Papers

Phenomenologically similar sign-switching dark-energy histories need not have comparable scalar-field realizations. We reconstruct minimally coupled scalars with fixed kinetic sign for three prescribed histories: the error-function model (ECDM), the compact smooth-step model (SSCDM), and the ladder-like model (L$\Lambda$CDM). Continuous negative-to-positive density crossings select the phantom branch. ECDM yields a smooth on-shell potential at every finite redshift; its equation-of-state pole at the density zero is only a ratio singularity. Exact SSCDM has a regular trajectory but a $C^1$, non-$C^2$ endpoint potential, $V-V_e\propto|\phi-\phi_e|^{4/3}$. Its non-Lipschitz force permits delayed departures from frozen plateaus, so the reconstructed potential and plateau data do not uniquely generate the prescribed history. The exact Ladder requires distributional kinetic stress and has no ordinary classical realization in the adopted one-field action. In conditional synthetic comparisons, the sigmoid–Gaussian family ranks highest for ECDM and the generalized axion-like family for SSCDM, although the fitted axion exponents $n<1/2$ imply a divergent endpoint force. Representative regular forward solutions exhibit negative-to-positive scalar-density crossings, with the potential zero preceding the density zero. In a closure test, unretuned evolution of the top-ranked ECDM template tracks the target approximately, $\max|\Delta\widetilde\Omega_\phi|\simeq0.16$. Closure fails structurally for compact SSCDM: no potential with a locally Lipschitz force can reproduce its exact finite-duration frozen plateaus from exactly frozen initial data. Field-map existence, invertibility, and endpoint regularity must be assessed before interpreting a phenomenological history as scalar dynamics. The phantom action is used only as a homogeneous effective proxy.

Neutron stars (NSs) provide a unique laboratory for testing gravity in the strong-field regime and for searching for deviations from General Relativity (GR). In this work, we investigate the effects of Energy-Momentum Squared Gravity (EMSG) on NS structure and examine whether its signatures can be identified from observable stellar properties using supervised machine learning (ML). We solve the modified Tolman-Oppenheimer-Volkoff equations for approximately $10^{4}$ nuclear equations of state (EOSs) for EMSG coupling parameters $\alpha=\{-5.01,-2.50,0,+2.50,+5.01\}\times10^{-38}\,\mathrm{erg}^{-1}\mathrm{cm}^{3}$, and calculate the gravitational mass $M$, radius $R$, dimensionless tidal deformability $\Lambda$, and fundamental $f$-mode oscillation frequency for each stellar configuration. Imposing observational constraints on $M$, $R$, and $\Lambda$, we split our datasets into train and test sets, and we employ Random Forest (RF), K-Nearest Neighbors (KNN), Support Vector Machine (SVM), Logistic Regression (LR), and Gaussian Naive Bayes (GNB) to classify the representative sectors $\alpha=\{-5.01,0,+5.01\}\times10^{-38}\,\mathrm{erg}^{-1}\mathrm{cm}^{3}$ using $(M, R,\Lambda,f)$. The RF classifier performs best, achieving an accuracy of approximately $99.85\%$ with precision, recall, and F1-scores exceeding $99.8\%$, while KNN also achieves accuracy above $99\%$. The nearly diagonal confusion matrices demonstrate that the observationally viable NS configurations associated with different EMSG sectors remain highly separable in the multidimensional observable space. Our results show that NS observables retain robust signatures of EMSG even after observational filtering, establishing ML-assisted NS observations as a promising complementary approach for probing modified gravity with current and future multi-messenger observations.

