Search Results (68)

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. Full article

In his foundational work on classical and quantum electrodynamics, Stueckelberg introduced an external evolution parameter, $\tau$, in order to overcome difficulties associated with the problem of time in relativity. Stueckelberg particle trajectories are described by the evolution of spacetime events under the monotonic advance of $\tau$, the basis for the Feynman–Stueckelberg interpretation of particle–antiparticle interactions. An event is a solution to $\tau$-parameterized equations of motion, which, under simple conditions, including the elimination of pair processes, can be reparameterized by the proper time of motion. The $4+1$ formalism in general relativity (GR) extends this framework to provide field equations for a $\tau$-dependent local metric ${\gamma }_{\mu \nu }(x,\tau )$ induced by these Stueckelberg trajectories, leading to $\tau$-parameterized geodesic equations in an evolving spacetime. As in standard GR, the linearized theory for weak fields leads to a wave equation for the local metric induced by a given matter source. While previous attempts to solve the wave equation have produced a metric with the expected features, the resulting geodesic equations for a test particle lead to unreasonable trajectories. In this paper, we discuss the difficulties associated with the wave equation and set up the more general ADM-like $4+1$ evolution equations, providing an initial value problem for the metric induced by a given source. As in the familiar $3+1$ formalism, the metric can be found as a perturbation to an exact solution for the metric induced by a known source. Here, we propose a metric, ansatz, with certain expected properties; obtain the source that induces this metric; and use them as the initial conditions in an initial value problem for a general metric posed as a perturbation to the ansatz. We show that the ansatz metric, its associated source, and the geodesic equations for a test particle behave as required for such a model, recovering Newtonian gravitation in the nonrelativistic limit. We then pose the initial value problem to obtain more general solutions as perturbations of the ansatz. Full article

Research at the intersection of quantum gravity and quantum information theory has seen significant success in describing the emergence of spacetime and gravity from quantum states whose entanglement entropy approximately obeys an area law. In a different direction, the Kaluza–Klein proposal aims to recover gauge symmetries by means of dimensional reduction in higher-dimensional gravitational theories. Integrating both of these, gravitational and gauge degrees of freedom in $3+1$ dimensions may be obtained upon dimensional reduction in higher-dimensional emergent gravity. To this end, we show that entangled systems of two and three qubits can be associated with $5+1$- and $9+1$-dimensional spacetimes, respectively, which are reduced to $3+1$ dimensions upon singling out a preferred complex direction. Depending on the interpretation of the residual symmetry, either the Standard Model gauge group, $SU\left(3\right)\times SU\left(2\right)\times U\left(1\right)/{\mathbb{Z}}_6$, or the symmetry of Minkowski spacetime together with the gauge symmetry of a right-handed ‘half-generation’ of fermions can be recovered. Thus, there seems to be a natural way to accommodate the chirality of the weak force in the given construction. This motivates a picture in which spacetime emerges from the area law contribution to the entanglement entropy, while gauge and matter degrees of freedom are obtained due to area-law-violating terms. Furthermore, we highlight the possibility of using this construction in quantum simulations of Standard Model fields. Full article

In the field of space gravitational wave detection, high-precision temperature measurement with a resolution at the micro-Kelvin level in the milli-Hertz frequency range is required to mitigate the interference caused by temperature fluctuations around the core components. This is a very challenging task due to resistance thermal noise and the inherent 1/f noise of electronic components. To overcome this problem, this paper proposes a low-noise, high-resolution temperature measurement method based on an inductive voltage divider and an alternating-current (AC) bridge. The proposed method has the following three characteristics: (1) it employs an AC excitation signal to drive the temperature measuring bridge to overcome the influence of 1/f noise in electronic components; (2) it uses as few resistance components as possible in the AC bridge and signal detection circuit to reduce the impact of resistance thermal noise on the measurement results; (3) it adopts a frequency-domain data processing algorithm based on discrete Fourier transform to improve the accuracy of the temperature measuring result. Using this method, a circuit board is designed and tested. The results show that the noise floor level of the designed temperature measurement circuit is below $7\times {10}^{-6}\mathrm{K}/\sqrt{\mathrm{Hz}}$ in a frequency range of 0.005~1 Hz. This demonstrates that our proposed method is able to detect extremely weak temperature change signals and meets the temperature measurement requirements of space gravitational wave detection. Full article

