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Accurate predictions of gravitational wave signals from asymmetric compact binaries are accessible through black hole perturbation theory and self-force calculations. Faithful waveform models will require contributions from first- and second-order terms in the small mass-ratio expansion. The problem of second-order Kerr perturbations is exacerbated by non-separability of the metric perturbation equations and non-linear mode coupling, which motivates this $m$-mode approach. This work moves towards the eventual goal of second-order Kerr perturbations by calculating first-order Schwarzschild metric perturbations via $m$-modes in the frequency domain for the first time. We solve the Lorenz gauge field equations as a system of coupled elliptic partial differential equations that govern each $m$-mode. Our Mathematica code implements a second-order finite difference representation of the field equations, which we solve as a sparse linear algebra problem. Regularization near the small body is achieved through the effective source method, and our presentation introduces a new puncture expansion of the singular field for a point mass in Kerr spacetime. Issues related to problematic near-horizon behavior are explored and then mitigated by applying sophisticated near-horizon boundary conditions. Our results illustrate the features of each component and $m$-mode of the metric perturbation, and we are able to calculate gravitational wave energy fluxes with sufficient accuracy to enable future second-order self-force calculations.

The spatial relationship between young and evolved massive-star tracers offers a means of probing recent star formation across galactic disks. We combine JWST/NIRCam, Swift/UVOT UVW2, and GALEX FUV/NUV images to investigate the spatial association between red-supergiant (RSG) candidates and UV-selected star-forming complexes (SFCs) in the spiral galaxy NGC 5584. We identify 5,310 RSG candidates using colour-magnitude criteria and define 106 UV-selected SFCs from the UVOT/UVW2 morphology, with their FUV and NUV luminosities measured independently using the GALEX images. We find that 82 % of the UV-selected SFCs overlap significant RSG overdensities, indicating a galaxy-wide statistical association between UV-bright SFCs and the evolved massive-star population. Among the 93 SFCs with reliable JWST coverage, the UV-β-corrected FUV and NUV luminosities correlate tightly with the JWST/NIRCam luminosities, with Pearson correlation coefficients of r = 0.962-0.971. MIST isochrone comparisons for 43 RSG-rich SFCs indicate a characteristic age of log (age/yr) ≃ 7.16. These results show that RSG overdensities and UV-selected SFCs trace related but distinct phases of recent massive-star formation. Their spatial correspondence is statistical rather than one-to-one and likely reflects differences in stellar age, dust extinction, spatial resolution, aperture coverage, and local star-formation history.

The general relativity may not be the final theory of gravity. One possible way to look for the gravity theory beyond general relativity is considering variable gravitational constant. Based on the quantum field theory, the gravitational constant as the coupling constant of gravity interaction may change along with the energy scale. Such scale dependent behavior of the gravitational constant can be well described by the functional renormalization group. In the current work, we investigate such behavior systematically. Firstly we find that such behavior is qualitatively independent of interactions such as the electromagnetic interaction included or not. But quantitatively the behavior is governed by two to-be-determined parameters. In general a limit scale may be introduced by the scale dependence of the gravitational constant. If we assume all physical scales are feasible, the two parameters are limited in some special regions. And more we compare the scale dependence behavior to the existing observations. We find the observation results constraint the two parameters strictly.

The Lambert $W$ (LW) model for the cosmic fluid equation of state was proposed by S. Saha and K. Bamba in 2019-2020. A recent (early 2026) paper by Dubey, et al, carries out a new fit of the LW model to observational data, in order to estimate the model's parameters. That paper exhibits a formula for the logarithm of the relative Hubble factor at redshift $z$, $\ln(H(z)/H_0)$, which is based upon a numerical integration. That integral can be evaluated analytically, and we present the details in this working paper. The resulting analytic expression for $H(z)/H_0$ may be convenient for exploration of the LW model.