The McVittie metric describes a self-gravitating compact object embedded in an expanding universe. It inherits two singularities: a curvature singularity at $r \to 0$ and a cosmological singularity at $a(t) \to 0$. Motivated by the construction of black-bounce geometries, we regularize both of these singularities and propose a regularized McVittie metric. The central singularity is regularized by replacing $r \to \sqrt{r^{2}+b^{2}}$, leading to a geometry that interpolates between a cosmological black hole, a black bounce, and a traversable wormhole. Similarly, the cosmological singularity is regularized by introducing a non-vanishing scale factor $a \rightarrow \sqrt{a^{2} + a_b^{2}}$. The resulting spacetime is supported by an effective imperfect fluid with finite anisotropic stress. We investigate the formation of the apparent horizon, analyze the circular geodesic structure, and argue that the geometry can also be interpreted as a conformally evolving Morris-Thorne wormhole embedded in a regular cosmological background.

We present NRHJSur3dq8, a family of numerical-relativity (NR) surrogates for non-eccentric aligned-spin binary-black-hole waveforms inspired by an action-angle parameterization. The model provides both the dynamics: the Hamiltonian values, azimuthal action $J_\phi(\Phi)$, the orbital clock $\tau(\Phi)$ as functions of its phasing, and the radiative pieces: the waveforms, their near-analytic derivatives, and modeling errors associated with each. The surrogated variables are conditioned into pieces that vary slowly on the radiation-reaction timescale, represented on shared $hp$-adaptive Chebyshev elements, and regressed across the intrinsic parameters with a Gaussian-process model. A time-parameterized merger-ringdown set of elements is attached where the adiabatic description breaks down. Leave-one-out validation of the central NRHJSur3dq8_AA flavor against NR reaches a $(2,2)$ unweighted mismatch of $1.3^{+32}_{-1.2}\times10^{-6}$ and an all-mode mismatch of $2.3^{+59}_{-2.2}\times10^{-6}$ over the full inspiral-merger-ringdown span. Sky-averaged and SNR-weighted over $32$ orientations per simulation, the released model's full-IMR in-sample mismatch against the NR simulations used for training is $8.9\times10^{-7}$ to $2.8\times10^{-5}$ across total masses $40$-$120\,M_\odot$. Waveforms are hybridized using post-Newtonian waveforms. Beyond accuracy, NRHJSur3dq8 provides two capabilities uncommon in NR surrogates: nearly analytic derivatives of the strain with respect to the physical parameters, and a calibrated Gaussian-process predictive uncertainty of the model. A full non-hybridized inspiral-merger-ringdown waveform evaluates in $12$ ms on a single CPU call. Batched evaluation amortizes this to $0.39$ ms per waveform at a batch of $4096$, measured at a starting frequency of $20$ Hz.

Gravitational-wave searches do more than identify individual sources - they provide a way to infer the underlying astrophysical populations that produce them. Currently, Pulsar Timing Arrays (PTAs) constrain the supermassive black-hole binary (SMBHB) merger-rate density through both the stochastic gravitational-wave background (SGWB) and searches for individual SMBHB signals. The latter implies converting source upper limits into rate upper limits using detection efficiencies estimated empirically. We instead develop a hierarchical Bayesian framework that places the SMBHB merger-rate density model directly inside the PTA likelihood. The unknown catalog of individual SMBHB merger signals is modeled as a Poisson point process on source-parameter space, so that the number of merger signals is inferred from the data rather than imposed by a detection threshold. We describe two computational routes: a catalog-marginal likelihood based on analyses with fixed numbers of candidate sources, and an explicit transdimensional sampling approach that jointly samples population hyperparameters, latent merger signals, and noise. We validate the method with a toy merger-only population model and then apply it to an astrophysical SMBHB merger-rate density model that jointly predicts the SGWB amplitude and the expected merger-catalog size. In simulations, an individual merger signal adds complementary information to the SGWB and can tighten constraints on the merger-rate population.

