We propose a data-driven approach to identifying the functionally independent invariants that can be constructed from a tensor with a given symmetry structure. Our algorithm proceeds by first enumerating graphs, or tensor networks, that represent inequivalent contractions of a product of tensors, computing instances of these scalars using randomly generated data, and then seeking linear relations between invariants using numerical linear algebra. Such relations yield syzygies, or functional dependencies relating different invariants. We apply this approach in an extended case study of the independent invariants that can be constructed from an antisymmetric 3-form $H_{\mu \nu \rho }$ in six dimensions, finding five independent invariants. This result confirms that the most general Lagrangian for such a 3-form, which depends on $H_{\mu \nu \rho }$ but not its derivatives, is an arbitrary function of five variables, and we give explicit formulas relating other invariants to the five independent scalars in this generating set.

We investigate vacuum polarization on the event horizon of a Schwarzschild black hole carrying a global monopole. For a massless scalar field $\mathrm{\Psi }$ in the Hartle-Hawking state and with arbitrary curvature coupling, we compute the renormalized vacuum expectation value $⟨{\mathrm{\Psi }}^2{⟩}_{\mathrm{ren}}$. The monopole produces a solid-angle deficit and makes the spacetime non-Ricci-flat. Working perturbatively in the monopole parameter $\eta$ and retaining terms through $O({\eta }^2)$, we find that $⟨{\mathrm{\Psi }}^2{⟩}_{\mathrm{ren}}$ on the horizon splits into two contributions: a genuinely monopole-induced term evaluated at the horizon and the usual Schwarzschild result—with the event horizon radius modified by the presence of $\eta$. We also investigate whether an analogous decomposition holds for $⟨{T^{\mu }}_{\mu }{⟩}_{\mathrm{ren}}$ when it is determined by this method. Our result parallels earlier analyses of Schwarzschild black holes pierced by a cosmic string.

We study the Casimir effect in nonlinear field theories through the effective geometries that govern their linearized fluctuations. Previous analyses of Lorentz-violating scalar fields showed that a constant kinetic background modifies the parallel-plate Casimir energy by a rescaling of the plate separation and an overall determinant factor. We show that this structure is not merely a consequence of diagonalizing the reduced Green function. It follows from a common Schur-complement structure; after Fourier reduction parallel to the plates, the same reduced quadratic form controls the spectral denominator of the reduced Green function and the numerator generated by the energy-density insertion. This observation allows the Lorentz-violating scalar result to be used as an effective-metric prescription for regular fluctuation sectors arising from the linearization of nonlinear theories around constant backgrounds. In nonlinear scalar theories, the effective tensor is the Hessian of the Lagrangian evaluated on a constant-gradient background. In nonlinear electrodynamics $\mathcal{L}(\mathcal{F})$, a constant magnetic background splits the fluctuations into an ordinary Maxwell branch and an extraordinary optical branch. For this electromagnetic sector, we compute the parallel-plate Casimir energy both by direct mode summation and by applying the effective-metric formula branch by branch, finding exact agreement. The resulting energy depends on the orientation of the magnetic background relative to the plates, providing a concrete anisotropic Casimir response in a regular nonlinear electromagnetic sector.

Horizon-scale imaging and precision lensing have turned black holes into quantitative laboratories for strong gravity and for nonstandard electromagnetic physics. We study the optical appearance and orbital dynamics of a new class of static spherically symmetric black holes sourced by a Palatini-inspired nonlinear electrodynamics model, minimally coupled to Einstein-Hilbert gravity. Using a unified geodesic analysis, we identify the key radii that organize the strong-field phenomenology. For photons we determine the unstable photon sphere, the associated critical capture threshold, and the resulting shadow size for a distant observer, and we map how these observables respond to the charge and to the nonlinearity index $n$. For massive probes we compute circular orbits and the innermost stable circular orbit, clarifying the departure from the Schwarzschild and Reissner-Nordström cases. We then connect to classical tests by evaluating the light deflection angle and periastron advance, providing additional diagnostics that complement the shadow. Our results furnish a practical reference model for confronting first-order nonlinear electrodynamics black holes with current and forthcoming imaging and lensing data.

