Search Results (364)

The effective-one-body (EOB) formalism accurately describes the conservative dynamics of general binary orbits, but current implementations of radiation reaction remain largely limited to quasi-circular inspirals. Extending EOB to eccentric orbits currently requires the corresponding post-Newtonian (PN) energy fluxes in EOB coordinates, which are only known to 1PN order. In this paper, we compute the instantaneous gravitational-wave energy flux in EOB coordinates to 2PN accuracy using a systematic coordinate transformation between the Arnowitt–Deser–Misner (ADM) and EOB phase-space variables. We derive the 2PN-accurate transformation laws for the relative coordinates and velocities between the two coordinate systems and re-express the 2PN instantaneous energy flux entirely in EOB variables. Working within the EOB test-particle framework (with finite mass ratio $\nu$) for an equatorial elliptic orbit, we adopt a Keplerian reparameterization in terms of the semilatus rectum p, eccentricity e, and two phase variables $(\xi ,\varphi )$ associated with the radial and azimuthal motion, which makes the calculations more transparent and facilitates the subsequent computation of gravitational waveforms. Using the conservative orbital angular frequency, we compute the orbit-averaged energy flux. In addition to the energy flux, we also compute the corresponding 2PN angular momentum flux in EOB coordinates using the same transformation method. Our results, expressed in gauge-invariant variables $x={\left(M\omega \right)}^{2/3}$ and eccentricity $e_t$, agree with known PN results and show improved accuracy compared to the 1PN EOB fluxes of Hinderer and Babak. Full article

This paper presents a further step in the development of scale invariant fully conformal cosmology (FCC), formulated in our previous study. Whereas the previous paper focused mainly on the global cosmological consequences of the fully conformal metric and their confrontation with selected astrophysical data, here we analyze its local gravitational and background consequences. On the background of the fully conformal metric we formulate an effective generalization of the weak Schwarzschild field in the corresponding FCC global coordinates and derive from it the associated modified intensity of the Newtonian central field. We further derive the cosmological state/constitutive equation p = − ε/3 as a direct consequence of the fully conformal metric rather than as an ad hoc additional postulate. Likewise, within the fully conformal metric, spatial flatness and the critical density ρ_crit are understood as direct consequences of this metric structure rather than as independently postulated inputs. From the condition of global equilibrium between negative cosmological pressure and the gravitational cohesive pressure of homogeneously distributed matter, the effective particulate fraction is obtained as β ≈ 0.45 of the total critical density ρ_crit. For the relatively well-confirmed baryonic matter fraction ${\overline{\mathrm{\Omega }}}^{bar} \approx 0.05$, this stable-equilibrium condition then leads to the corresponding particulate fraction of collisionless dark matter ${\overline{\mathrm{\Omega }}}_{FCC}^{dm} \approx 0.40$, which is in principle determined by the global cosmological equilibrium within this framework. Because direct identification of the entire dark fraction with standard collisionless cold dark matter would very probably be incompatible with the main structural observables, we discuss an effective phenomenological decomposition into a structuring cold dark matter component (cdm) and an almost homogeneous residual warm-dark-matter-like component (wdm). In this interpretation, the paper preserves the previously introduced global FCC framework while simultaneously providing a concrete background prediction for the matter content and a physically motivated basis for further testing of structure formation within scale invariant fully conformal cosmology. Full article

We propose an exploratory framework for a Bohmian model of quantum matter propagating on a classical curved spacetime background. The gravitational sector is governed by classical Einstein field equations throughout; no quantisation of spacetime is attempted. The wave function emerges as the scalar contraction $\mathrm{\Psi }={\psi }_{\nu }{\psi }^{\nu }\in \mathbb{C}$ of a complex-valued tensorial field ${\psi }^{\mu }$, encoding quantum dynamics in a geometric object. The wave tensor interacts with spacetime via the stress–energy tensor $T_{\mu \nu }$, mediated by a real scalar field a of dimension volume, so that $a{T}_{\mu \nu }{\psi }^{\mu }{\psi }^{\nu }$ yields the correct potential energy. We derive a covariant Adapted Schrödinger Equation as the unique minimal covariant lift of the standard equation, justify it from four guiding principles, and verify three internal consistency checks. Under seven explicit approximations the framework reproduces the Schrödinger equation with Coulomb potential for the hydrogen atom. We also derive a dynamical equation for ${\psi }^{\mu }$ that entails the Adapted Schrödinger Equation by contraction. Two open problems are then resolved. First, a complete Lagrangian formulation is provided: a real-valued action for $\mathrm{\Psi }$ yields the Adapted Schrödinger Equation via the Euler–Lagrange equations; a separate action for ${\psi }^{\mu }$, extended by a non-polynomial term, yields the full dynamical equation variationally. Second, two experimental predictions are derived. Expanding to first post-Newtonian order, the perturbation Hamiltonian has coefficients $(3, 1)$ on the kinetic and potential operators; via the virial theorem these produce a coordinate-time blueshift, which after photon propagation yields the universal Einstein gravitational redshift $\delta \nu /\nu =\mathrm{\Phi }/c^2$, confirming consistency with the equivalence principle. The same kinetic coefficient independently predicts that free quantum wave packets spread more slowly by the fractional amount $3\left|\mathrm{\Phi }\right|/c^2$, a correction absent in standard non-relativistic quantum mechanics. Full article