Thanks to the almost 400 gravitational wave events detected, we are currently able to grasp the fundamental features of black hole mass, spin, and distance distributions. However, such a fast increase in the precision of the measurements does not necessarily correspond to a better theoretical understanding of gravitational wave sources, especially in current scenarios where the number of free parameters is significantly larger than the number of inferred properties of the black hole population. In this work, we showcase how the landscape of theoretical models can be chipped away by complementary data-analysis strategies, in particular by studying the statistical properties of gravitational wave anisotropic distribution. Specifically, we show how gravitational wave clustering is sensitive to two unique features of each binary formation mechanism: the time-delay distribution and the properties of the binary hosts. First, we consider a model-agnostic scenario and show the impact that different time-delay distributions have on the gravitational wave bias. Then, we consider a realistic scenario where gravitational wave events are sourced either by isolated binary evolution or dynamical processes in globular clusters, and study how the gravitational wave bias is unique sensitive to the specific properties of the environment. In both scenarios, we show how the cross-correlation between galaxy and gravitational wave catalogs is able to distinguish between models with different time delays or with different binary sub-populations originated in specific formation channels.

We investigate three flavor neutrino phenomena in an effective holonomy corrected Schwarzschild geometry. We derive the weak-deflection angle through second post-Minkowskian order, obtain the semiclassical phases along radial and nonradial trajectories, and formulate the two-image flavor probability by including magnifications, Fermat phases, and wave packet overlap. The cross path phase acquires a logarithmic holonomy contribution and can retain information about the absolute neutrino mass scale. We also characterize flavor mode correlations and trajectory-flavor entanglement through the balance among path predictability, interference visibility, and I-concurrence. Neutrino-antineutrino annihilation outside an effective neutrinosphere is examined, with holonomy entering the integrated power through the radial proper volume measure. For a solar mass lens and $10\,\mathrm{MeV}$ neutrinos, the numerical results show displaced oscillation fringes and a geometry dependent redistribution among the electron, muon, and tau channels. The electron-neutrino trajectory-flavor concurrence reaches approximately $0.23$, with an entropy near $0.10$ bit, while remaining weakly sensitive to the mass ordering in the selected configuration. By contrast, the annihilation power increases monotonically, reaching an increase of approximately $39.3\%$ relative to Schwarzschild spacetime (for a particular configuration, i.e., $\lambda=2$ and $M/R_{\nu}=1/3$). Furthermore, at fixed source parameters and $M/R_\nu=1/3$, an assumed maximum excess of $10\%$ in the integrated annihilation power relative to Schwarzschild yields the conditional bounds $a/(2M)\leq0.2879$ and $|\lambda|\leq0.6358$.

Supermassive black holes (SMBHs) in "little red dots" (LRDs) discovered by the James Webb Space Telescope (JWST) may result from runaway mergers of primordial black holes (PBHs) in clusters—through long-short mode coupling on small scales in the early Universe. In this framework, we derive the SMBH mass function, together with the compactness and overmassive features of LRDs. We also estimate that the dense gas residing in PBH clusters is consistent with LRD observations. In addition, SMBHs formed from PBH clusters can help accelerate galaxy formation at high redshifts, thus alleviating tension with $\Lambda$CDM cosmology.

Currently, the only second-order gravitational self-force calculations have been based on directly solving the perturbative Einstein equations in the Lorenz gauge. That method relied on the complete separability of the Einstein equations in a Schwarzschild background. In this paper, we present a new scheme based on the second-order Teukolsky equation. Crucially, this method promises to extend (reasonably straightforwardly) to the more realistic case of a Kerr background. Here we implement the scheme in the simplest setting of quasicircular orbits around a Schwarzschild black hole. In addition to working with the Teukolsky equation, our scheme incorporates several other advances over previous second-order self-force calculations: compactified hyperboloidal slicing, transformation to a Bondi-Sachs gauge, and a combination of spectral and variation-of-parameters methods. We also use these tools to re-examine the infrared divergences that arise in second-order Lorenz-gauge calculations, showing they are less pronounced in the Teukolsky case and completely eliminated in the Bondi-Sachs gauge. We conclude by calculating the asymptotic energy fluxes and benchmarking them against previous Lorenz-gauge calculations.