Four-fermion interactions appear in effective descriptions of particle physics, many-body systems, and gravitational theories with fermions. Although the same local operator may enter perturbative scattering, a vacuum Nambu-Jona-Lasinio (NJL) instability, or finite-density Bardeen-Cooper-Schrieffer (BCS) pairing, these regimes are distinguished by their interaction channels, quadratic kernels, and quantum states. We give a pedagogical functional account of these distinctions and compute the local one-loop contribution of a scalar-channel NJL mean field to the energy-momentum tensor in curved spacetime. We first display the state data in the in-out functional and construct the closed-time-path functional required for an in-in expectation value. For the NJL saddle, a Hubbard-Stratonovich field shifts the fermion mass, and the parity-even Dirac determinant generates local volume, curvature, and curvature-squared operators. We find the covariant quantum effective action before specializing to a spatially flat FLRW background and derive the corresponding energy density and pressure. The constant-condensate limit agrees with the direct flat-space mean-field calculation. We also explain which additional state and channel data are required for finite-density BCS pairing and comment on renormalization conditions in curved spacetimes.

We present several representations of the Schwarzschild spacetime. Some of these are classical, such as the embedding, Tortoise, and Kruskal representations. The latter two motivate the introduction of pulsating coordinates (or the Diamond representation), a compact approach recently proposed for spherically symmetric static metrics. We then introduce the Golden representation for the Schwarzschild spacetime, where what we call the Fibonacci metric, and the golden ratio, become ubiquitous. We conclude by offering some visual and physical interpretations of this approach.

We present a numerical method that constructs geometrically defined coordinates on black-hole horizons, from which the multipole moments are computed without assuming axisymmetry. This method, which we denote the conformal-mapping method (CMM), provides a numerical realization of the conformal construction proposed by Ashtekar et al. in 2022, combining discrete Ricci flow, spectral embedding onto the unit sphere, and Möbius gauge fixing by the vanishing-area-dipole condition. We first test the CMM against analytic Kerr benchmarks, and then apply it to an equal-mass, non-spinning binary black-hole merger. We also compare it with an approximate-symmetry-based method. The CMM allows the multipole moments to be expressed in a fixed reference frame, whereas the symmetry-adapted frame can reorient abruptly when the preferred approximate axis changes. In a frame aligned with the orbital angular momentum, the amplitude of the quadrupole mode grows during inspiral and decays after merger, displaying a qualitative ringdown behavior. These results show that the CMM is a useful tool for studying horizon geometry in dynamical situations where no stable symmetry axis is available.

In this paper, to reconstruct the equation of state (EOS) of dark energy (DE) $w(z)$ with the redshift binning method, we first introduce a $w_i$CDM model with a piecewise-constant EOS in $7$ redshift bins. Then, we turn to the Learning the Universe Implicit Likelihood Inference (LtU-ILI) pipeline to perform a multi-round ILI of $w_i$ from the cosmological data combination, including $TT$, $TE$, $EE$ and lensing power spectra of Planck 2018, distance ratios of DESI DR2 and corrected apparent magnitudes of SNIa from Pantheon+ sample. More precisely, we build the Cosmic Microwave Background (CMB) power spectrum, Baryon Acoustic Oscillation (BAO) distance ratio and Type Ia Supernovae (SNIa) apparent magnitude simulators by $\mathtt{CLASS}$ and embed them into the LtU-ILI pipeline. And, using Sequential Neural Likelihood Estimation (SNLE), we sequentially train neural networks with $6$ rounds of total $6\times20000$ simulations to target a ``black box'' likelihood of our forward model $w_i$CDM. Finally, with the estimated posteriors of $w_i$, we find that except for the unconstrained $w_5$ and $w_6$ (the last two bins), our reconstruction of $w(z)$ marginally favors dynamical DE in the first bin and is consistent with the cosmological constant at $68\%$ C.L. in the other bins.

We challenge the common belief that if there is no absolute time parameter in physics, a quantum system described without reference to an external clock can be assumed to be in a stationary state of its Hamiltonian. We present a time-reparameterisation invariant quantum evolution law, which for a given initial condition predicts the same trajectory in state space as the Schrödinger equation, except that for nontrivial trajectories it does not predict the speed at which the trajectory is traversed. The solutions of this evolution law are all time-reparameterised solutions of the Schrödinger equation. We show how the predictions of the Schrödinger equation are recovered relative to an internal clock in this framework. In contrast to the Page-Wootters formalism or Dirac's quantisation of the Hamiltonian constraint, here the global sate is not stationary. We discuss the assumptions leading to the common conclusion that the state can be taken stationary and suggest that they need to be revisited.

