Accurate quantification of ocean tide loading (OTL) is essential for sustainable coastal geodetic monitoring, infrastructure stability assessment, and the interpretation of GNSS vertical displacement time series. This study analyzes long-term vertical displacements observed at the Palmido GNSS station, located in Korea’s largest tidal-range environment, to resolve dominant semi-diurnal and diurnal tidal constituents. Coherent-gain–corrected Fast Fourier Transform (FFT) and continuous wavelet analysis were applied to decompose the GNSS time series, with particular emphasis on the principal lunar (M2) and principal elliptical lunar (N2) constituents. The extracted tidal amplitudes and phases were benchmarked against the NAO99 ocean tide loading model after applying load Love number (LLN) and site-scale corrections. Quantitative evaluation demonstrates that the corrected NAO99 predictions reduce the root mean square difference (RMSD) of the M2 constituent from approximately 14.5 mm to 13.3 mm (≈8% improvement) and that of the N2 constituent from about 2.1 mm to 1.2 mm (≈40% improvement), compared to uncorrected model outputs. Linear regression analyses further show that amplitude scaling improves toward unity for M2 after correction, while maintaining strong phase coherence. Continuous wavelet scalograms reveal persistent semi-diurnal energy with a clear fortnightly modulation, whereas diurnal components appear intermittently and are more sensitive to local environmental conditions. These results demonstrate that combining coherent-gain–corrected FFT, time–frequency wavelet diagnostics, and physics-based NAO99 benchmarking significantly enhances the reliability and interpretability of GNSS-derived tidal loading estimates. The proposed workflow provides a transferable and reproducible framework for high-precision coastal deformation monitoring and long-term sustainability assessments in macrotidal environments.

We extract the equation of state of hot quark matter from a holographic 2 + 1 flavor quantum chromodynamics (QCD) model, which could form the core of a stable compact star. By adding a thin hadron shell, a new type of hybrid star is constructed. With the temperature serving as a parameter, the EoS varies and we obtain stable stars with mass ranging from about 5 to 30 solar masses, and the maximum compactness around 0.2. The I-Love-Q-C relations are further discussed, and compared with the neutron star cases. These compact stars are candidates for black hole mimickers, which could be observed by gravitational waves and distinguished by properties like nonzero tidal Love number and electromagnetic signals.

A bstract We study tidal Love numbers of static black holes in four-dimensional quadratic theory of gravity, extending the result of GR. We use worldline effective field theory (WEFT) methods to compute metric perturbations from one-point functions, treating the higher-derivative terms perturbatively. We show that insertions of scalar fields on the worldline induce non-zero tidal tails, and the corresponding Love number displays no RG running. The same conclusion holds for the insertions of tensor fields. Furthermore, for scalar dipole perturbations, we derive a Yukawa-deformed Frobenius solution and match the asymptotic behavior to fix the UV charge, finding agreement with EFT predictions of Wilson coefficients. Our work demonstrates that quadratic higher-curvature corrections induce non-zero but scale-independent tidal responses, offering a robust EFT framework to test deviations from GR in gravitational wave observations.

We introduce a novel method to compute gravitational wave amplitudes within the framework of effective field theory. By reinterpreting the Feynman diagram expansion as a Born series, our method offers several key advantages. It directly yields partial wave amplitudes, streamlining the matching with black hole perturbation theory. Long-distance gravitational interactions are unambiguously factorized from short-distance tidal effects, including dissipation, which are systematically incorporated via an in-in worldline effective action. Crucially, at every order in perturbation theory, integrals are expressed in terms of harmonic polylogarithms, enabling an end-to-end computation scalable to arbitrary orders. We illustrate the method with new predictions for scalar black hole Love numbers and their renormalization group equations to O(G^{7}).

In this article, we study scalar wave perturbations of arbitrary frequency to the five-dimensional (5D) Schwarzschild-Tangherlini black hole (STBH) within general relativity. For the first time, we derive a closed formula for the 5D partial wave gravitational Raman scattering amplitude applicable to a broad class of boundary conditions, expressed in terms of the Nekrasov-Shatashvili (NS) function for the reduced confluent Heun problem. Furthermore, up to O ( G 2 ) we compute the dynamical ℓ = 0 , and the static ℓ = 1 , scalar tidal Love numbers of the STBH by matching an effective field theory description for a scalar wave scattering off the black hole, to our novel ultraviolet-NS solutions. The matched Love numbers do not vanish and present renormalization group running behavior.