The recent observations of the supermassive black holes M87* and Sagittarius A* by the Event Horizon Telescope collaboration (EHT) have shown the need for robust, efficient, and accessible numerical tools to model light propagation in strongly curved spacetimes. Comparing theoretical accretion models with observational data relies heavily on ray-tracing algorithms that calculate the trajectories of photons traveling from a source plasma to a distant observer. In this paper, we present TARTARUS (Tracer for Astrophysical Ray Trajectories Around Relativistic Ultra-compact Sources), a new, highly modular, and extensible Python-based framework for computing null geodesics around compact objects. By leveraging Just-In-Time (JIT) compilation via Numba, TARTARUS bridges the gap between Python's high-level accessibility and the execution speed of compiled languages like C++ or FORTRAN. The code supports multiple native solvers (including adaptive embedded Runge-Kutta pairs, a Bulirsch-Stoer extrapolator, and a Verlet scheme), event-detection mechanics for handling structural intersections (e.g. event horizons and accretion disks), and support for both analytical and numerically generated background metrics. We demonstrate the code's physical accuracy and computational efficiency through some tests, including the evaluation of the Hamiltonian constraint conservation and ray-tracing of the shadow and the Novikov-Thorne thin accretion disks around a Kerr black hole.

Can a universe undergo a regular Euclidean-Lorentzian signature transition when the gravitational coupling itself is dynamical? We address this question in scalar-tensor gravity with nonminimal coupling $F(\phi)R$. Although the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) sector can be mapped to the Einstein frame for $F>0$ and a nondegenerate scalar redefinition, not all transition properties are frame independent. For a finite, positive, and sufficiently regular conformal factor, the existence and transverse character of the type change are preserved, whereas the extrinsic geometry is not. We therefore use the Einstein frame as a solution-generating representation and impose total geodesy in the physical Jordan frame. We construct two exactly integrable classes of solutions. In the oscillator-ghost-oscillator branch, the scalar field is stationary at the transition and Jordan-frame total geodesy follows under suitable regularity assumptions on the conformal factor. In the critical exponential-potential branch, the scalar is generically nonstationary and total geodesy instead requires \begin{equation*} H_E\big|_\Sigma = \frac12 \left( \frac{d\ln F}{d\psi} \right)_\Sigma \dot\psi_\Sigma . \end{equation*} We also distinguish this condition from the stronger smoothness requirements of a Kossowski-Kriele-type transverse metric. Finally, while the canonical Einstein-frame scalar does not allow effective phantom evolution, the dynamical nonminimal coupling can generate a locally superaccelerating Jordan-frame regime near the transition when $\left(\frac{d\ln F}{d\psi}\right)_\Sigma>0$ for the chosen oscillator branch. Thus signature change persists beyond Einstein gravity, with regularity and effective cosmological behavior remaining intrinsically frame sensitive.

This is a concise and compact introduction to a framework for spacetime, gravity, and fundamental physics based on the IKKT matrix model, focusing on conceptual and structural aspects. The approach rests on nontrivial vacua or matrix backgrounds, which serve as 3+1-dimensional noncommutative spacetime. We discuss a specific class of backgrounds describing expanding homogeneous and isotropic FLRW spacetime, which provide a solution of the one-loop effective action with finitely many dof per volume. Perturbations of the background give rise to fields propagating on spacetime governed by a weakly-coupled gauge theory, as well as a nonstandard description of (quantum) gravity leading to some IR modifications. Maximal supersymmetry of the model is essential to ensure effective locality.

We investigate the dynamics of a neutral scalar particle in a charged traversable wormhole background, considering harmonic and modified harmonic oscillator couplings. By solving the Klein–Gordon equation, the radial problem is reduced to a generalized Heun equation, whose polynomial truncation yields the bound-state energy spectrum and quantized oscillator frequencies. Although the particle is electrically neutral, the energy spectrum depends indirectly on the wormhole charge through the geometric deformation of spacetime. We also analyze the dependence of the oscillator frequency on the angular momentum, throat parameter, electric charge, and the additional interaction parameter $V_{0}$. The appropriate limits recover the corresponding results for the uncharged wormhole and the standard harmonic oscillator.

