We study geodesic motion of a test particle in Schwarzschild spacetime. Bound and scattering geodesics are commonly described using Darwin variables, which provide a convenient parametrization of the radial motion. However, this description breaks down at the separatrix and does not extend straightforwardly to plunging trajectories. We construct an analytic continuation of Darwin variables that yields a real parametrization of bound, scattering, and plunging Schwarzschild geodesics, thereby providing a unified kinematical description of all types of test-mass motion. As a proof of concept, we then apply these variables to a simple non-geodesic evolution in which the energy and angular momentum are driven by a constant external force. This toy model is not intended to represent a physical radiation-reaction model, but rather to illustrate how the extended variables can be used to follow an orbit through a transition to plunge using a single orbital phase variable across the separatrix. less

We introduce a fast, one-dimensional Newtonian {reduced model} to capture uniform rotation in cold white dwarfs, encoding centrifugal support as an effective pressure anisotropy. Using $Δ_{\rm rot}(r)=\frac{1}{3}ρ(r)Ω^2 r^2$ derived from the stationary Euler equation with $\langle\sin^2θ\rangle=2/3$, the model incorporates rotation into hydrostatic balance without a two-dimensional solver. Applying the Chandrasekhar degenerate-electron equation of state, we compute interior structures and global sequences for $ ρ_c \in [10^6, 10^{11}]~{\rm g\,cm^{-3}} $ with rotation proxies $f \le 0.35$, finding monotonic increases in limiting mass and radius, with a percent-level mass gain at $f = 0.35$. We quantify applicability using sub-Keplerian diagnostics evaluated on the rotating configurations, $\max(Ω/Ω_K)$ and $\max(ε)$, together with a bulk-interior smallness measure $A_{10^{-2}}\equiv \max_{p_r/p_c\ge 10^{-2}}(Δ_{\rm rot}/p_r)$. Within the scanned domain these diagnostics remain below unity. The model is therefore best viewed as a reduced Newtonian benchmark for slow-to-moderate rotation, not as a replacement for fully axisymmetric calculations of rotating stars. less

Cosmology has entered a precision era in which discrepancies between independent datasets, most notably the $H_0$ and $S_8$ tensions, have become robust and statistically significant. These tensions are no longer isolated anomalies but increasingly appear as global consistency constraints on the underlying cosmological model, defining what we will refer to here as a \emph{consistency triangle} of background expansion ($H_0$), structure-growth amplitude ($S_8$), and the redshift-dependence of growth - summarised by the growth index $γ$, or equivalently the shape of $fσ_8(z)$. The third vertex is non-trivial because in modified-gravity scenarios with a redshift-dependent effective gravitational coupling, growth amplitude and growth shape evolve independently, breaking the rigid coupling characteristic of $Λ$CDM. In this work, we use $f(Q)$ gravity as a test case for this emerging paradigm. By drawing on a focused set of recent Bayesian and dynamical-system analyses of the three best-studied functional families - power-law, exponential, and logarithmic - we show that while $f(Q)$ models can alleviate individual tensions, the requirement of simultaneous consistency across $H_0$, $S_8$ and the growth index severely restricts the viable parameter space. A bulk-viscous extension is then briefly examined as a representative illustration of how additional matter-sector freedom is constrained by the same consistency requirement. Our reading of the current literature supports the view that cosmological tensions should be interpreted as global consistency conditions, and that viable extensions of $Λ$CDM must satisfy this multi-probe constraint \cite{CosmoVerse,DiValentino2025Corfu}. Within this framework, only a restricted subset of $f(Q)$ models remains competitive. less

We investigate spin-induced scalarization of Kerr black holes in an Einstein-scalar-Gauss-Bonnet (EsGB) model that does not admit a linear tachyonic instability of the scalar-free solution. The scalarization mechanism is therefore genuinely nonlinear. We first analyze the decoupled scalar dynamics on fixed Kerr backgrounds and show that sufficiently rapid rotation modifies the Gauss-Bonnet invariant such that a negative near-horizon region develops near the poles. This region provides a geometric trapping mechanism for nonlinear scalar growth, which becomes effective above a threshold spin $χ=0.5$. We then construct stationary scalarized black hole solutions with full backreaction and determine their domain of existence. We find that the solutions occupy a finite low-mass high-spin wedge in the spin-mass plane. This is in contrast to spin-induced spontaneous scalarization, where the scalarized solutions form a narrow band. In this wedge, toward the high-spin end, the scalar hair becomes stronger, and the solutions approach a near-extremal regime, while toward the low-spin boundary, the scalar field is strongly suppressed and approaches a weak-hair limit as $χ\to 0.5$. less

This is a first study of the cosmology of classical fractional gravity, a nonlocal proposal endowed with self-adjoint fractional d'Alembertian operators which serves as the basis for an ultraviolet-complete theory of quantum gravity. We derive the classical covariant nonlocal equations of motion for an arbitrary fractional exponent $γ$ and reduce them to the Friedmann equations on a homogeneous and isotropic cosmological background. We find that de Sitter is an exact stable solution and that bouncing exact solutions are sustained by phantom ($w<-1$) or ghost ($ρ<0$) fluids, in the latter case with a new type of finite-future singularity in the barotropic index. Different representations of the form factor give exactly the same solutions, thus confirming that the formulation of fractional field theories relies on a universality class of form factors. We compare these preliminary results with what obtained in multi-fractional cosmological models mimicking the spacetime geometry of fractional quantum gravity. less