Hellings-Nordtvedt theory is a vector-tensor theory in which a vector field $A_{\mu }$ is nonminimally coupled to curvature through two independent interactions $A^2\mathcal{R}$ and $A^{\mu }{A}^{\nu }{\mathcal{R}}_{\mu \nu }$. When supplemented by a potential whose zero-energy minimum occurs at nonzero $A^2$, the restricted $A^{\mu }{A}^{\nu }{\mathcal{R}}_{\mu \nu }$ sector is known to admit black-hole and neutron-star solutions with a global monopolelike asymptotic vacuum structure. We examine whether this structure is a generic consequence of the nonzero vector vacuum or instead relies on the special Ricci-tensor coupling. By analyzing the field equations near spatial infinity, we show that the asymptotic vacuum condition is incompatible with generic nonzero values of both couplings and instead selects two allowed single-coupling sectors. The $A^{\mu }{A}^{\nu }{\mathcal{R}}_{\mu \nu }$ sector reproduces the known global monopolelike asymptotics, whereas the $A^2\mathcal{R}$ sector admits an asymptotically flat Schwarzschild metric with a nontrivial radial vector field. We further compute the Noether mass in the $A^2\mathcal{R}$ sector, derive the corresponding Solar-System constraints, and construct neutron-star configurations. Although the weak-field deviation is constrained to be small, neutron stars can still show appreciable departures from both general relativity and the Ricci-tensor-coupling sector in their masses, radii, and moments of inertia. Our results identify that the $A^2\mathcal{R}$ sector of massive Hellings-Nordtvedt theory as a viable and useful framework for studying strong-field compact objects with a nonzero vector vacuum while remaining compatible with weak-field tests.

The Leggett-Garg inequality (LGI) is a temporal analog of Bell’s inequality and provides a quantitative test of the nonclassicality of a system through its violation. We analytically investigate the violation of the LGI in the context of photon-graviton conversion in a magnetic field background, motivated by its potential applications to testing the nonclassicality of gravity. When gravitational perturbations are quantized as gravitons, the conversion of an initial single photon state gives rise to a superposition of photon and graviton states. We show that the temporal correlations obtained from successive projective measurements on the photon-graviton system violate the LGI. Observation of such a violation would provide a novel avenue for probing the quantum nature of gravity.

We show how a mass term for gravitational axions (“gravi-axions”) with a Chern-Simons coupling to gravity can naturally arise due to nonperturbative contributions from Euclidean wormholes, breaking the continuous shift symmetry of the standard theory. The induced mass can be generated in a cosmologically relevant range to be the dark matter or dark energy of the universe for a reasonable and well-motivated range of the symmetry breaking scale. Upon generating the gravi-axion mass term, we discuss the cosmology of the theory. We find that the gravi-axion can be produced to be the dominant dark matter component via misalignment or gravitational particle production, and that in a different regime, the gravi-axion can act as dynamical dark energy. We discuss gravi-axion decay into gravitons as a potential observational window for this theory. Finally, we find that, for late-time, astrophysical compact objects, cosmologically relevant gravi-axions behave as minimally coupled, massive scalar fields.

Solar System constraints on a general scalar-tensor theory with generic nonminimal coupling function, noncanonical kinetic function, and scalar potential are investigated in both the metric and Palatini formalisms. A unified post-Newtonian treatment is developed, yielding analytical expressions for the effective scalar mass, the effective gravitational coupling, and the parametrized post-Newtonian parameters $\gamma$ and $\beta$. The results show explicitly how the choice of variational principle affects the weak-field phenomenology. Comparison with Solar System observations, primarily the Cassini bound on $\gamma$, indicates that the observational impact of the formalism is strongly model dependent. Generic nonminimally coupled scalar fields may satisfy significantly weaker local bounds in the Palatini case because of stronger Yukawa suppression, whereas in Brans-Dicke gravity the differences are typically small and become appreciable only in restricted regions of parameter space. For the point-particle source considered here, Palatini $f(\widehat{R})$ gravity reproduces the general relativistic exterior post-Newtonian limit, unlike metric $f(R)$ gravity.

