Abstract We study the gravitational potential generated by static, spherically symmetric matter distributions in a quadratic $f(R)$ gravity model. In the weak-field regime, the linearized field equations lead to a fourth-order modified Poisson equation whose solutions contain Newtonian and Yukawa-type contributions. Imposing regularity at the origin and asymptotic flatness uniquely fixes the integration constants, yielding potentials fully determined by the mass density. Analytical expressions are derived for several classical profiles, including Plummer, Hernquist, and Navarro–Frenk–White (NFW), as well as for new analytic density models introduced in this work. The dependence on the quadratic gravity parameter $\alpha$ is analyzed, and the Newtonian limit of General Relativity is consistently recovered as $\alpha \to \infty$. As an application, circular velocity curves are computed and compared with the observed rotation curve of NGC 3198. A chi-squared analysis shows that the linearized quadratic $f(R)$ model provides improved fits relative to the Newtonian case in the inner and intermediate galactic regions $r \lesssim 30$ kpc, while predicting a decline at larger radii due to Yukawa suppression.

Abstract We develop a metric-free theory of gravitation generated by geometrical defects. Spacetime geometry is described by a velocity-distortion coframe β a =Ψ a μ dφ μ and a spin-bend-twist connection κ a b =Ψ a μ d(Ψ -1 ) μ b , defined in terms of the motion field φ μ and the intrinsic deformation field Ψ a μ . Their field strengths are the intrinsic torsion Σ a =dβ a +κ a b Λβ b and intrinsic curvature Λ a b =dκ a b +κ a c Λκ c b . The fundamental field equations Σ a =α a and Λ a b =Θ a b balance these geometric quantities against spacetime dislocations α a and disclinations Θ a b —incompatibilities in the motion and intrinsic deformation fields. Geometrical point defects π a b correspond to incompatible frame transformations. The Newtonian limit of the time-space field equations Λ i 0 =Θ i 0 results in the conversion between physical mass-energy ρ and the geometric mass density ρ geom =¬ e i ¬ u Θ i 0 time-space wedge disclination. Gravitation thus emerges directly from geometric incompatibility rather than from curvature sourced by matter. An invariant volume capacity —a 4-form constructed from orientation and deformation determinants—replaces √(- g ) and enables variational principles and integration without a metric. Variation of an intrinsic-frame gravitational Lagrangian capacity produces the corresponding stress and couple-stress capacity currents and their dynamical equations. In this formulation, there is no Newtonian gravitational potential: gravitational accelerations are carried by the time-space components of the connection, which act as the fundamental dynamical variables. The theory reproduces gravitational waves, black hole exteriors, and the Newtonian limit in a metric-free formulation; when needed, a metric-compatible sector restriction and metric reconstruction are used only for comparison with standard GR. It provides a natural foundation for extensions such as f(Λ) theories that may remain valid where metric descriptions fail.

This study looks into the magneto hydrodynamics (MHD) flow of a micropolar hybrid nanofluid in a stretching permeable arterial channel. It considers external magnetic and electric fields, along with velocity slip and thermal effects. Transforming the nonlinear momentum, micro rotation, energy, and concentration equations into a system of ordinary differential equations using similarity transformations, and solve this system with a collocation shooting method. Validation against Newtonian and non-micropolar limits shows deviations below 1.8%, confirming the model’s reliability. The results indicate that increasing the Hartmann number ( M = 0 − 4) reduces axial velocity by up to 27% and raises nanoparticle concentration by 15–20%. A higher thermophoresis parameter (Nt = 0.1 − 0.5) increases the wall Nusselt number by 12%. In contrast, Brownian motion (Nb = 0.2 − 0.8) lowers the Sherwood number by 9%. The micropolar coupling parameter greatly affects microrotation and reduces wall shear stress by 18% compared to Newtonian flow. These findings show that external fields can effectively control nanoparticle transport and suggest promising applications for better intravascular drug delivery.

