We study the primary constraint structure of Newer General Relativity, a gravity theory based on a torsionless teleparallel geometry. The gravitational action is built from a scalar formed by quadratic combinations of the nonmetricity tensor, with arbitrary coefficients $c_i$ in the Lagrangian. We decompose the Lagrangian and compute the canonical momenta conjugate to the metric. We characterize the primary constraints arising from these momenta by identifying when the map between velocities and momenta becomes non-invertible, and organize the outcome through a fully nonlinear decomposition into scalar, vector and tensor sectors. Comparing with previous results in the literature, we recover five and three primary constraints associated with the tensor and vector sectors, respectively. We also identify a previously unreported degeneracy in the scalar sector, which yields either one or two scalar primary constraints depending on the conditions imposed on the parameters $c_i$. Finally, we obtain the primary constraints associated with the covariant formulation of symmetric teleparallel gravity. less

We develop a theoretical framework to describe the full interaction between vector vortex light fields and gravitational waves (GWs). Using perturbation theory and the canonical quantization of the electromagnetic field, we calculate the quantum transition probabilities of vector Bessel beams propagating through GWs. We demonstrate that GWs induce fourteen different quantum transition channels across orbital angular momentum (OAM) $l$ and spin angular momentum (SAM) $σ$, mapping initial states $\ket{σ,l}$ to $\ket{σ+Δσ,l+j-Δσ}$, where $Δσ\in \{-2, 0, 2\}$ represents the change in SAM and $j \in \{-3, \dots, 3\}$ denotes the change in total angular momentum. Among these channels, SAM-conserving transitions between OAM states, specifically $\ket{σ, l}\rightarrow \ket{σ, l\pm 1}$, provide the most viable mechanism for experimental detection. Conversely, spin-flip transitions are shown to be heavily suppressed relative to OAM transitions. Additionally, the reversal of SAM induces an asymmetric shift in the OAM transition channels, reflecting the underlying coupling between SAM and OAM during the gravitational interaction. Based on these transition channels, we propose a new cavity-based GW detection configuration. By relying on quantum transitions rather than macroscopic arm-length changes, this scheme is inherently insensitive to displacement-based disturbances like seismic noise, offering a new paradigm and frequency bands for GW observation. less

We investigate the geodesic structure and optical appearance of compact objects with primary scalar hair in shift- and parity-symmetric beyond Horndeski gravity. The analytic solution considered here depends on a theory parameter and a dimensionless mass parameter \cite{Bakopoulos:2023sdm}. For a fixed theory parameter, varying the mass traces a family of static spacetimes that can interpolate between timelike naked singularities, regular solitons, regular black holes, Reissner-Nordström-like black holes, multi-horizon black holes, and Schwarzschild-like black holes. We classify these branches by their horizon structure and analyze null and timelike geodesics, focusing on light rings, innermost stable circular orbits, and static spheres. We then compute thin-disk optical images by ray tracing. We find that the number of horizons is not directly encoded in the image: horizonless objects can show shadow-like central depressions, while multi-horizon black holes can closely resemble single-horizon black holes when their exterior light ring and disk structures are similar. Thus, the optical appearance is governed mainly by the photon potential and the disk inner edge, with the deeper horizon structure leaving only an indirect imprint. Quantitative radial-profile diagnostics confirm that the degeneracy is mainly morphological: the profiles differ at fixed impact parameter, but become much closer after rescaling by the critical impact parameter. These results provide a concrete example of how distinct compact object branches in beyond Horndeski gravity can share similar observational signatures. less

We study black hole (BH) formation from the nonlinear growth and collapse of primordial perturbations during the matter-dominated era. Modelling cold dark matter (CDM) as pressureless dust, we describe the collapse in a fully nonlinear relativistic framework using the Lemaître-Tolman-Bondi (LTB) and quasi-spherical Szekeres solutions as exact perturbations of a spatially-flat Friedmann-Lemaître-Robertson-Walker (FLRW) $Λ$CDM background. At first order in relativistic scalar perturbation theory, the growing mode of any relevant quantity can be expressed in terms of the conserved gauge-invariant curvature perturbation $\mathcal{R}_c$, which acts as a potential for the 3-curvature of hypersurfaces orthogonal to the matter 4-velocity. We use this result to express the active gravitational mass and curvature functions of the LTB and Szekeres models in terms of the initial values of $\mathcal{R}_c$ and its spatial derivatives. From these initial curvature data we derive: (i) the turn-around, collapse, and apparent-horizon formation times, and (ii) the regularity conditions required for BH formation. We show that sinusoidal and Gaussian profiles do not provide viable BH-forming channels, whereas broad compensated curvature peaks, naturally predicted by peak theory, do. We then estimate the formation times of $10^{3}-10^{6}~\mathrm{M}_\odot$ massive BH seeds produced by the direct collapse of primordial CDM curvature peaks, finding full BH formation at redshifts $z>5$, with core collapse beginning at $10 \lesssim z \lesssim 16$. Finally, we characterize the local dynamics and singularity type of the collapse (point-like, cigar-like, or pancake-like) directly from the initial comoving curvature data, clarifying the role of the initial shear in selecting the collapse end-state. less