Continuous-wave searches for rotating neutron stars usually cover wide parameter spaces and produce a large number of candidate signals. Stochastic sampling methods therefore play an important role in candidate follow-up and parameter estimation. We present the integration of the Bayesian inference library BILBY into the open-source continuous-wave analysis package PyFstat, enabling access to the broad range of stochastic samplers available through BILBY while preserving the existing PyFstat analysis infrastructure. The implementation is validated through injection studies in Gaussian noise for two representative single-stage follow-up configurations: candidates from a directed search and candidates from an all-sky search. Using the nested sampler DYNESTY, we obtain detection efficiencies consistent with the theoretical sensitivity predictions. In this setup, DYNESTY performs comparably to the existing PTEMCEE-based implementation of PyFstat for the directed case, and also provides an effective single-stage approach for the all-sky candidate follow-up considered here, where we did not identify a PTEMCEE setup with similar recovery performance. Percentile-percentile tests for DYNESTY further show well-calibrated credible intervals, demonstrating reliable parameter estimation. While a full exploration of DYNESTY settings, multi-stage setups, and other samplers is left for future work, these results demonstrate that this flexible and publicly available framework opens useful new possibilities for Bayesian continuous-wave analyses.

We establish spacetime counterparts of fill-in inequalities for spin initial data sets satisfying the dominant energy condition in dimensions three through seven, controlling the minimum and the integral of the norm of the spacetime mean curvature vector by intrinsic boundary data. The proof relies on a Reilly–MIT estimate for complete spin manifolds with compact boundary. As further consequences, under suitable nonnegativity assumptions, Gromov's hyperspherical-radius fill-in inequality and Bär's recent total mean-curvature estimate extend to complete, possibly noncompact spin manifolds with compact boundary.

Unsupervised analysis of gravitational-wave detector data combines expensive scientific stages with data acquisition, provenance checks, statistical calibration, follow-up products, and reporting. Reproducing such an analysis requires more than preserving model weights or a final candidate table: the execution graph, scientific contracts, retry semantics, and verification boundary must also be explicit. We present a local workflow layer for the Domain-Adaptive Network for Transient Evaluation (DANTE) that represents a corrected O4a analysis as a content-addressed, 15-stage directed acyclic graph. The architecture separates immutable stage evidence from mutable operational progress, binds command-line and browser interfaces to the same run identity, and resumes only work compatible with the frozen contract. The tagged v1 release records all 15 stages as verified in a machine-readable receipt and passed a documented human usability gate. The release verifies adopted scientific artifacts rather than recomputing them, and therefore makes no new claim of global significance, astrophysical discovery, or public real-time operation. This paper describes the architecture, its fail-closed controls, and the bounded evidence supporting reproducible local use.

In this article we provide a systematic reduction to static spherical symmetry for (classical) gauge theoretic models with structure group SU(2) x U(1), coupled to gravity. In particular, we derive the most general static spherically symmetric ansatz for the Einstein-Yang- Mills-Higgs-Dirac-Yukawa equation system. This model is reminiscent of the lepton sector of the Standard Model coupled to gravity. The resulting total system of ordinary differential equations is rather large, so that finding global solutions is non-trivial. For this reason, an open-source interactive solver GUI written in C++ is provided together with the article.

Uniform acceleration induces a thermal response to the Minkowski vacuum and can thereby modify quantum correlations. For measurement-induced nonlocality (MIN), a form of nonclassical correlation distinct from entanglement, previous field-mode analyses of bosonic fields found that it decreases with increasing acceleration and vanishes in the infinite-acceleration limit. This raises the question of whether the disappearance of MIN is a generic consequence of the Unruh effect or depends on the physical description of the accelerated quantum system. To address this question, we study two uniformly accelerating Unruh-DeWitt detectors interacting with a massless scalar field. We find that the response of MIN to the Unruh temperature depends sensitively on the initial detector state: it can decrease monotonically, vanish at an intermediate temperature and subsequently recover, or increase monotonically. Moreover, for a broad class of initial states, MIN approaches a nonzero value in the high-temperature limit. These results show that the suppression of MIN under strong acceleration is not universal. Instead, Unruh-induced detector dynamics gives rise to a state-dependent response in which measurement-induced nonlocality can be suppressed, restored, or enhanced.