The global well-posedness and Newtonian limit for the relativistic Boltzmann equation in a periodic box

Abstract We show that an ansatz for $$1+3+n$$ 1 + 3 + n dimensional static spacetime with spherical symmetry in three dimensions and Euclidean symmetry in n dimensions, parametrized by only one function of radial coordinate, leads to a limited set of vacuum solutions of the Einstein field equations. They can also be identified as Weyl solutions. We investigate properties of these spacetimes through the Kretschmann scalar, Newtonian mass defined through the Newtonian limit, Komar mass, Einstein, Landau–Lifshitz, and ADM mass. In addition to $$1+3+n$$ 1 + 3 + n dimensional Minkowski spacetime, there are two classes of solutions. The first class is a trivial product of the Schwarzschild spacetime and Euclidean spaces in extra dimensions, while the second class is non-trivial. In the case with no horizon, there is a naked singularity, all masses are equal, and they are negative. In the case when there is a horizon, this horizon accommodates a physical singularity, which corresponds to Kaluza–Klein bubbles featuring exotic properties. Einstein, Landau–Lifshitz, and ADM masses are positive, while Newtonian and Komar masses are negative. This differentiates these solutions from trivial higher-dimensional extensions of the Schwarzschild solution.

Publisher Correction: The Newtonian limit of orthonormal frames in metric theories of gravity

Abstract We extend well-known results on the Newtonian limit of Lorentzian metrics to orthonormal frames. Concretely, we prove that, given a one-parameter family of Lorentzian metrics that in the Newtonian limit converges to a Galilei structure, any family of orthonormal frames for these metrics converges pointwise to a Galilei frame, assuming that the two obvious necessary conditions are satisfied: the spatial frame must not rotate indefinitely as the limit is approached, and the frame’s boost velocity with respect to some fixed reference observer needs to converge.

Abstract We present \textbf{RoMOND} (Rotating Modified Newtonian Dynamics), a relativistic extension of MOND constructed on a stationary, axisymmetric spacetime with a non-vanishing frame-dragging term. The framework introduces a scalar and a unit-timelike vector field, coupled through a disformal relation, and reduces to GR in the Newtonian limit while reproducing MOND phenomenology at low accelerations. The MOND acceleration scale emerges as $a_0(r)\sim r\omega^2(r)$, offering a geometric interpretation tied to cosmic rotation. We derive the full field equations, analyze perturbative stability, and compute effective contributions to galactic and cluster dynamics, including a ``geometric mass'' term $M_{\rm geom}(r)=r^3\omega^2(r)/G$. Observable consequences include anisotropic clustering, galaxy spin alignments, and possible imprints in the CMB. Numerical profiles of $\omega(r)$ consistent with observations are discussed, and Appendix~A provides full derivations of key results. The framework opens a testable alternative to dark matter, linking local galactic dynamics with global spacetime rotation.

Abstract The field of gravitational wave (GW) detection is progressing rapidly, with several next-generation observatories on the horizon, including LISA. GW data is challenging to analyze due to highly variable signals shaped by source properties and the presence of complex noise. These factors emphasize the need for robust, advanced analysis tools. In this context, we have initiated the development of a low-latency GW detection pipeline based on quantum neural networks (QNNs). Previously, we demonstrated that QNNs can recognize GWs simulated using post-Newtonian approximations in the Newtonian limit. We then extended this work using data from the LISA Consortium, training QNNs to distinguish between noisy GW signals and pure noise. Currently, we are evaluating performance on the Sangria LISA Data Challenge dataset and comparing it against classical methods. Our results show that QNNs can reliably distinguish GW signals embedded in noise, achieving classification accuracies above 98%. Notably, our QNN identified 5 out of 6 mergers in the Sangria blind dataset. The missed event corresponds to the lowest signal-to-noise ratio (SNR) source, indicating that model sensitivity improvements are needed for weak signals. This can potentially be addressed using additional mock training datasets, and by testing different QNN architectures and ansatzes. Compared with a recurrent neural network baseline, the QNN achieves comparable accuracy on higher-SNR events while using orders of magnitude fewer trainable parameters. These results demonstrate the feasibility of QNNs for GW detection and motivate further investigation of quantum-enhanced data analysis techniques for LISA.