We aim to test the validity of the CIE framework in the ICM by performing line diagnostics based mainly on resolved Fe-K emission lines. Methods. We analyse Resolve full-array spectra of 17 galaxy clusters. Prominent Fe-K line components (the Fe xxv w, x, y, z, and Fe xxvi Lyα1,2 lines) are removed from plasma emission models and instead fitted with Gaussian profiles, enabling direct measurements of line fluxes without relying on synthetic spectral models. Some cool-core systems show w/z ratios lower than predicted by about 20 per cent, and a broader w than z, consistent with resonant scattering effects. The y/x ratios exhibit marginal deviations from model predictions for some objects, suggesting possible origins of cascade process due to electron recombination and contribution from low-ionised Fe. The Fe Lyα2/Lyα1 ratios are globally close to the expected value of about 0.5, and the samples with good photon statistics prefer 0.55. This subtle excess is consistent with an unresolved contribution to Lyα2 from the magnetic-dipole (M1) transition, which is absent from one of the atomic codes considered here. More interestingly, systems at around 7 keV preferentially exhibit Lyα2/Lyα1 ratios above 0.55. Although the statistical significance of this trend is limited, it suggests that resolved Fe Lyα spectroscopy may provide a sensitive probe of additional atomic processes to collisional excitation, including dielectronic and radiative recombination and polarisation effects.

We construct a novel class of black bounce solutions within General Relativity, sourced by a canonical scalar field non-minimally coupled to linear electrodynamics, establishing a self-consistent framework in which regular black holes and traversable wormholes are supported by ordinary bulk matter, with the necessary exoticity confined to an infinitesimally thin defect at the bounce.

Relativistic quantum-information studies in noninertial and black-hole settings often determine resource behavior through explicit calculations for particular input states and state functionals, leaving unclear whether the recurring monotonic trends originate from those choices or from a common underlying structure. In this work, we formulate the effective single-mode fermionic horizon transformation as a pair of complementary exterior and interior quantum channels, corresponding respectively to the physically accessible and inaccessible sectors, and establish exact post-processing orders in opposite directions. As the relativistic channel parameter $q$ increases, the exterior channel becomes progressively degraded, whereas the interior channel is ordered in the reverse direction. These relations extend to arbitrary multipartite settings. Consequently, every state functional that is non-increasing under the corresponding intermediate maps is non-increasing in homogeneous exterior sectors and non-decreasing in homogeneous interior sectors. The framework therefore applies to broad classes of quantum resources and correlations, including entanglement and occupation-basis coherence monotones, optimized Bell-functional quantities, and contractive-divergence correlation measures. We further numerically evaluate collective coherence based on the quantum Jensen-Shannon divergence (QJSD) in the Garfinkle-Horowitz-Strominger (GHS) dilaton-black-hole spacetime, illustrating the predicted homogeneous monotonicity. The recurring trends are therefore traced to a common channel-ordering structure, while the physical setting determines the parameterization of $q$ and the resource-theoretic monotonicity determines which output-state quantities inherit the order.

We investigate the thermodynamics of the apparent horizon in an exponential $f(Q)$ gravity model characterized by the two parameters $b$ and $n$, within a spatially flat Friedmann--Lemaître--Robertson--Walker background and the coincident gauge. Focusing on the $n=1$ solution, we use the approximate cosmological solution for the Hubble parameter up to second order in the exponential parameter $b$ to study the redshift evolution of the apparent-horizon radius and the Kodama--Hayward temperature. We formulate Hayward's unified first law in terms of the Misner--Sharp--Hernandez mass, the work density, and the energy-supply vector, and show that the horizon dynamics admits an equilibrium thermodynamic description. The associated entropy differential is proportional to $f_Q+2Qf_{QQ}$, yielding exponentially suppressed corrections to the Bekenstein--Hawking area law and recovering $S=A/4$ in the limit $b\to0$. We then examine the generalized second law (GSL) by including the entropy of matter inside the apparent horizon. When the matter and horizon temperatures are identified, we adopt the GSL viability criterion $f_Q+2Qf_{QQ}\geq0$ previously derived in the literature. The observationally motivated best-fit values of $b$ satisfy this condition over the redshift interval studied and produce departures from $Λ$CDM mainly at late times. In contrast, sufficiently large positive values, approximately $b>0.26$, can violate the GSL in the future region $z<0$. These results show that apparent-horizon thermodynamics provides a complementary constraint on the parameter space of exponential $f(Q)$ cosmology.