Motivated by the singularity theorems of Poincaré Gauge (PG) theory, we investigate extensions of the Holst quadratic model by introducing cubic order invariants constructed from the curvature and torsion tensors into the gravitational action. Such models are characterised by a kinetic structure that is governed by a pseudoscalar mode, whereas the remaining irreducible modes of torsion contribute through nonlinear interactions that can have important implications for the space-time geometry. In particular, in line with other well-known models of PG theory, the Birkhoff theorem does not hold in general, allowing for new exact static and spherically symmetric black hole solutions with dynamical torsion. Across the different torsion sectors, corresponding to the irreducible modes and parity components of the torsion field involved in the analysis, we find both singular and regular configurations. Among the singular solutions, we obtain Kiselev-like and Boulware-Deser-like geometries, as well as new geometries with distinct algebraic and Lambert $W$ metric corrections. In addition, we find regular black holes with both primary and secondary torsion hair, which evade the singularity theorems through violations of the causal convergence conditions induced by the nonlinear torsion interactions. Therefore, we show that Holst-type PG models can support a rich variety of black hole geometries, while providing explicit mechanisms for evading the singularity theorems of PG theory.

We revisit gravitational decoherence of matter superpositions using the leading soft sector of the graviton $S$-matrix. Starting from Weinberg's soft theorem and the overlap of coherent radiation states, we derive, for branch configurations with the same total four-momentum, a gauge-invariant, nonnegative leading-soft decoherence exponent and evaluate the polarization sum and angular integrals exactly at this order. In the vacuum, coherence between branches with distinguishable soft radiation vanishes as the infrared cutoff is removed. The leading nonrelativistic term is purely quadrupolar as a consequence of energy–momentum conservation. We extend the analysis to single- and two-mode squeezed graviton states, including the two-mode case motivated by inflation. Squeezing can enhance or suppress decoherence depending on the relative phase, while phase averaging gives an enhancement governed by the graviton occupation. For a phase-averaged relic background with an approximately flat energy-density spectrum over the relevant soft frequency band, the sharp-cutoff identification of the infrared scale with the inverse observation time gives a contribution that grows with the gravitational-wave energy density and with the fourth power of the observation time. These results connect soft-graviton scattering, infrared quantum information, and decoherence in nonvacuum gravitational backgrounds.

Tidal disruption events (TDEs) offer a unique dynamical probe of the spacetime geometry around supermassive black holes (SMBHs). While conventional TDEs occur around SMBHs of $M_\bullet \sim 10^6 - 10^7 M_\odot$, where stars are disrupted far from the event horizon, here we identify a special class of TDEs around rapidly spinning SMBHs with masses $M_\bullet \gtrsim 10^8 M_\odot$, where the tidal-disruption radius approaches the gravitational radius. We term these events "near-horizon TDEs" and, by calculating geodesics in Kerr spacetime, investigate how the proximity of the horizon modifies the debris evolution and subsequent fallback. We find that for stars encountering the SMBH on parabolic orbits, up to $\sim (90 \%-95 \%)$ of the stellar debris either plunges directly into the SMBH or escapes the system. Bound orbits, by contrast, retain a substantially larger fraction of the debris. Using the resulting debris distribution, we calculate the fallback rates and find that bound orbits produce intrinsically higher peak fallback rates and shorter decay timescales, by factors of $\sim 10^3$ relative to parabolic orbits. However, when the stellar orbital angular momentum is particularly low, the peak fallback rate can be substantially suppressed by debris lost to plunge orbits. This combination of rapid fallback and a mass deficit naturally explains overluminous TDEs such as ASASSN-15lh, which standard TDE models have struggled to reproduce. Our work establishes near-horizon TDEs as a new probe of strong-field gravity and a promising tool for identifying massive, rapidly spinning SMBHs.