It is well known that axions or axion-like particles can mediate spin-dependent interactions. If such interactions exist, they may violate the equivalence principle of general relativity, causing a polarized fermion with nonzero mass to experience different gravitational effects for different spin orientations. In this work, we derive the spin-dependent gravitational interaction generated by a spherically symmetric celestial body and apply the formalism to the Earth. We compare existing experimental searches for spin-dependent gravitational effects with the constraints implied by axion-mediated interactions. We further note that a rotating polarized neutron star may generate a time-dependent spin–mass interaction field acting on an unpolarized probe mass, which could be detected with high-frequency, high-Q torsion oscillators. Full article

(1) Background: For the study of highly magnetized neutron stars observed as magnetars and to quantify the effect of this intense magnetic field on the star’s structure and shape, which can be particularly relevant for the study of the emission of continuous gravitational waves, both numerical and perturbative approaches have been developed. (2) Methods: We compare these two approaches in General Relativity with the limitation to the case where the magnetic field has a purely poloidal structure. The perturbative one assumes that the deformation induced by the magnetic field is small and that this field arises only from dipole currents. The fully numerical one is based on the lorene library. (3) Results: We used both approaches to compute the magnetic-field distribution and the deformation of the star, varying the value of the magnetic field at the pole, the compactness of the star and its equation of state. (4) Conclusions: Whereas the perturbative approach breaks down for very high polar magnetic-field values (typically above a few times ${10}^{16}$ G), it achieves very good results for observed values, even in magnetars. On the contrary, the numerical code exhibits resolution problems for relatively low magnetic-field values (typically ${10}^{10}$ G), which translates into imprecise computation of the star’s deformation and mass quadrupole moment. Full article

A generalized mathematical model is constructed to describe the isothermal two-phase flow of a three-component system and to investigate light non-aqueous phase liquid (LNAPL) displacement during surfactant-enhanced remediation in vertical porous media. The model integrates the dominant physical mechanisms governing immiscible fluid redistribution, including gravitational and capillary forces under different wettability conditions. The hyperbolic part of the system is analyzed within the framework of a Riemann problem, allowing for the characterization of shock and rarefaction wave formation in saturation and concentration profiles. Numerical simulations performed using a first-order upwind (FOU) scheme reveal pronounced artificial dissipation, as confirmed by von Neumann stability analysis. To overcome this limitation, a high-order non-oscillatory scheme based on nonlinear flux limiters and polynomial reconstruction is developed, enabling accurate resolution of sharp displacement fronts. A comparative analysis of limiter functions reveals that their suitability depends on the degree of nonlinearity in relative phase permeabilities, highlighting the necessity for careful selection in multiphase flow modeling. Parametric investigations quantify the effects of gravity, capillary parameters, Peclet number, and wettability alteration on displacement efficiency in homogeneous porous media. The proposed framework is validated against experimental MRI data, demonstrating its reliability for describing two-phase displacement in porous media. Overall, the developed numerical model provides a predictive framework for resolving nonlinear front dynamics and optimizing surfactant-enhanced remediation strategies in contaminated subsurface reservoirs. Full article

We propose a novel method for testing gravity models using seismic waves’ velocities. By imposing observational constraints on Earth’s moment of inertia and mass, we rigorously limit the gravitational models’ parameters within a $2\sigma$ accuracy. Our method, taking the PREM model as our reference and assuming its viability, constrains the parameters governing additional terms to the General Relativity Lagrangian to the following ranges: $-2\times {10}^9\lesssim \beta \lesssim {10}^9{\mathrm{m}}^2$ for Palatini $f\left(R\right)$ gravity, $-8\times {10}^9\lesssim ϵ\lesssim 4\times {10}^9{\mathrm{m}}^2$ for Eddington-inspired Born–Infeld gravity, and $-{10}^{-3}\lesssim \mathrm{{\rm Y}}\lesssim {10}^{-3}$ for Degenerate Higher-Order Scalar–Tensor theories. We also discuss potential avenues to enhance the proposed method, aiming to impose even tighter constraints on gravity models. Full article