We present an analysis of the perturbative modes of dissipation in the minimal warm inflation model where an axion-inflaton is coupled to a gluon thermal bath through the axion-gauge coupling. The corresponding friction coefficient, which generically is governed by IR physics, for the processes we consider is dominated by Landau damping of soft space-like gluons and the plasmon decay of hard on shell gluons. Since both of these processes are IR dominated, the friction coefficient becomes sensitive to the non-perturbative magnetic mass scale $m_{g}^{-1} \sim (αT)^{-1}$ which in turn leads to the friction coefficient's overall linear proportionality to $α$, which is much less suppressed in $α$ powers compared to the well understood term from Chern-Simons (CS) diffusion $(\propto α^5)$. On the other hand, this contribution to the friction coefficient is suppressed due to slow roll. We show that this can be viewed as a suppression of local spontaneous CPT violation for derivative couplings in general and that time correlations of nonlocal variables which do not fall off at large time separations are what allow an unsuppressed friction coefficient.

We study gravitational wave production from strongly supercooled first-order phase transitions while consistently tracking the evolution of the cosmological background. Our analysis includes the reheating process that ends the period of thermal inflation and restores radiation domination. We find that this background evolution leaves the spectral shape largely intact, except for a causality-driven tail on super-horizon scales. However, for sufficiently slow transitions, the peak amplitude and frequency exhibit a weaker dependence on the transition rate β than the usual scaling of <mml:math><mml:mrow><mml:mo>∝</mml:mo><mml:msup><mml:mi>β</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> and ∝β, respectively.

We investigate the nonseparability of multipartite bosonic and fermionic $GHZ$ and $W$ states in a causal diamond spacetime using the Abe-Rajagopal (AR) $q$-conditional entropy. The finite lifetime of the observer gives rise to a causal diamond horizon, which induces an Unruh-like thermal effect and leads to a nontrivial restructuring of nonseparability in $N$-partite systems. Our main result is that the thermal effect can enhance a net nonseparability of fermionic $W$ states, in sharp contrast to the general expectation that relativistic thermalization leads to a monotonic degradation of bosonic nonseparability. In addition, we find that fermionic nonseparability is generally more robust than its bosonic counterpart under causal diamond restrictions. Among different entangled resources, $GHZ$ states exhibit stronger nonseparability and greater robustness than $W$ states under identical causal conditions. We further show that the nonseparability of $W$ states decreases with increasing particle number $N$, whereas that of $GHZ$ states remains independent of $N$ in causal diamond spacetime. These results demonstrate that particle statistics, entanglement structure, and observer lifetime jointly determine the persistence of nonseparability in causally restricted spacetimes, providing insights for relativistic quantum information processing.

We study radial nonlinear instability of compactly supported nonrotating equilibria of the three-dimensional Euler--Poisson system with a physical-vacuum boundary. Let $n^u(μ)$ denote the radial instability index furnished by the turning-point theory of Lin and Zeng. Under general structural assumptions on the pressure law, suppose that $n^u(μ)>0$ and that the equilibrium is not a mass extremum, $M'(μ)\neq0$. Conditional on the existence of a sufficiently regular radial solution on the relevant time interval, we establish two nonlinear escape criteria. First, every perturbation with Hamiltonian strictly below that of the equilibrium exits a fixed neighborhood on a logarithmic time scale controlled by the least unstable linear growth rate. For the subclass of data for which the associated Lyapunov functional is initially nonnegative, we also obtain an explicit exponential lower bound in the weighted displacement norm. Second, sufficiently small perturbations whose Riesz projection onto the finite-dimensional unstable subspace is not too small escape on a logarithmic time scale. The second argument uses the exponential trichotomy of the linearized Hamiltonian flow and an invariant-cone estimate. In the polytropic class, the conditional estimates combine with the radial physical-vacuum local theory to yield unconditional nonlinear instability in the corresponding classical-solution topology. The results complement Jang's nonlinear instability theorem for Lane--Emden stars by treating mechanisms that do not require initial alignment with a leading growing eigenmode and by applying, conditionally, to unstable branches for general equations of state.