We present an iteration algorithm for vacuum and Einstein scalar-field equations in double-null gauge, which transform the non-linear PDE into systems of ODE. The numerical realization combines characteristic constraint solves, LGL spectral elements, pole-free spherical operators, Galerkin projection, and independent first-order residual and consistency checks.

We investigate the Casimir effect of a complex scalar field on a two-dimensional sphere threaded by a fixed Wu–Yang magnetic monopole at the center. In this background the charged scalar field is a section of a nontrivial complex line bundle over $S^2$, reflecting the monopole's nontrivial topology. We solve the Klein–Gordon equation analytically and compute the Casimir energy using a generalized Abel–Plana formula for multivalued functions. We find that the monopole can reverse the sign of the Casimir pressure, turning an attractive force into a repulsive one when the monopole strength is sufficiently large. This behavior persists across a broad range of curvature couplings and suggests that Wu–Yang monopoles may provide a source of repulsive vacuum stress, with possible implications for gravitational and cosmological settings.

We discuss the cosmological dynamics of general teleparallel quadratic gravity. Using a suitable set of variables, we write the cosmological field equations as a homogeneous dynamical system. We find that this system generically features projective fixed points, where the dynamics can be solved analytically, and exhibits finite time singularities as well as an asymptotically vanishing cosmological expansion.

This work focuses on the analysis of particle dynamics and the thermodynamic properties associated with a particular branch of hairy black hole solutions. These solutions are obtained by using extended geometric deformation gravitational decoupling on the seed solution of the Schwarzschild solution. This resulting geometry satisfies the dominant energy condition and the condition $Q^{2}=2\chi\ell M$. We analyze the motion of massive particles and photons in this geometry and the thermodynamics of this solution. In particular, for massless particles, we study the effective potential and determine the radii of the photon sphere and the shadow of the black hole. For massive particles, we calculate the specific energy and angular momentum of circular orbits, the ISCO, the radiative efficiency of an accretion disk, and representative particle trajectories. Finally, we investigate the thermodynamic properties of this hairy black hole geometry, including the Hawking temperature, the Bekenstein-Hawking entropy, and the heat capacity in the fixed-$(Q,\ell)$ ensemble.

Rotating black holes in dynamical Chern-Simons gravity are known nonperturbatively mainly through numerical solutions, which limits their direct use in strong-field applications. We construct a Kerr-referenced analytical parametrization of the near-general-relativistic numerical branch using a compact radial coordinate, low-order angular multipoles, and continued fractions. The resulting two-parameter family accurately reproduces the numerical metric throughout the validated weak-coupling and moderate-spin domain. Independent off-grid solutions confirm that the parametrization retains its accuracy away from the calibration set. We further assess the model through equatorial light rings, critical impact parameters, and full two-dimensional null-geodesic ray tracing without assuming separability. The resulting shadow observables closely match those obtained from the numerical geometries. This parametrization therefore provides a practical analytical metric for geodesic and strong-field calculations without relying on a slow-rotation expansion.

We present a simple model of a higher dimensional spacetime in which the 4d submanifold is a FLRW metric, while the extra dimensions are compactified to a hypersphere. We calculate the Friedmann equations of this model finding that the extra dimensions interact in a non-trivial way with the 4d submanifold evolution. We prove that what is observed as Dark Energy could be explained only as an effect due to the Gaussian curvature and the expansion rate of the extra dimensions. We calculate the luminosity distance in this model and derive the acceleration parameter q. We find that {\Omega}m and q are in some sense dressed by terms coming from the extra dimensions, thus a Universe filled only with matter (both luminous and dark) and with extra dimensions can explain the observational data. We find that the extra dimensions do not affect the CMB spectrum, but this is not a solution to the Hubble tension. We fit our model to SNe data and find evidence for the presence of 3-4 extra dimensions which are presently contracting.