The evolution of neutron stars (NSs) embedded within massive stellar envelopes is a critical phase in binary stellar evolution, potentially leading to the formation of Thorne-Żytkow Objects (TŻOs) or catastrophic collapse. We present the first fully coupled general relativistic hydrodynamics simulations of hypercritical accretion onto NSs that simultaneously incorporate gray two-moment (M1) neutrino transport and an $\alpha$-chain nuclear reaction network. By investigating four distinct progenitor evolutionary stages, we resolve the complex interplay between intense neutrino cooling, multidimensional fluid dynamics, and nuclear feedback. Our results show that, while vigorous convection is triggered in the postshock region, the global energy budget is primarily governed by neutrino cooling, which effectively balances the accretion power. Crucially, even though our M1 transport scheme captures neutrino absorption and localized heating, the efficient cooling sink and high ram pressure of the infalling envelope prevent the formation of any core-collapse supernovalike explosion. We find that all nucleosynthetically processed material ($T>5\mathrm{GK}$) remains strictly gravitationally bound, challenging the assumption that these systems contribute significantly to galactic nucleosynthetic yields via convective dredge-up. The lack of sustained outflows and the persistent hypercritical accretion rates suggest that embedded NSs will rapidly exceed the Tolman-Oppenheimer-Volkoff mass limit on timescales of minutes to hours. We conclude that these systems are not stable TŻOs but are rather transient precursors to catastrophic black hole formation and potential central engines for high-energy transients.

The origin of a 2.7-kpc-long, narrowly stretched in the plane, vertically sinusoidal, and kinematically coherent complex of dense gas clouds and star-forming regions in the Milky Way Galaxy’s disk near the Sun—the “Radcliffe wave” (RW)”—remains unclear. Analogous large-scale waves, containing young stars that weave above and below the galactic disk, also known as vertical corrugations, have been observed in the stellar disks of nearby rotation-flattened giant galaxies, as well as in the Galaxy. To resolve the issue, we consider a self-gravitating differentially rotating stellar disk of the Galaxy, allowing for noncircular motion of stars. A dispersion relation is derived to describe the collective dynamics of spontaneous bending gravity perturbations developing in the disk by exploring a linear kinetic theory based on the self-consistent system of the Vlasov and Poisson equations. These odd-to-the-mean plane perturbations compress/disperse the medium in spirals perpendicular to its plane and propagate horizontally, making the disk rippled. The self-excitation of oscillatory growing spiral bending waves via the wave-star resonant interaction is proposed to be responsible for the vertically short $\sim 200–300\mathrm{pc}$, still radially long $\sim 2–3\mathrm{kpc}$ wavelength RW rippling outward to the outer parts of the disk. Self-gravity effects are essential for the formation of waves. This is a collisionless phenomenon that relies solely on the kinetic energy exchange between stars and waves; the regular circular rotation represents a free energy source that the stars will decrease as instability develops. It resembles an inverse Landau damping, so a fluid-dynamics description cannot be used to disclose the phenomenon because, in this case, the equations of a theory lose microstructure.

We perform a systematic Bayesian analysis of quark-star equations of state under current multimessenger constraints, with particular emphasis on the roles of prior assumptions, the GW190814 secondary component, and the tidal information from GW170817. Quark matter is modeled within an interacting MIT bag framework that consistently accommodates color-superconducting phases (2SC, $2\mathrm{SC}+\mathrm{s}$, and CFL) together with perturbative QCD corrections. The GW170817 tidal information is incorporated through an explicit event-level likelihood, implemented by reweighting the baseline posterior samples obtained from the remaining observational constraints. We find that quark-star models naturally accommodate the ultra-low-mass object HESS $\mathrm{J}1731-347$, a configuration that is difficult to reproduce in standard gravity-bound neutron-star models. In the high-mass regime, the interpretation of the secondary component of GW190814 is found to be strongly prior dependent: only broad priors admit the substantial stiffness required to support such a massive object ($\sim 2.6M_{\odot }$), whereas narrower priors favor softer equations of state more consistent with standard pulsar populations. At the microscopic level, current data tightly constrain the effective bag parameter and the overall self-bound stiffness scale of quark matter, but do not provide statistically robust discrimination among different color-superconducting phases. We further show that the inference can be reduced to effective three- and two-parameter descriptions without significant loss of constraining power. Our results indicate that, if quark stars exist, their sound speed generally exceeds the conformal limit, $c_s^2/c^2>1/3$, over the density range relevant for stellar interiors.

