimator together with simple Fisher forecasts for pulsar timing sensitivity. As a proof of principle, we show that second-order GWs sourced by primordial magnetogenesis can be characterized by large three-point functions. Our results demonstrate that GW three-point correlations provide a novel observational window on physics beyond general relativity.

We present a comprehensive analysis of the dynamic and thermodynamic stability of neutron stars composed of superconducting-superfluid mixtures within the Iyer-Wald formalism. We derive the first law of thermodynamics and the necessary and sufficient condition under which dynamic equilibrium implies thermodynamic equilibrium. By constructing the phase space and canonical energy, we show that the dynamic stability for perturbations, restricted in symplectic complement of trivial perturbations with the Arnowitt-Deser-Misner 3-momentum unchanged, is equivalent to the non-negativity of the canonical energy. Furthermore, dynamic stability against restricted axisymmetric perturbations guarantees the dynamic stability against all axisymmetric perturbations. We also prove that the positivity of canonical energy on all axisymmetric perturbations within the Lagrangian displacement framework with fixed angular momentum is necessary for thermodynamic stability. In particular, the equivalence of dynamic and thermodynamic stability is established for radial perturbations of static, spherically symmetric isentropic configurations.

We present a polynomial basis that exactly tridiagonalizes Teukolsky’s radial equation for quasinormal modes. These polynomials naturally emerge from the radial problem, and they are “canonical” in that they possess key features of classical polynomials. Our canonical polynomials may be constructed using various methods, the simplest of which is the Gram-Schmidt process. In contrast with other polynomial bases, our polynomials allow for Teukolsky’s radial equation to be represented as a simple matrix eigenvalue equation. We expect that our polynomials will be useful for better understanding the Kerr quasinormal modes’ properties, particularly their prospective spatial completeness and orthogonality. We show that our polynomials are closely related to the confluent Heun and Pollaczek-Jacobi type polynomials. Consequently, our construction of polynomials may be used to tridiagonalize other instances of the confluent Heun equation. We apply our polynomials to a series of simple examples, including: (1) the high accuracy numerical computation of radial eigenvalues, (2) the evaluation and validation of quasinormal mode solutions to Teukolsky’s radial equation, and (3) the use of Schwarzschild radial functions to represent those of Kerr. Along the way, a potentially new concept, “polynomial/nonpolynomial duality,” is encountered and applied to show that some quasinormal mode separation constants are well approximated by confluent Heun polynomial eigenvalues. We briefly discuss the implications of our results on various topics, including the prospective spatial completeness of Kerr quasinormal modes.

A scalar product for quasinormal mode solutions to Teukolsky’s homogeneous radial equation is presented. Evaluation of this scalar product can be performed either by direct integration, or by evaluation of a confluent hypergeometric functions. The related scalar product will be useful for better understanding analytic solutions to Teukolsky’s radial equation, particularly the quasinormal modes, their potential spatial completeness, and whether the quasinormal mode overtone excitations may be estimated by spectral decomposition rather than fitting. With that motivation, the scalar product is applied to confluent Heun polynomials where it is used to derive their peculiar orthogonality and eigenvalue properties. A potentially new relationship is derived between the confluent Heun polynomials’ scalar products and eigenvalues. Using these results, it is shown for the first time that Teukolsky’s radial equation (and perhaps similar confluent Heun equations) are, in principle, exactly tridiagonalizable. To this end, “canonical” confluent Heun polynomials are conjectured.