We investigate extremal black holes with scalar hair in the generic Einstein-Euler-Heisenberg (EEH)-scalar theory with two scalar couplings to the Maxwell term. One is an exponential coupling with coupling constant $\alpha$ and the other is its polynomial coupling. We first construct scalarized black holes on the cold (C)-horizon of EEH black holes described by mass $M$ and magnetic charge $P$ both at the linear level, through the existence curves $\alpha_n(q)$ with $q=P/M$, and as fully backreaction solutions. As extremality ($q=q_e$) is approached, all existence curves accumulate, following $\alpha_n-\alpha_c\sim 1/\ln^2(q_e-q)$, at the critical branch $\alpha_c$ fixed by the Breitenlohner-Freedman bound for the near-horizon (AdS$_2\times S^2$) throat. We obtain scalarized extremal black hole (SEBH) with constant secondary hair and it is recovered exactly from the entropy function approach working on the near-horizon throat. Its entropy is an attractor invariant, being independent of the asymptotic modulus, so the scalar hair remains secondary. Exploiting this constant scalar, we seek further SEBHs with scalar hair keeping its charge $Q_s$ for the zero asymptotic scalar ($\phi_\infty=0$). In the $(q,\alpha)$ plane, we observe that these extremal solutions occupy $q\ge q_e$. Hence, the existence curves $\alpha_n(q)$ existing for $q\le q_e$ and the extremal branches bound the scalarized domain from opposite sides and they meet only at $q=q_e$.

The symmetry content of static spherical $f(R)$ gravity is reconsidered for the pure quadratic model. We first derive the radial action without prematurely eliminating the equation carried by the radial metric variable. The Schwarzschild-type gauge may then be imposed while retaining its associated gravitational constraint. For the resulting system, radial translations and one combined scaling are exact off-shell Noether symmetries. The scaling charge reduces, on the constraint surface, to a conserved radial flux of the scalar curvature. The same flux follows independently from the trace of the four-dimensional field equations. Noether invariance, the strong point-Mei criterion, and Lie invariance of the Euler–Lagrange system are examined separately. Within the full polynomial point ansatz of total degree at most two, the Lie algebra contains precisely three independent generators. The flux also separates the solution space into a nonzero constant-curvature Einstein sector, a degenerate scalar-flat sector, and a dynamical-curvature sector. In particular, the scalar-flat sector permits a Reissner–Nordström-form metric, although its inverse-square coefficient has no electromagnetic meaning in the absence of a Maxwell field.

Gravitational-wave denoising must handle the full diversity of spinning, precessing binaries, since the recovered waveform underpins parameter estimation, tests of general relativity, and population studies. Matched filtering achieves this at a cost that becomes prohibitive as next-generation detectors push event rates higher; deep learning offers real-time reconstruction, but current methods are developed on narrow parameter spaces, precluding principled comparison and reliable deployment. We present the first controlled comparison of five neural-network architectures for gravitational-wave denoising, trained identically across the full astrophysically-motivated spinning binary-black-hole parameter space. A unifying principle emerges: matching network structure to the spectral anatomy of a coalescence – inspiral, merger, ringdown – outperforms brute-force model scaling. Our Multi-Scale Frequency-Aware architecture embodies this via dedicated parallel branches per frequency regime, achieving the best fidelity while using fewer parameters than larger models. It generalizes from simulated training to real LIGO-Virgo-KAGRA data without retraining, recovering merger morphology across confirmed events spanning three observing runs and both detectors, despite training on a single detector's simulated noise. We construct population-level uncertainty bands from denoising residuals, validate their calibration, and stress-test the framework on extended mass ratios and a spin population resembling hierarchical-merger remnants. Applied to real noise with no known signal, the network suppresses its output almost everywhere, with rare exceptions traced to noise transients rather than a general weakness – indicating the statistic discriminates signal from noise and motivating a future detection study. Released weights give a deployable, reproducible benchmark for future extensions.