Gravitational wave constraints were investigated on quantum gravity effects through the Generalized Uncertainty Principle (GUP), focusing on tidal deformability modifications in neutron star binary systems. Our comprehensive analysis demonstrates that GUP corrections systematically alter the Love numbers characterising stellar response to external tidal fields, leading to measurable changes in gravitational wave phase evolution during the inspiral phase of binary mergers. Employing detailed stellar structure calculations with GUP-modified equations of state, we compute the tidal deformability parameter for neutron stars across the observed mass range and rigorously assess the detectability of quantum gravity signatures with current and next-generation gravitational wave detectors. Through Bayesian parameter estimation using data from GW170817 and subsequent LIGO-Virgo detections, we derive the constraint at 95% confidence level on the GUP parameter, representing the most stringent gravitational wave limit to date. Our projections indicate that third-generation detectors, including Einstein Telescope and Cosmic Explorer, will enhance this sensitivity by more than an order of magnitude, potentially reaching through analysis of approximately 1000 neutron star merger observations accumulated over five years of operation. These results establish gravitational wave astronomy as a powerful probe of fundamental physics, demonstrating the complementary nature of multi-messenger constraints on quantum gravity theories and providing crucial guidance for theoretical developments in the quantum gravity research program.

Abstract Quantifying tidal effects on giant planets has recently made significant advances, thanks in particular to the Cassini space probe. During its thirteen-year orbit around Saturn, numerous measurements from different instruments made it possible to characterize fundamental parameters such as Saturn’s Love number k2 and quality factor Q at different frequencies. In this article, we summarize the various measurements and methods that have allowed to arrive at such a result, as well as the extrapolations that can be deduced for other systems. More generally, the state of the art concerning the four giant planets of the Solar System is presented, as well as the case of exoplanets.

We provide further evidence that information is preserved during black hole evaporation and may be recoverable, provided quantum gravitational effects resolve the singularity. We demonstrate that due to quantum gravity effects, black holes acquire quantum hair, manifested by nonzero tidal Love numbers, revealing a distinct internal structure similar to neutron stars. Interestingly, the magnitude of these Love numbers is Planck-scale suppressed, implying significant tidal deformation in the late stage of evaporation. Depending on the final state of the black hole, information may be retrieved through correlations in Hawking radiation, baby universes or via remnants.

Tidal Love numbers of neutron stars in Horndeski theories

We investigate the moment of inertia, quadrupole deformation, and tidal deformation within the framework of nonlocal gravity, utilizing the exact modified Tolman-VII (NEMTVII) density model with an isotropic perfect fluid. The Love number (k 2) is derived using standard even-parity perturbation theory. Additionally, we explore the observational implications by analyzing the tidal deformability parameter (λtid) in comparison with the constraints from GW170817, GW190425, PSR J0348+0432, and PSR J0740+6620. We found that the results are consistent with the tidal constraint when α ≳ 1.6 with the small β. For slowly rotating object, the dimensionless moment of inertia (I̅), rotational Love parameter (λ̅ rot), and quadrupole moment (Q̅) are fully determined by the perturbed metric. Our findings reveal that the nonlocal parameter (β) significantly affects the star radius. For a fixed β and varying α, the I-Love-Q relations are found to be universal. For varying β, the I-Love-Q relations become non-universal.

Dark matter admixed relativistic stars: Structural properties and tidal Love numbers

Abstract We obtain the full set of tidal Love numbers of non-rotating black holes in an effective field theory extension of general relativity. We achieve our results using a recently introduced modified Teukolsky equation that describes the perturbations of black holes in this theory. We show how to identify the Love numbers and their beta functions in a systematic and gauge invariant way, applying analytic continuation on the angular number ℓ when necessary. We observe that there are three types of Love numbers: electric, magnetic, and a “mixing” type, associated to parity-breaking theories, that we identify here for the first time. The modified Teukolsky equation proves to be very useful as it allows us to obtain all the different Love numbers in a unified framework. We compare our results with previous literature that utilized the Regge-Wheeler-Zerilli equations to compute Love numbers, finding perfect agreement. The method introduced here paves the way towards the computation of Love numbers of rotating black holes beyond general relativity.