The Gravity Recovery and Climate Experiment (GRACE) mascon data relies on minor gravitational field variations to map terrestrial water storage anomaly (TWSA). However, the coarse spatial resolution of three degrees by three degrees restricts their application for evaluating small-scale changes in water storage. To address this challenge, in this study, GRACE and GRACE Follow-On (GRACE-FO) data from 2003 to 2023 were downscaled to 800-m resolution across the Coastal Lowland Aquifer System (CLAS) in Texas, Louisiana, Mississippi, Alabama, and Florida. This downscaling used machine learning (ML) models, including Random Forest (RF), Artificial Neural Network (ANN), and Deep Neural Network (DNN). These models incorporated variables such as anomalies in total precipitation (APT), mean temperature (ATM), normalized difference vegetation index (ANDVI), evapotranspiration (AET) from 2003 to 2023, Shuttle Radar Topography Mission DEM, slope angle, soil type, and lithology to generate monthly 800-m TWSA maps. The ANN model showed strong predictive performance (R² = 0.869–0.989 with low RMSE), although the DNN achieved slightly better statistical accuracy and spatial evaluation metrics; however, ANN was selected for its more realistic and spatially consistent outputs regionally. Building on this improved spatial resolution, analysis of the downscaled TWSA data from 2003 to 2023 identified an overall declining trend in water storage. Trend analysis using linear regression shows that the western CLAS—particularly the Gulf Coast aquifer in Texas and western Louisiana—experiences the strongest depletion, with rates of −0.30 and −0.17 cm/year in Zones 1 and 2, respectively, with Zone 1 being statistically significant. In contrast, the eastern CLAS shows relatively stable conditions, with weak, non-significant increases (+0.05 to +0.18 cm/year), likely reflecting natural variability rather than sustained long-term gain. Therefore, ML-based downscaling of GRACE data enables high-resolution TWS assessment and provides a framework for future extraction of groundwater storage anomalies (GWSA), supporting improved groundwater management. Full article

To address the limitations of the standard Informed-RRT* algorithm in manipulator path planning, including low initial path search efficiency, susceptibility to local optima in complex obstacle environments, and high path redundancy, this paper proposes an improved Informed-RRT* algorithm tailored for manipulator applications. First, we construct a phased adaptive sampling framework that separates the initial path search and path optimization stages. A target region constraint strategy is introduced, and the sampling confidence probability is dynamically adjusted based on the current search phase and real-time path quality. This design significantly enhances the efficiency of feasible path discovery while effectively preventing premature convergence to local optima. Second, an adaptive step size mechanism guided by gravitational–repulsive coordination is developed. This mechanism dynamically adjusts the extension step size according to the local obstacle distribution, reducing invalid sampling and increasing the number of effective sampling points while strictly ensuring obstacle avoidance safety, thereby accelerating both path search and optimization processes. Finally, a dichotomy-based dynamic boundary path smoothing strategy is integrated to generate smooth intermediate path points near obstacle boundaries. This strategy eliminates redundant inflection points and reduces path length while maintaining a safe distance from obstacles. The performance of the proposed algorithm is comprehensively verified through multiple sets of comparative experiments in both 2D grid maps and ROS-based manipulator simulation environments. The experimental results demonstrate that compared with the standard Informed-RRT* algorithm, the proposed method achieves a relative reduction of 77.17% in the average time to first initial path in complex environments. The path planning success rate increases from 21% to 95%, corresponding to an absolute increase of 74 percentage points and a relative increase of 352.38%. Additionally, the average path length is relatively reduced by 24.81%. Full article

General relativity is often perceived by undergraduate and advanced high-school students as conceptually and mathematically inaccessible. This paper does not provide new results in gravitation but rather introduces a lucid pedagogical framework for understanding gravitomagnetic effects in rotating systems. Starting from the Langevin metric, which describes flat spacetime in a uniformly rotating reference frame, the paper considers an apparent paradox: two clocks moving with identical velocities in an inertial frame but located at different radii on a rotating platform. While the equality of proper time of the clocks is expected in the inertial frame, its reconstruction in the rotating frame is not immediately transparent. It is shown here that this equality emerges from an exact compensation between three distinct contributions: a centrifugal potential term, a kinematic time dilation term, and a velocity-dependent term being formally analogous to a gravitomagnetic potential. The explicit identification and interpretation of these contributions constitute the pedagogical significance of this paper. Although the consideration presented is performed in flat spacetime, the formal analogy with gravitomagnetic effects provides students with an accessible pathway to more advanced concepts such as frame-dragging and the Sagnac effect, while highlighting the importance of velocity-dependent interactions in relativistic physics. Full article