Abstract The flow of non-Newtonian fluids through corrugated geometries is central to numerous applications such as microfluidics, printing, coating, and biomedical transport. In this study, we present exact analytical expressions relating the pressure drop and volumetric flow rate for steady, laminar flow of power-law fluids through five different two-dimensional converging–diverging channel geometries: linear wedge, parabolic, hyperbolic, hyperbolic cosine, and sinusoidal. The analysis is performed under the lubrication approximation for low-Reynolds-number Stoke flow regime. It is noticed that when the flow viscosity is taken as a constant, the method approaches the Newtonian flow physics. Our results demonstrate how flow rate, velocity profile and pressure drop are influenced by fluid rheology and geometric shape of the channel. It is observed that the flow rate is maximum for the wedge profile followed by hyperbolic and sinusoidal geometries, then parabolic and minimum for the cosine hyperbolic profile. Additionally, as the value of power index increases, i.e. as the fluid transitions from shear-thinning to shear-thickening, the flow rate decreases. The velocity profiles show accelerated flow in the converging section and deceleration in the diverging section, with sharper peaks as the power-law index increases. The pressure gradient is negative throughout the channel, steeper in the converging part and gradually approaching zero at the exit. It becomes more negative with increasing n , indicating enhanced resistance to flow in shear-thickening fluids. The present method can be utilized for several types of fluids ranging from shear thinning to shear-thickening and specific channel profiles. In cases where complex mathematical and practical considerations pose a challenge in obtaining analytical expressions, the present investigation provides a strong frame of reference for obtaining accurate numerical results. The model is validated in the Newtonian limit and serves as a reliable benchmark for numerical modeling of non-Newtonian flows in complex geometries.

Abstract Standardizing the definition of eccentricity is necessary for unambiguous inference of the orbital eccentricity of compact binaries from gravitational wave observations. In previous works, we proposed a definition of eccentricity for systems without spin-precession that relies solely on the gravitational waveform, is applicable to any waveform model, and has the correct Newtonian limit. In this work, we extend this definition to spin-precessing systems. This simple yet effective extension relies on first transforming the waveform from the inertial frame to the coprecessing frame, and then adopting an amplitude and a phase with reduced spin-induced effects. Our method includes a robust procedure for filtering out spin-induced modulations, which become non-negligible in the small eccentricity and large spin-precession regime. Finally, we apply our method to a set of Numerical Relativity and Effective One Body waveforms to showcase its robustness for generic eccentric spin-precessing binaries. We make our method public via Python implementation in gw_eccentricity.

Accretion is the process of capturing matter by a massive object (a neutron star, a black hole, etc.) from nearby space, which leads to a change in the mass of the central object. This process is a widespread phenomenon in the universe and is responsible for the formation of stars, planets and galaxies. It is assumed that supermassive black holes in the centers of spiral and elliptical galaxies could form due to the accretion process. Recently, inter est in black hole accretion has increased again after numerous isolated black holes were discovered during expe riments at the Laser Interferometric Gravitational Wave Observatory (LIGO). The difference between accretion to an isolated black hole and a black hole with a satellite is the ratio of mass and energy. In the case of a black hole that has a companion star (a close binary system), the mass reserve will depend on the state of the companion, and an isolated black hole can accumulate matter if there is scattered gas in its vicinity or a stream of matter affects it. For the first time, a model of spherically symmetric accretion, known as the Bondi model, for an isolated star in the Newtonian approximation was proposed by H. Bondi and was considered in the relativistic approximation for a Schwarzschild black hole by F. Michel. A special feature of the Bondi model is that it allows you to observe the evolution of the mass of a compact object. The paper considers the accretion of phantom energy and baryonic matter (dust, hard matter, and quintes sence) onto an isolated black hole with quantum deformation described by Kazakov–Solodukhin [5]. It is shown that with the accretion of dark energy (ρ 0) the mass of the central object decreases, and with the accretion of baryonic matter it increases. The effect of quantum deformation on the radial velocity, fluid density, and accretion rate is negligible.