We extend the frequency-domain analysis of quasinormal modes in a dynamical, spherically symmetric black hole spacetime undergoing constant-rate mass evolution. In particular, we report a novel feature of the spectrum: the presence of purely imaginary eigenvalues in addition to the usual light-ring modes. We study the frequencies of these modes both analytically and numerically. The analytical calculation uses a novel formalism based on recent advances in connection coefficients of Heun functions. We then compute the frequencies numerically using a spectral method on hyperboloidal slices and find excellent agreement between the two approaches. Finally, we validate the frequency-domain results against an independent set of time-domain simulations. Our analysis shows that the purely imaginary modes govern the late-time signal through exponentially decaying tails. In the Schwarzschild limit, both frequency- and time-domain studies consistently show that the purely imaginary modes give rise to the familiar Schwarzschild power-law tail. less

The possibility that Dark Matter (DM) is partially or totally constituted by stable Planckian remnants of light Primordial Black Holes (PBHs), suggested for instance by Loop Quantum Gravity (LQG), is investigated. Distinct phenomenological regimes are identified, including scenarios that trigger an early matter-dominated epoch. New constraints are derived on the initial PBH and final remnant abundances. We show that a significant initial abundance of PBHs lighter than $10^3$ kg would overproduce Planckian relics, implying that any observational evidence for such PBHs would challenge models with quasi-stable remnants. Conversely, the products of Hawking radiation from PBHs with masses between $10^3$ and $10^{12}$ kg impose that Planckian relics could only be a highly subdominant DM component. We identify a PBH mass around $10^3$ kg for which Hawking evaporation naturally reheats the Universe while the remnants entirely constitute the present-day DM. Such a scenario does not require fine-tuning the initial abundance of PBH of this mass, which could range from $10^{-10}$ to order one. These early-Universe cosmologies yield distinct observational signatures: scalar-induced gravitational waves sourced by primordial or Poisson fluctuations that are amplified by the early PBH-dominated era. Current and future observations of LIGO/Virgo/KAGRA, the Einstein Telescope and LISA, as well as probes of the effective number of relativistic degrees of freedom, can be used to probe and constrain the initial PBH abundance and the present-day abundance of Planckian relics. less

Non-singular gravitational theories are expected to be relevant in the early universe. In this paper, we derive a set of effective Friedmann equations describing the dynamics of matter shells in the presence of a gravitational regulator $\ell$. We find that such a regulator induces a primordial black hole mass gap such that below a certain mass $M_\text{gap}(\ell, R_H)$ no black holes can form. The order of magnitude of this mass gap is set by the regulator $\sim c^2\ell/G$, with subleading dependence on the horizon radius at time of formation $R_H$. Finally, we show that over a wide range of equation of state parameters $ω= 0 \dots 1/3$, the mass gap implies a Carr criterion of the form $δ_H > 2G M_\text{gap}/R_H - 1$. If the horizon size is of the same order of the regulator, $R_H \sim \ell$, this new criterion is stronger than the traditional Carr criterion for primordial black hole formation. This connects the primordial black hole abundance directly to the presence of gravitational regulators. less

We investigate thin-disk imaging of Kerr black holes with synchronized scalar hair, focusing on backreacted parity-odd excited states of a complex scalar field minimally coupled to Einstein gravity. The spacetime displays a core-double-torus lensing structure, with a central black hole surrounded by two scalar clouds. We study the dependence of the images on hair strength and viewing angle, identifying a weak-hair regime close to Kerr. With increasing hair, the photon ring and shadow region shrink and become more distorted. In the strong-hair regime, gravitational lensing produces new features, including multiple disconnected shadow components, crescent-shaped structures, and signatures of chaotic lensing. For nearly edge-on viewing angles, repeated equatorial crossings generate nested ring-like patterns. These results highlight possible geometric signatures of black holes with excited scalar hair. less

A new two-parameter asymptotically flat (AF) toric gravitational instanton is identified as a special case of the Euclidean double Kerr-NUT solution, by imposing certain symmetry and regularity conditions on its rod structure. These conditions are solved explicitly, except for one which takes the form of a fifth-order polynomial. This gravitational instanton has Euler number $χ=4$ and Hirzebruch signature $τ=0$, and its global topology is $\mathbb{C}P^2\#\overline{\mathbb{C}P^2}$ with a circle $S^1$ removed appropriately. It is the third of an infinite sequence of AF toric gravitational instantons that was proved to exist by Li and Sun, the first two being the Kerr and Chen--Teo instantons. It is also the first known example of a Ricci-flat gravitational instanton that is not Hermitian. less

With the multitude of gravitational wave observations that have been made in the past ten years, probing the dynamical and nonlinear nature of strong gravity is becoming more and more feasible. One promising way to test the nonlinear nature of Einstein's theory of general relativity (GR) is through the gravitational wave null memory effect: a nonlinear prediction of GR which corresponds to initially comoving observers being permanently displaced due to a burst of gravitational radiation. Previous studies have shown that, while it is unlikely that the memory effect will be observed in a single event by the LIGO-Virgo-KAGRA (LVK) detectors, evidence for memory in the population of LVK events should be attainable after $\sim$2,000 gravitational wave detections. These works, however, largely relied on Bayes factors to perform their memory analyses: an approach that can depend sensitively on the analysis priors and, when naively multiplied across many events, can even favor incorrect conclusions. In this work, using the GWTC-4.0 catalog of binary black hole observations, we instead perform hierarchical Bayesian inference -- which is not subject to the issues associated with Bayes factors -- to measure the evidence for memory in current LVK observations. We find that we can constrain what we call the memory enhancement factor -- the constant appearing in front of the contribution to the strain from the supermomentum flux -- to $0.32^{+6.30}_{-5.12}$ (with $\pm$ values denoting the 68% credible interval), consistent with its GR value of 1. We forecast that $\sim$2,500 detections will be needed to constrain the memory enhancement factor away from zero at the $1σ$ level. less