Gravitational wave (GW) observations of binary black hole (BBH) coalescences provide a unique opportunity to test general relativity (GR) in the strong-field regime. To ensure the reliability of these tests, it is essential to identify and address potential sources of error, particularly those arising from missing physics in the waveform models used in GW data analysis. This paper investigates potential biases in these tests arising from strong gravitational lensing, an effect not currently incorporated into the standard framework for GR tests. In the geometric optics approximation, strong lensing produces three types of images: type I, type II, and type III. While type I and type III images do not distort the signal, type II images introduce a characteristic phase shift that can mimic GR deviations for signals with higher-order modes, precession, or eccentricity. We assess the response of four standard GR tests on simulated type II lensed BBH signals, including the two parametrized tests (TIGER and FTI), the modified dispersion relation test and the inspiral-merger-ringdown consistency test. We focus on precessing waveforms for binaries with total masses of $20M_{\odot }$ and $80M_{\odot }$, and dimensionless spins of 0.5 and 0.95, considering a fixed signal-to-noise ratio of 25 using the design $\mathrm{A}+$ sensitivity of the LIGO-Virgo network. Our findings indicate that more mass-asymmetric and higher-spin binaries show larger false deviations from GR in the TIGER and modified dispersion relation tests when applying GR tests to type II lensed signals. These results highlight the risk of false GR violations as detector sensitivity improves in future observational runs. Therefore, it is crucial to consider the possibility of strong lensing before drawing conclusions about deviations from GR in GW signals.

We provide a construction of a new class of axisymmetric extremal isolated horizons admitting a structure of U(1)-principal fiber bundle over a two-sphere. In contrast to the previous examples, the null generators are assumed to be transversal to the bundle fibers. We impose the Einstein equations at the horizon and explicitly derive all intrinsic geometries of the extremal horizon, consisting of a two-sphere metric and a rotation one-form, in the above class. The two-geometries turn out to be equivalent to the classification of conically singular horizons with product topology. Both the rotating and nonrotating horizons are then embedded in the Plebański-Demiański spacetimes, which naturally admit horizons of this type. Furthermore, we compare our results with previously obtained solutions to the Einstein vacuum extremal horizon equation with cosmological constant and the solution of Petrov type D equation with transversal bundle structure.

We constrain the parameter space of the bumblebee model in a cosmological background and then investigate the properties of gravitational waves within the constrained parameter space. Our analysis reveals seven perturbative degrees of freedom in the cosmological background: two tensor, two vector, and two scalar modes, along with an additional mode from the matter sector. The stability conditions for all these modes are derived. By incorporating the observed accelerated expansion of the Universe and the observational constraints on tensor gravitational waves, we derive bounds on the parameter space of the bumblebee model. Our results indicate that the nonminimal coupling parameter $\xi$ must be nonpositive, a constant background value $b_t$ of the bumblebee field implies $\sigma \ne -\frac{1}{2}\xi$, and the Lorentz-violating parameter $\xi b^2$ has a lower bound on the order of ${10}^{-15}$. We then investigate the propagation characteristics and polarization modes of gravitational waves in both the small-scale and Minkowski limits. The propagation modes of gravitational waves in the bumblebee model consist of two tensor modes, two vector modes, and one scalar mode. Notably, the tensor modes travel at subluminal speeds, whereas the vector and scalar modes propagate at superluminal speeds, when $\xi b_t^2\ne 0$. These results provide a concrete theoretical framework and specific observational signatures for testing Lorentz invariance in the gravitational sector with future gravitational-wave detectors.

A self-interacting dark-matter (SIDM) density spike around merging supermassive black holes may be able to supply the dynamical friction needed to shrink binaries from $\sim 1$ to $\sim {10}^{-2}\mathrm{pc}$, thereby resolving the long-standing “final-parsec problem.” Embedding the binary-halo system in a cosmological population model, we evolve the inspiral under the combined influence of gravitational-wave emission and SIDM drag, compute the resulting nanohertz gravitational-wave background, and confront it with the NANOGrav 15-year pulsar-timing data. A six-parameter Bayesian analysis, performed with a Gaussian-process-accelerated Markov chain Monte Carlo, yields posterior constraints on the cross section per unit mass and maximum circular velocity values that were consistent with independent galaxy-rotation and cluster-lensing limits. Within this parameter space, the SIDM spike remains intact, supplies sufficient friction to overcome the stellar depletion barrier, and produces a characteristic-strain spectrum that matches the NANOGrav signal as well as phenomenological astrophysical models.