This paper examines the rotational motion of a compound mechanical system comprising a rigid carrier body equipped with internal gyroscopic devices and a point mass that moves along a prescribed trajectory relative to the body. The system undergoes free motion in a uniform gravitational field. We derive the complete equations of motion accounting for the constant gyrostatic torque (GT) generated by internal rotors. Using asymptotic methods, we develop approximate dynamical equations valid under two distinct physical scenarios: (i) when the moving mass is small relative to the carrier mass and executes rapid oscillations and (ii) when the mass oscillates with small amplitude near a fixed location within the body, regardless of mass ratio. The accuracy and validity range of these approximations are rigorously established. For the first scenario, we have approached the idea that gyrostatic coupling fundamentally alters the system’s integrability properties while introducing beneficial stabilization mechanisms. We characterize families of permanent rotational states and analyze their stability using linear perturbation theory. The second scenario reveals that the approximate dynamics correspond to gyrostat motion rather than the classical Euler–Poinsot case. Comprehensive numerical simulations validate theoretical predictions and demonstrate applications to spacecraft attitude control problems. The results provide practical design guidelines for gyrostabilized systems with internal moving components. Full article

We present a high-precision joint gravitational-lensing and kinematic analysis of nine massive galaxy clusters from the CLASH and CLASH-VLT surveys to test chameleon screening gravity and its $f\left(R\right)$ sub-class at Mpc scales. We investigate the dependence on the assumed parametrization of the total cluster mass profile by adopting three models, namely Navarro–Frenk–White (NFW), Burkert, and Hernquist. When cuspy models (NFW or Hernquist) are assumed in the general chameleon framework, the combined constraints from the nine clusters are fully consistent with General Relativity (GR), excluding large regions of the modified-gravity parameter space (the coupling constant $\mathcal{Q}$ and the background chameleon field ${\varphi }_{\infty }$), providing one of the tightest bounds on general chameleon models with clusters to date. In contrast, adopting a Burkert profile—disfavored by lensing data—leads to a mild (∼2σ) departure from the GR expectation in joint analysis. When considering the $f\left(R\right)$ sub-case, we obtain a bound on the background scalaron field of $|f_R| \lesssim 2-5 \times {10}^{-5}$ (95% C.L.) for NFW and Hernquist models, in agreement with current constraints at cosmological scales, and an apparent deviation from standard gravity of ${log}_{10}|f_R|=-4.7\pm 1.2$ for the Burkert case. We investigate the impact of systematics in the kinematical analysis, showing that the tension is mitigated when clusters exhibiting clear dynamical disturbance are excluded from the sample. Our results show that galaxy clusters provide competitive tests of screened modified gravity at mega-parsec scales, while highlighting the critical role of accurate mass modeling and dynamical-state assessment. The upcoming generation of wide-field lensing surveys and spectroscopic follow-up programs will enable similar analyses on substantially larger samples, offering the prospect of tightening cluster-based constraints on gravity and the dark sector. Full article

We study the SU(N) symmetric model, which describes interaction of gravity with three field multiplets: first, the multiplet of pseudoscalar fields, which is at present associated with the multi-component cosmic dark matter; second, the multiplet of vector fields, which represents the so-called color aether, now known as dynamic aether; third, the multiplet of Yang–Mills fields, which provides the SU(N) invariance of the model as a whole. It was previously known that the decay of the color aether in the early Universe could have given rise to emergence of an axionic singlet according to the Peccei–Quinn mechanism; we proposed an extended scheme, according to which the color aether activates an additional internal tool for generating not only a simple axionic singlet, but an entire SU(N) symmetric multiplet of pseudoscalar fields. Late-time evolution of the considered field configuration is analyzed in the framework of the Bianchi-I cosmological model, and a hypothesis is proposed that the aforementioned pseudoscalar multiplet can be associated with the multi-component cosmic dark matter. Full article

We investigate the effects of dark matter on the properties of strange quark stars within the framework of general relativity with two fluids coupled only by gravity. Adopting the color–flavor-locked model for strange quark matter and considering both fermionic (free fermion gas) and bosonic (polytropic) equations of state for dark matter, we systematically study the structure and tidal deformability of dark matter-admixed strange stars. Our results show that the presence of dark matter significantly modifies the mass–radius relations, with the maximum mass of dark matter-admixed strange stars exhibiting a non-monotonic dependence on the dark matter mass fraction $\chi$, which reaches a minimum at an intermediate value of $\chi$. The tidal deformability $\mathrm{\Lambda }$ of dark matter-admixed strange stars shows complex behavior depending on both the stellar mass and dark matter fraction, with $\mathrm{\Lambda }-\beta$ (the compactness parameter) relations deviating from the universal relations observed for pure strange stars or dark stars. Our findings demonstrate that dark matter-admixed strange stars with different configurations but identical masses and radii can be distinguished by their tidal deformabilities, providing potential observational signatures for detecting dark matter in compact astrophysical objects. The results are compared with current astrophysical constraints from gravitational wave observations and pulsar measurements. Full article