We derive the explicit embedding of the effective Kerr spacetimes, which are pertinent to the vanishing of static Love numbers, soft hair descriptions of Kerr black holes, and low-frequency scalar-Kerr scattering amplitudes, as solutions within N=2 supergravity. These spacetimes exhibit a hidden SL(2,R)×U(1) or SO(4,2) symmetry resembling the so called subtracted geometries with SL(2,R)×SL(2,R) symmetry, which accurately represent the near-horizon geometry of Kerr black holes and, as we will argue most accurately represents the internal structure of the Kerr black hole. To quantify the differences among the effective Kerr spacetimes, we compare their physical quantities, internal structures, and geodesic equations. Although their thermodynamic properties, including entropy, match those of Kerr, our study uncovers significant differences in the interiors of these effective Kerr solutions. A careful examination of the internal structure of the spacetimes highlights the distinctions between various effective Kerr geometries and their quasinormal spectra.

Massive states produce higher derivative corrections to Einstein gravity in the infrared, which are encoded into operators of the Effective Field Theory (EFT) of gravity. These EFT operators modify the geometry and affect the tidal properties of black holes, either neutral or charged. A thorough analysis of the perturbative tidal deformation problem leads us to introduce a tidal Green function, which we use to derive two universal formulae that efficiently provide the constant and running Love numbers induced by the EFT. We apply these formulae to determine the tidal response of EFT-corrected non-spinning black holes induced by vector and tensor fields, reproducing existing results where available and deriving new ones. We find that neutral black hole Love numbers run classically for ℓ ≥ 3 while charged ones run for ℓ ≥ 2. Insights from the Frobenius method and from EFT principles confirm that the Love number renormalization flow is a well-defined physical effect. We find that extremal black holes can have Love numbers much larger than neutral ones, up to 𝒪(1) within the EFT validity regime, and that the EFT cutoff corresponds to the exponential suppression of the Schwinger effect. We discuss the possibility of probing an Abelian dark sector through gravitational waves, considering a scenario in which dark-charged extremal black holes exist in the present-day Universe.

Determining the internal composition of planetary bodies remains a challenging problem due to observational degeneracies. In the 2030s, ESA’s Juice mission will orbit Ganymede and provide key constraints on its interior structure, including estimates of the polar moment of inertia, Love numbers, libration amplitudes, and the amplitude and phase of the induced magnetic field due to a subsurface ocean. To impose these constraints in the most effective way, a joint inversion of all available parameters would be ideal. In this work, we applied a machine learning approach to predict the thicknesses and densities of Ganymede’s internal layers, the viscosity of the icy shell, and the ocean conductivity from these observables. We generated a synthetic dataset of plausible internal structures via Monte Carlo sampling and computed the corresponding observables using existing physical models. A neural network was then trained to learn the intricate relationships between them. The trained model retrieves the internal structure parameters with varying degrees of accuracy across different layers. It performs well in predicting the thicknesses and densities of the icy shell and ocean, with mean absolute errors on the order of 10 km and 10 kg m−3, respectively. These errors increase to about 40 km and 20 kg m−3 for the high-pressure ice layer beneath the ocean. The trained model also estimates the shell viscosity with a mean absolute error of 0.05 log10 Pa s, and the ocean conductivity with an error of 0.1 S m−1. However, the neural network performs poorly in the task of inferring the thickness and density of the deeper interior, suggesting limited sensitivity of these parameters to the chosen set of observables. The Monte Carlo dropout method was utilized to estimate the uncertainties in the predicted parameters. These results highlight the potential of machine learning as a fast, preliminary tool for detecting families of internal structures compatible with the observed parameters.