In this paper, based on the action of a complex scalar field minimally coupled to a gravitational field, we numerically obtain a series of massive boson star solutions in a spherically symmetric background with a quartic-order self-interaction potential. Then, considering a thin accretion flow with a certain four-velocity, we further investigate the observable appearance of the boson star using the ray-tracing method and stereographic projection technique. As a horizonless compact object, the boson star’s thin disk images clearly exhibit multiple bright rings and a dark central region, with up to five bright rings. As the observer’s position changes, the bright rings of some boson stars deform into a symmetrical “horseshoe” or “crescent” shape. When the emitted profile varies, the images may display distinct observational signatures of a “central emission region.” Meanwhile, it shows that the corresponding polarized images not only reveal the spacetime features of boson stars but also reflect the properties of the accretion disk and its magnetic field structure. By comparing with black hole, we find that both the polarized signatures and thin disk images can effectively provide a possible basis for distinguishing boson stars from black holes. However, within the current resolution limits of the Event Horizon Telescope (EHT), boson stars may still closely mimic the appearance of black holes, making them challenging to distinguish at this stage.

Recently, the Pierre Auger Observatory has found strong evidence supporting the extragalactic origin of the most energetic cosmic rays. Despite several observed excesses in the distribution of arrival directions for the highest energy cosmic rays, the sources remain unidentified. Accretion shocks in galaxy clusters have been proposed as potential sources in the past. These immense shock waves, which can have radii on the order of megaparsecs, are generated by the infall of material from the intergalactic medium into the gravitational potential wells of galaxy clusters. In this work, we investigate the possibility that ultrahigh-energy cosmic rays are accelerated in these regions. Nearby massive galaxy clusters, including Virgo, are treated as a discrete component of the cluster mass distribution. Less massive galaxy clusters, as well as distant massive ones, are assumed to follow a continuous distribution in agreement with cluster mass statistics. We fit the flux at Earth and the composition profile measured by the Pierre Auger Observatory, assuming the injection of different nuclear species by these sources, to determine the values of the model parameters. Our results indicate that cosmic ray acceleration in cluster accretion shocks may account for at least a fraction of the observed UHECR flux at energies below the suppression scale. At higher energies, direct acceleration from the thermal pool would be feasible only if local fluctuations create favorable conditions, such as magnetic fields about an order of magnitude stronger than those typically expected in cluster accretion shocks, or for particular shock normal-magnetic field configurations. Moreover, in these scenarios, where the energy spectrum of accelerated cosmic rays is modeled as $\propto E^{-\gamma }$ with an exponential cutoff, the spectral index obtained from fitting the experimental data lies in the range $\gamma \sim 0.7–1.6$. This is smaller than 2, which is the value expected from the first-order Fermi acceleration mechanism for strong shocks.

The spin dynamics of fermions in a fermionic system under the influence of a magnetic field have been extensively studied using the Landau-Lifshitz-Gilbert (LLG) equation, where spin polarization and dissipation terms result from the combined effects of spin-magnetic-field interactions and spin-spin interactions between fermions in the medium. In this work, we extend the LLG equation to a fermionic system subject to an external field and two-body random collisions for the first time. We derive the corresponding Gilbert damping factor, which characterizes the spin polarization rate, within the framework of linear response theory. The fermionic medium is assumed to consist of quarks governed by strong interactions. We analyze the dependence of the heavy-quark spin polarization rate on the scattering cross section, the magnetic field strength, medium temperature, and heavy-quark mass in detail. This framework provides a foundation for the phenomenological study of spin dynamics in heavy quarks and heavy-flavor hadrons, such as charmonium spin alignment, in relativistic heavy-ion collisions, where both hot quark matter and strong magnetic fields are simultaneously generated.