A comprehensive Darcy-type law for viscoplastic fluids is proposed. Different regimes of yield-stress fluid flow in porous media can be categorized based on the Bingham number (i.e., the ratio of the yield stress to the characteristic viscous stress). In a recent study [Chaparian, ], we addressed the yield/plastic limit (infinitely large Bingham number), namely, the onset of flow when the applied pressure gradient is just sufficient to overcome the yield-stress resistance. A purely geometrical universal scale was derived for the nondimensional critical pressure gradient, which was thoroughly validated against computational data. In the present work, we investigate the Newtonian limit (infinitely large pressure difference compared to the yield stress of the fluid—ultralow Bingham number) both theoretically and computationally. We then propose a Darcy-type law applicable across the entire range of Bingham numbers by combining the mathematical models of the yield/plastic and Newtonian limits. The Exhaustive computational data generated in this study (using an augmented Lagrangian method coupled with anisotropic adaptive mesh at the pore scale) confirm the validity of the theoretical proposed law.

ABSTRACT Intermediate-mass black holes (IMBHs, $\sim 10^2\!-\!10^5\, \mathrm{M}_{\odot }$) are often dubbed as the missing link between stellar mass ($\lesssim 10^2\, \mathrm{M}_{\odot }$) and supermassive ($\gtrsim 10^{5-6} \, \mathrm{M}_{\odot }$) BHs. Observational signatures of these can result from tidal disruptions of white dwarfs (WDs), which would otherwise be captured as a whole by supermassive BHs. Recent observations indicate that IMBHs might be rapidly spinning, while it is also known that isolated WDs might have large spins, with spin periods of the order of minutes. Here, we aim to understand the effects of ‘coupling’ between BH and stellar spin, focusing on the tidal disruption of spinning WDs in the background of spinning IMBHs. Using smoothed particle hydrodynamics, we perform a suite of numerical simulations of partial tidal disruptions, where spinning WDs are in eccentric orbits about spinning IMBHs. We take a hybrid approach, where we integrate the Kerr geodesic equations while being in a regime where we can treat the internal stellar fluid dynamics in the Newtonian limit. The coupling of BH and stellar spin results in distinctive behaviour of mass distribution of debris, compared to non-rotating cases. Further, while late-time fallback rates of debris into the BH is unaffected by only BH spin, these have noticeable deviations in the presence of stellar spin, in particular, this causes a broadening of the fallback curves at late times. On the other hand, gravitational wave signatures are unaffected by stellar spin in the parameter regime that we consider.

Abstract In this study, we investigate the gravitational collapses of rotating stellar systems accounting for gamma-ray burst jet progenitors. Based on the virial theorem of hadron collisional relaxations and Newtonian slow-rotating approximation, we analyze the conversion of gravitational binding energy into kinetic energy of hadrons, whose collisions produce photons and electron-positron pairs forming fireballs. Our qualitative analysis implies that rotation effects collimated and spinning fireballs with nontrivial angular momenta along the propagating direction, thus making ultra-relativistic jets. Results reveal the possible trends that the fireball becomes more collimated and the jet angle decreases as the total angular momentum and mass ratio J/M of the slow-rotating collapsing core increases. Discussing the extrapolation of these trends to fast-rotating collapsing systems, we speculate that the ratio J/M should be a key quantity for differentiating long bursts (massive core collapses) from short bursts (binary coalescence). We derive the intrinsic correlations of collimated fireball quantities that should be imprinted on a large sample of observed GRB data as empirical correlations.

We study regular self-gravitating nontopological soliton solutions of the U(1) gauged nonlinear O(3) sigma model with the usual kinetic term and a simple symmetry breaking potential in 3+1 dimensional asymptotically flat. Both parity-even and parity-odd configurations with an angular node of the scalar field are considered. Localized solutions are endowed with an electric charge; spinning configurations are also coupled to the toroidal flux of magnetic field. We confirm that such solutions do not exist in the flat space limit. Similar to the usual boson stars, a spiral-like frequency dependence of the mass and the Noether charge of the gauged solutions is observed. Depending on the relative strength of gravity and the electromagnetic interaction, the resulting gauged O(3) boson stars at the mass threshold either possess the usual Newtonian limit, or they are linked to a regular strongly gravitating critical configuration. We explore domain of existence of the solutions and investigate some of their physical properties.