We investigate isospin-breaking effects in double-charm molecular pentaquarks with the $D^{(*)}{\mathrm{\Sigma }}_c^{(*)}$ configuration, using the one-boson-exchange potential framework. In these systems, the isospin-breaking effects arise from two sources: the strong interaction, which manifests as the threshold difference of the $D^{(*)}{\mathrm{\Sigma }}_c^{(*)}$ components in the same isospin multiplet and the mass splittings of the exchanged isovector mesons ($\pi$ and $\rho$), and the electromagnetic interaction between charged $D^{(*)}$ and ${\mathrm{\Sigma }}_c^{(*)}$ components. We calculate the binding properties and the isospin mixing angle between the $I=1/2$ and $I=3/2$ states of the $D^{(*)}{\mathrm{\Sigma }}_c^{(*)}$ system. Our results show that the isospin-breaking effect contributes a significant correction of roughly 10%–30% to the binding energy. This effect is particularly pronounced in loosely bound molecular candidates, which are characterized by small binding energies and large root-mean-square radii. We therefore conclude that the explicit inclusion of isospin-breaking effects is essential for achieving the precision in theoretical calculations necessary to match rapidly advancing experimental programs. Our results are expected to provide valuable guidance for future high-precision experimental studies of deuteronlike molecular states.

We investigate the decays of $B$ mesons, i.e., $B_d$, $B_s$, $B^{+}$, and their antiparticles, to two light vector mesons ($B\to V_1{V}_2$). We use the SU(2) $U$-spin symmetry, which relates $\mathrm{\Delta }S=0$ and $\mathrm{\Delta }S=1$ decay amplitudes through the interchange $d\leftrightarrow s$ and is an approximate symmetry of the Standard Model (SM), to relate the helicity amplitudes of these decays. Treating all the helicity amplitudes for these decays, and, hence, the reduced matrix elements, as free parameters, we find an acceptable solution within the SM, although this is driven by the fact that the number of observables is smaller than what is needed for a meaningful fit. To reduce the number of free parameters, we then use some apparently reasonable and theoretically motivated approximations, like the dominance of factorizable contributions over the nonfactorizable ones and, hence, a distinct hierarchy between the helicity amplitudes. We find that once the assumption of hierarchy is imposed, there is no solution, both in the exact $U$-spin limit as well as when substantial $U$-spin breaking is allowed for. The tension is primarily driven by the longitudinal polarization fractions in almost all $\mathrm{\Delta }S=1$ decays, which are significantly smaller than the corresponding theoretical predictions based on the SM and $U$-spin symmetry. This is particularly true for $B_s\to K^{*0}\overline{K^{*0}}$, for which the individual disagreement with $U$-spin-based expectation is more than $7\sigma$. Within the SM framework, the only effective resolution would be to entirely disregard the hierarchy between the longitudinal and transverse helicity amplitudes in the heavy-quark limit, as dictated by naive factorization, implying that there must be large nonfactorizable contributions to all these decay amplitudes. We also explore whether some new physics in the $b\to s$ sector that does not respect the hierarchy among the helicity amplitudes can reduce the tension for all the $\mathrm{\Delta }S=1$ modes. While the answer is partially in the affirmative, we find that, for simplistic new physics scenarios, the tension still exists and the fit remains poor enough, if the hierarchy exists among the SM amplitudes. Some possible scenarios for a complete solution of the puzzle are also suggested.

We present an experimentally testable leptogenesis mechanism based on the standard type-I seesaw model that successfully operates at right-handed-neutrino (RHN) masses around the GeV scale. The mechanism takes place in a cosmological background with an asymmetry between right-handed electrons and left-handed positrons generated at high temperatures, and does not require oscillations between RHNs or any $CP$ violation in the combined active-sterile neutrino sector. In contrast to standard leptogenesis via freeze-in, our mechanism works even in the presence of a single RHN around the GeV scale. The mechanism is illustrated for the minimal type-I seesaw with two RHNs, where we show that successful baryogenesis via leptogenesis is viable in large regions of parameter space even without a small mass splitting between the RHNs.