Some recent pulsar observations cannot naturally fit into the conventional picture of neutron stars: the compact objects associated with HESS J1731-347 and XTE J1814-338 have too small radii in the low-mass regime, while the secondary component of GW190814 is too massive for neutron stars to be compatible with constraints from the GW170817 event. In this study, we demonstrate that all these anomalous observations and tensions, together with other conventional ones such as recent NICER observations of PSR $\mathrm{J}0740+6620$, $\mathrm{J}0030+0451$, and PSR J0437-4715, can be naturally explained simultaneously by a new general type of self-bound hybrid stars with large density discontinuities, and thus are radially stable in either the slow or rapid phase transition context. As a proof of concept, we use hybrid quark stars, inverted hybrid stars, and hybrid strangeon stars as benchmark examples to explicitly demonstrate the advantage and feasibility of self-bound hybrid stars with strong phase transitions in relieving all tensions related to compact stars’ masses, radii, and tidal deformabilities.

Gravitational lensing of gravitational waves (GWs) offers a novel observational channel that complements traditional electromagnetic approaches and provides unique insights into the astrophysical environments of GW sources. In this work, we investigate the repeated lensing of continuous gravitational wave (CW) sources in active galactic nucleus disks by central supermassive black holes (SMBHs), focusing on the imprint of SMBH spin via the Lense-Thirring effect. Although typically weak and challenging to observe, the spin-induced precession of source orbits can accumulate over time, thereby modulating the lensing geometry. Such modulations influence the magnification, duration, and waveform structure of each repeated lensing event, and enhance the overall probability of lensing occurrences. Using matched filtering, we demonstrate that spin-dependent signatures may be detectable, suggesting that if such repeated lensing of CW signals were to be observed in the future, the framework developed here would offer a means to interpret the associated modulation features and to constrain the underlying system parameters.

We extend the applicability of achilles (A CHIcagoLand Lepton Event Simulator) by incorporating the single pion production mechanism in a fully exclusive fashion. The electroweak interaction vertex is modeled by combining the state-of-the-art dynamical coupled-channels approach with realistic hole spectral functions, which account for correlations in both the initial target state and the residual spectator system. Final-state interactions are treated using a semiclassical intranuclear cascade that leverages nuclear configurations to determine the correlated spatial distribution of protons and neutrons. The meson-baryon scattering amplitudes used in the cascade are computed within the dynamical coupled-channels framework, consistent with the electroweak vertex. To model pion absorption, we employ the optical potential approach of Oset and Salcedo [Nucl. Phys. A484, 557 (1988).]. As an alternative approach, we explicitly model the production and propagation of resonances which mediate pion-nucleon scattering and pion absorption. We validate our approach against pion-nucleon and pion-nucleus scattering data, and present comparisons with electron- and neutrino-nucleus measurements from $\mathrm{e}4\nu$, T2K, $\mathrm{MINER}\nu \mathrm{A}$, and MicroBooNE.

This work explores the potential of the proposed FASER2 experiment at the LHC to determine the properties of a discovered heavy neutral lepton (HNL), including its mass, couplings, and whether it is a Majorana or Dirac fermion. We first consider a Majorana HNL with mass $m_N=1.84\mathrm{GeV}$ that is primarily produced through decays $D\to \mu N$ at the ATLAS interaction point. Such HNLs may travel macroscopic distances in the far-forward direction and then decay, yielding approximately $8600N\to \mu \pi$ decays in FASER2 at the High-Luminosity LHC. With FASER2 measurements alone, the HNL’s mass and couplings can be measured to fractional uncertainties of approximately 0.1% and 3% at 95% confidence level (CL), respectively, and the Dirac fermion hypothesis can be rejected at 99.8% CL. We then consider a second, more difficult, case of a Majorana HNL with mass $m_N=2.00\mathrm{GeV}$, yielding only $80N\to \mu \pi$ decays in FASER2. With FASER2 alone, measurements of HNL properties are still possible, but somewhat less precise. However, by using FASER2 as a trigger for ATLAS and measuring the charge of the muon produced in association with the HNL at ATLAS to search for lepton number violation, one can precisely measure the HNL’s properties and reject the Dirac fermion hypothesis at 99.7% CL. These results show that FASER2, sometimes in coordination with ATLAS, can precisely determine HNL properties, with far-reaching implications for our understanding of neutrino masses, baryogenesis, and the fundamental symmetries of nature.