Quantum dynamics on curved spacetime has never been directly probed beyond the Newtonian limit. Although we can describe such dynamics theoretically, experiments would provide empirical evidence that quantum theory holds even in this extreme limit. The practical challenge is the minute spacetime curvature difference over the length scale of the typical extent of quantum effects. Here, we propose a quantum network of alkaline earth (like) atomic processors for constructing a distributed quantum state that is sensitive to the differential proper time between its constituent atomic processor nodes, implementing a quantum observable that is affected by post-Newtonian curved spacetime. Conceptually, we propose to delocalize one clock between three locations by encoding the presence or absence of a clock into the state of the local atoms. By separating three atomic nodes over approximately kilometer-scale elevation differences and distributing one clock between them via a W state, we demonstrate that the curvature of spacetime is manifest in the interference of the three different proper times that give rise to three distinct beat notes in our nonlocal observable. We further demonstrate that N-atom entanglement within each node enhances the interrogation bandwidth by a factor of N. We discuss how our proposed system can probe new facets of fundamental physics, such as the linearity, unitarity, and probabilistic nature of quantum theory on curved spacetime. Our protocol combines several recent advances with neutral atom and trapped ions to realize a novel quantum probe of gravity uniquely enabled by quantum networks.

Abstract By studying the chameleon gravity on galaxy scales, we investigate the effects of the chameleon dark matter. To perform this task, we consider the dynamics of the chameleon scalar field in the region of galactic halos in static spherically symmetric spacetimes that differ only slightly from classical general relativity, but have similar symmetry behind this region. Hence, we demonstrate its ability to act as dark matter. In fact, by obtaining the expression for the tangential speed in this region, we apply this approach to explain the issue of flat galactic rotation curves. We obtain that the mass associated with the chameleon scalar field varies linearly with the radius of galaxy, and hence, the tangential speed in that region is constant, which is consistent with observational data without any need to introduce a mysterious dark matter. Accordingly, we show that the presented chameleon gravity has a well-defined Newtonian limit and can describe the geometry of spacetime in the region of flat galactic rotation curves, and is consistent with the corresponding results of the $$ \Lambda CDM $$ Λ C D M model with the NFW profile. We also consider a test particle moving in a timelike geodesic and obtain the fifth-force, which varies proportionally to the inverse of the radius of galaxy. Moreover, we obtain the effects on the angle representing the deflection of light and on the time representing the radar echo delay of photons passing through the region of galactic halos. We show that as the radius of galaxy increases, the effect on the angle of light passing through the region around galactic halos decreases. Also, the obtained result indicates that the relevant time delay decreases with increasing radius towards the end of the galactic halo.

We review a metric theory of gravitation that combines Newtonian gravity with Lorentz invariance. Beginning with a conformastatic metric justified by the Weak Equivalence Principle. We describe, within the Newtonian approximation, the spacetime geometry generated by a static distribution of dust matter. To extend this description to moving sources, we apply a Lorentz transformation to the static metric. This procedure yields, again within the Newtonian approximation, the metric associated with moving bodies. In doing so, we construct a gravitational framework that captures key relativistic features—such as covariance under Lorentz transformations—while remaining rooted in Newtonian dynamics. This approach offers an alternative route to describing weak-field gravitational interactions, without relying directly on Einstein’s field equations.

Direct orthogonal collocation has been applied to generate optimal hypersonic trajectories, but often previous research has struggled to capture the effects of vehicle orientation. In this work, an aerodynamic model was developed for an elliptic cone glide geometry at a variety of angles of attack using Newtonian approximations, while polynomial approximations were used to define the functional relationship between an input angle of attack and the vehicle lift and drag coefficient. This allowed for variability of the aerodynamic parameters during flight, with angle of attack serving as a control input. This model was implemented into a direct orthogonal collocation framework, and a series of boost–glide trajectories were successfully simulated, with objectives of minimum distance to target, minimum time to target, and maximum velocity at final time for a single target. The optimal control problem was then expanded into a reachability study, where a wide range of cost functions, constraints, and mission scenarios were simulated, along with studies on maximum range for the vehicle model. Results demonstrated a robust framework for the creation of hypersonic trajectories and the ability to implement a rapidly generated aerodynamic model to capture higher-fidelity behavior in the simulation.