The exploration of exotic hadrons provides a crucial testing ground for quantum chromodynamics in its nonperturbative regime. In this work, we perform a systematic study of the two-body strong decay properties of single-charm molecular pentaquarks in the $Y_c{\overline{K}}^{(*)}$ systems, where $Y_c={\mathrm{\Lambda }}_c$, ${\mathrm{\Sigma }}_c$, ${\mathrm{\Xi }}_c$, and ${\mathrm{\Xi }}_c^{\prime }$. Employing an effective Lagrangian approach combined with hadronic molecular wave functions derived from the one-boson-exchange model, we compute the decay widths and branching ratios for a series of predicted states with strangeness $|S|=1$ and $|S|=2$. Our calculations reveal distinctive decay patterns that serve as fingerprints for molecular identification. The total decay widths vary dramatically, from less than 1 MeV for the narrow ${\mathrm{\Sigma }}_c\overline{K}$ $(I(J^P)=1/2(1/2^{-}))$ state to several tens of MeV for broader coupled-channel molecules like ${\mathrm{\Lambda }}_c{\overline{K}}^{*}/{\mathrm{\Sigma }}_c{\overline{K}}^{*}$. A key finding is the stability of the predicted branching ratios against variations in the binding energy. The decay dynamics are dominated by light meson (particularly pion) exchange, leading to a strong preference for final states containing a charmed baryon and a strange meson. Furthermore, coupled-channel effects and isospin-related interference play essential roles in both the formation and decay mechanisms of specific candidates. The results provide concrete, testable predictions for future experimental searches at facilities such as LHCb and Belle II.

The decay $B^0\to {\mathrm{\Lambda }}_c^{+}{\overline{\mathrm{\Lambda }}}_c^{-}{K}_{\mathrm{S}}^0$ is studied at LHCb for the first time using proton-proton collision data recorded by the LHCb experiment at a center-of-mass energy of $\sqrt{s}=13\mathrm{TeV}$, corresponding to an integrated luminosity of $5.4{\mathrm{fb}}^{-1}$. The branching ratio relative to the decay $B^{+}\to {\mathrm{\Lambda }}_c^{+}{\overline{\mathrm{\Lambda }}}_c^{-}{K}^{+}$ is measured to be [$\mathcal{B}(B^0\to {\mathrm{\Lambda }}_c^{+}{\overline{\mathrm{\Lambda }}}_c^{-}{K}_{\mathrm{S}}^0)]/[\mathcal{B}(B^{+}\to {\mathrm{\Lambda }}_c^{+}{\overline{\mathrm{\Lambda }}}_c^{-}{K}^{+})]=0.53\pm 0.05\pm 0.05$ where the first uncertainty is statistical and the second is systematic. Evidence is found for contributions from two resonant states, ${\mathrm{\Xi }}_c(2923{)}^{+}$ and ${\mathrm{\Xi }}_c(2939{)}^{+}$, in the ${\mathrm{\Lambda }}_c^{+}{K}_{\mathrm{S}}^0$ system. The two states show a significance of $3.9\sigma$ relative to the nonresonant hypothesis. These two ${\mathrm{\Xi }}_c^{+}$ states are consistent with being the isospin partners of the states observed in the ${\mathrm{\Lambda }}_c^{+}{K}^{-}$ system.

We examine three exclusive nuclear ground state shell models implemented in the NEUT neutrino event generator and benchmark them against the recent ${\mathrm{JSNS}}^2$ measurement of missing energy using a monoenergetic neutrino source. The nature of the measurement allows a detailed investigation of nuclear ground-state modeling using a neutrino source, and gives access to a direct measurement of the neutron spectral function in a ${}^{12}\mathrm{C}$ nucleus. The NEUT intranuclear cascade and nuclear deexcitation nucdeex are used to simulate inelastic final-state interactions and nuclear deexcitations respectively. We find that the spectral function models perform better than relativistic mean field models in modeling both the ground state and the tail of the missing energy distribution when the NEUT cascade and nuclear excitation channels are turned on. We also find that taking into account the missing energy threshold for single nucleon knockout interactions results in all nuclear models being accepted based on the obtained $p$-values.

We explore the combined lepton and hadron kinematic observables from the exclusive Valencia $2p2h$ model. We present variables of interest that are available due to the exclusive kinematics and compare them with the democratically distributed outgoing nucleon kinematics as currently treated in neutrino event generators. We also show the effect of nuclear rescattering based on the NEUT semiclassical cascade. We comment on the observability of these variables in current and future long baseline neutrino detectors.

We study how to recover timelike worldlines in AdS from CFT data as a toy model for holographically reconstructing realistic observers. We give a bulk extremization procedure that determines composite timelike-spacelike geodesics that connect timelike-separated boundary points. The total geodesic length matches the length extracted from CFT correlators at the timelike-separated points. We show agreement in Poincaré AdS, for generic boundary points in global AdS, and also for the Bañados-Teitelboim-Zanelli solution, in which the timelike segment probes behind the horizon. We refine related methods to compute timelike entanglement entropy in ${\mathrm{AdS}}_3/{\mathrm{CFT}}_2$ and recover known results.