The upcoming Chinese Tianwen-4 mission, featuring both primary and secondary satellites, promises to significantly enhance our understanding of Jupiter's gravity field. We provide here a comprehensive evaluation of its contribution to modeling of Jupiter's gravity field. nm ) associated with the Galilean moons by incorporating spacecraft-to-spacecraft tracking (SST) alongside traditional two-way (2W) observations. We analyze various observational factors, such as orbital altitudes, noise levels, data durations, and tidal responses, to evaluate their impact on gravity field estimation accuracy. Our analysis demonstrates that the combined 2W and SST mode enhances the precision of gravity field estimates by up to an order of magnitude, reducing formal errors, and improving spatial resolution compared to the 2W mode alone, even when using shorter arcs data. Furthermore, the combined mode yields a superior performance in the estimation of Love numbers, with lower orbital altitudes and longer data collection periods further improving accuracy, despite introducing operational challenges. The enhanced sensitivity and accuracy provided by the SST configuration offer valuable insights into Jupiter’s internal structure and dynamics, thereby guiding the design of future missions aimed at maximizing scientific returns.

We present a detailed investigation on the structure of neutron stars, incorporating the presence of hyperons within a relativistic model under the mean-field approximation. Employing coupling constants derived from QCD sum rules, we explore the particle fraction in beta equilibrium and establish the mass-radius relationship for neutron stars with hyperonic matter. Additionally, we compute the stellar Love number (K2) and the tidal deformability parameter (Λ), providing valuable insights into the dynamical properties of these celestial objects. Through comparison with theoretical predictions and observational data, our results exhibit good agreement, affirming the validity of our approach. These findings contribute significantly to refining the understanding of neutron star physics, particularly in environments containing hyperons, and offer essential constraints on the equation of state governing such extreme astrophysical conditions.

The influence of a dark energy fluid on the equation of state of neutron stars is investigated. A detailed analysis is conducted for such models, including the computation of the moment of inertia, the quadrupole moment, and the tidal Love number. The results demonstrate that these quantities are interconnected through the well-known equation of state independent I-Love-Q relations. This work extends the applicability of these universal relations to a broader class of neutron star models.

Abstract We compute scalar static response coefficients (Love numbers) of non-dilatonic black p-brane solutions in higher dimensional supergravity. This calculation reveals a fine-tuning behavior similar to that of higher dimensional black holes, which we explain by “hidden” near-zone Love symmetries. In general, these symmetries act on equations for perturbations but they are not background isometries. The Love symmetry of charged p = 0 branes is described by the usual SL(2, ℝ) algebra. For p = 1 the Love symmetry has an algebraic structure SL(2, ℝ) × SL(2, ℝ). The p = 0, 1 Love symmetries reduce to isometries of the near-horizon Schwarzschild-AdS p+2 metric in the near-extremal finite temperature limit. They further reduce to the AdS p+2 isometries in the extremal zero-temperature limit. We call this process geometrization. In contrast, for the p > 1 cases, the Love symmetry is always an SL(2, ℝ), and there is no limit in which it becomes geometric. We interpret geometrization and its absence as a consequence of the local equivalence between the Schwarzschild-AdS p+2 and pure AdS p+2 spaces for p = 0, 1, which does not hold for p > 1. We also show that the static Love numbers of extremal p-branes are always zero regardless of spacetime dimensionality, which contrasts starkly with the non-extremal case. Overall, our results suggest that the Love symmetry is hidden by nature, and it can acquire a geometric meaning only if the background has an AdS2 or AdS3 limit.

We compute tidal signatures in the gravitational waves (GWs) from neutron star binary inspirals in scalar-tensor gravity, where the dominant adiabatic even-parity tidal interactions involve three types of Love numbers that depend on the matter equation of state and parameters of the gravitational theory. We calculate the modes of the GW amplitudes and the phase evolution in the time and frequency domain, working up to first order in the post-Newtonian and small finite-size approximations. We also perform several case studies to quantify the dipolar and quadrupolar tidal effects and their parameter dependencies specialized to Gaussian couplings. We show that various tidal contributions enter with different signs and scalings with frequency, which generally leads to smaller net tidal GW imprints than for the same binary system in General Relativity.