The present study aims to unveil a scenario with a nonminimal secluded dark sector (DS) in an effective field theory (EFT) framework. To explore this, we have examined a suitable extension of the type-X two Higgs doublet model (2HDM) as a potential origin for the secluded DS. The DS comprises a dark matter (DM) candidate and a mediator particle “$a$” and possesses some nonminimal characteristics. It becomes nonthermally populated through diverse dim-6 four-Fermi operators, effectively generated by integrating out the heavier Higgs particles. The analysis further focuses on the consequences of the collision processes $\mathrm{DM}+a\leftrightarrow a+a$ and $\mathrm{DM}+\mathrm{DM}\leftrightarrow a+a$ occurring within the DS. We have investigated the significance of employing an EFT approach in tracking the temperature evolution of the DS. Within the present framework, the observed relic abundance of the DM can be realized through both dark freeze-out and freeze-in mechanisms. Further, we have delineated the permissible ranges of the relevant parameters, viz., the DM mass ($m_{\chi }\gtrsim 20\mathrm{GeV}$), the portal coupling ($C_{\tau }\lesssim {10}^{-14}{\mathrm{GeV}}^{-2}$), and the DS coupling ($\lambda \lesssim {10}^{-6}{\mathrm{GeV}}^{-2}$), by taking into account the perturbativity of the involved couplings while reproducing the observed DM relic and complying with the bounds from successful big bang nucleosynthesis (BBN) and $\gamma$-ray searches.

The search for physics beyond the Standard Model (BSM) at collider experiments requires model-independent strategies to avoid missing possible discoveries of unexpected signals. Anomaly detection (AD) techniques offer a promising approach by identifying deviations from the Standard Model (SM) and have been extensively studied. The sensitivity of these methods to untunable hyperparameters has not been systematically compared, however. This study addresses it by investigating four semisupervised AD methods—AutoEncoders, Deep Support Vector Data Description, Histogram-based Outlier Score, and Isolation Forest—trained on simulated SM background events. In this paper, we study the sensitivity of these methods to BSM benchmark signals as a function of these untunable hyperparameters. Such a study is complemented by a proposal of a nonparametric permutation test using signal-agnostic statistics, which can provide a robust statistical assessment.

The $I=\frac{3}{2}$ $\pi K$ $s$-wave scattering phase shift is computed by lattice quantum chromodynamics with $N_f=3$ flavors of Asqtad-improved staggered fermions. The energy-eigenvalues of $\pi K$ systems at one center of mass frame and six moving frames using moving wall source technique are used to get phase shifts by Lüscher’s formula and its extensions. The calculations are good enough to acquire effective range expansion parameters: scattering length $a$, effective range $r$, and shape parameter $P$, which are in good agreement with our explicit analytical predictions in three-flavor chiral perturbation theory at next-to-leading order. All results are fairly consistent with experimental measurements, phenomenological studies, and lattice estimations. Numerical computations are implemented at a fine ($a\approx 0.082\mathrm{fm}$, $L^{3}T=40^{3}96$) lattice ensemble with physical quark masses.

We study chiral symmetry breaking and restoration in accelerating and rotating frames using low-energy effective models. By analyzing the chiral condensate in Rindler coordinates, we show that different renormalization schemes lead to distinct conclusions in the accelerating frame: the scheme with subtracting divergences in the Rindler vacuum supports an acceleration-independent critical temperature, while the other scheme with subtracting divergences in Minkowski vacuum suggests an enhanced critical temperature. We further investigate a system with both rotation and acceleration. We find that the critical acceleration for chiral symmetry restoration decreases with angular velocity, indicating cooperative effects from acceleration-induced thermalization and rotation-induced effective chemical potential.