Gravitational Wave (GW) data bring an exceptional avenue to test the underlying models of coalescing compact objects. In the regime of strong gravity and high curvature, they allow the exploration of minute deviations from the best-fit models, which are difficult to uncover with other observational modalities. These deviations can stem from departures from General Relativity (GR) or unaccounted astrophysical effects. They may not be explainable within the current description of GW strain data, or may simply be difficult to model. However, they are expected to be correlated between detectors and across the population of observed events. The recently developed SCoRe analysis pipeline leverages these properties by focusing on the correlated power between detectors and combining results from multiple events. In this paper, we apply the framework on the Third Gravitational-Wave Transient Catalog to search for source-dependent deviations. In particular, we explore whether there is evidence for a mass-scale in the observed events, which can act like a line of demarcation in their physical properties by exhibiting a deviation that is different above and below this mass-scale. This mass scale dependency naturally arises in gravitational theories described through effective field theories, due to environmental effects or in scenarios involving exotic compact objects, where the GW signature can differ from the standard binary black holes in GR. Using the 30 highest Signal-to-Noise Ratio events in the catalog, we find Bayes factors ranging from 0.16--0.5 (depending on where the threshold mass is set), thus disfavoring the hypothesis of existence of any mass-scale between $\sim 2.5$ M$_\odot$ and $60$ M$_\odot$. We also compute the distribution of excess cross-correlated power across events and find a Bayes factor of $0.07$, which agrees with expected noise statistics. less

We derive a class of inner-extremal regular black hole solutions characterized by a degenerate inner horizon. These geometries arise as polymerized vacuum configurations inspired by loop quantum gravity and constitute effective quantum-gravity solutions that admit a Birkhoff-type theorem, rendering them unique within the considered framework. We show that such inner-extremal horizon configurations exist only for a finely tuned value of the mass determined by the parameters of the theory. Building on this construction, together with the corresponding non-degenerate regular black hole solutions, we perform a generic analysis of the mass inflation phenomenon in four-dimensional spacetimes using a colliding null-shell setup near the inner horizon. We identify the conditions under which mass inflation becomes significant and examine how the presence of a minimal length scale affects this behavior, with particular emphasis on the case where such a scale is motivated by loop quantum gravity. Finally, we comment on the stability of these configurations under the null-shell perturbations considered in our analysis. less

We numerically study a formation of near extremal horizons from a gravitational collapse of radially symmetric gravitational waves in $4+1$ dimensions within the framework of pure Einstein gravity with positive cosmological constant. Evolution of a regular initial data with cosmological horizon leads to a formation of a black hole with mass exceeding $99\%$ of the extremal value corresponding to the black hole and cosmological horizons coinciding. We demonstrate how our results fit within the framework of characteristic gluing, and present some evidence that the third law of black hole thermodynamics may not hold in the cosmological context, where the extremality corresponds to the maximal mass of the Schwarzschild black hole in de--Sitter space. less

We prove a low-regularity version of Hawking's singularity theorem for Lorentzian metrics in $W^{1,p}$ with Riemann curvature in $L^p$, where $p>2n$ and $n$ the dimension of spacetime. This extends previous results beyond the Lipschitz regime. Under suitable lower Ricci bounds and upper mean curvature assumptions, expressed in terms of temporal functions, we establish both the globally hyperbolic version of Hawking's theorem, in the form of an upper bound on the time separation from a spacelike Cauchy hypersurface, and the version with a compact achronal spacelike hypersurface, yielding timelike RT-geodesic incompleteness. The proof combines regularisations, based on the elliptic RT-equations, to raise the regularity of the metric by one derivative, with a refinement of the previously used manifold convolution. We introduce a new smeared-out notion of mean curvature adapted to the low metric regularity before, and the $W^{2,p}$-hypersurfaces arising after regularisation. As further consequences, we show that $W^{1,p}$-Lorentzian metrics with $L^p$-bounded curvature are causally plain, and we prove a corresponding low-regularity version of Myers's theorem in the Riemannian setting. less

Dipole-radiation-like deviations from general relativity are most prominent during the early inspiral of compact binaries, making space-ground multiband observations a potential probe of such effects. In the same regime, orbital eccentricity can leave a significant imprint on the waveform and is therefore essential for robust dipole-radiation constraints. For the first time we present a multiband Bayesian inference pipeline for stellar-mass binary black holes that simultaneously incorporates eccentricity and a theory-agnostic dipole-radiation correction. We find strong degeneracies among the dipole parameter, chirp mass, and eccentricity, which substantially weaken the inferred dipole constraints when eccentricity is included. Even so, for a GW231123-like source, one year of TianQin or LISA observation with ground-informed priors from a next-generation detector network can still constrain the dipole parameter to $|b|\lesssim\mathcal{O}(10^{-7})$ under inference with noisy data. Our results show that multiband binary black hole observations provide a promising and distinct channel for testing theory-agnostic dipole radiation, while also highlighting the need for more complete waveform modeling in future precision tests of gravity. less