Energy harvesting from ambient vibrations has received significant attention as an alternative renewable, clean energy source for microelectronic devices in diverse applications such as wearables and environmental monitoring. However, typical vibrations in remote environments exhibit ultra-low frequencies with variations and uncertainty leading to operation away from resonance and severe underperformance in terms of power output. Pendulum-based energy harvesters offer a promising solution to these issues, particularly when designed for parametric resonant response to driven displacement of the pendulum pivot. Parametric excitation has been shown to trigger fast rotational motion of the pendulum VEH that is beneficial for energy generation and the necessary space utilization. Nevertheless, low-frequency ambient vibrations typically come at very weak amplitudes, a fact that establishes significant design barriers when traditional gravitational pendula are used for rotary energy harvesting. In this paper, we propose a novel concept that utilizes permanent magnet arrays to establish pendulum dynamics. Extensive investigation of the restoring torque of the proposed magnetic pendulum concept is conducted with analytical tools and FEA verification. The resulting oscillator exhibits frequency tuning that is decoupled from gravity and adjustable via the circularly arranged magnetic fields, leading to increased flexibility in the concurrently necessary amplitude tuning. Numerical integration of the nondimensional equation of motion is performed in the system’s parameter space to identify the impact on the regions triggering rotational response to parametric excitation. Finally, a theoretical case study is numerically investigated with the device space constrained within 20 cm³, showing a multi-fold improvement in the achieved power density of over 600 μW/cm³/g²/Hz over a broad range of frequencies and driving amplitudes as low as 1.1 Hz at 0.2 g. Full article

Deep gravitational slope deformations (DsGSDs) are a geological and engineering challenge with important implications for slope stability, the reliability of existing infrastructures, land use and, above all, the safety of settlements. This paper focuses on the DsGSD phenomenon that affects a large part of the Borrano hamlet, located in the municipality of Civitella del Tronto (Abruzzo Region, Central Italy). This instability is characterized by slow movements of large volumes of material. The main factors initiating deformations are a combination of geological and hydrogeological aspects. These factors include the complex local stratigraphy, composed of pelitic and arenaceous facies at high slope dip angles, and extreme natural events such as heavy rainfall and earthquakes. This study employs a multidisciplinary approach integrating in field activities such as remote-controlled surface monitoring (clinometers and strain gauges), in-depth monitoring (inclinometers and piezometers), aero-photogrammetric analysis and numerical modelling. These techniques permitted us to characterize the evolution of the slope and to identify both the critical sliding surfaces and the mechanisms governing the ground movements. Soil deformations were mainly observed in the central zone of the hamlet. Significant deformations were recorded along planes of weakness at depth between arenaceous and pelitic materials. These planes represent contact zones between the clayey–marly facies, characterized by low strength, and the arenaceous facies, characterized by higher stiffness, creating a mechanical contrast that favours the development of large deformations. The numerical analyses confirmed good correlation with the monitoring data, revealing in detail the instability of both local and territorial processes. The 3D numerical analysis showed how the movements are controlled by planes of weakness, highlighting the key rule of geological discontinuities. Full article

The unified Einstein–Euler–Heisenberg theory is utilized to investigate the particle motion and weak gravitational lensing characteristics of black holes. This black hole solution is developed using spherically symmetric possessing electric and magnetic charges. Quantum electrodynamics corrections reveal a screening effect for BH electric charges and paramagnetic impacts on magnetic charges. We analyzed the motion of massive as well as massless particles by studying their effective potential, event horizon, photon orbit and inner circular orbit. It was demonstrated that magnetic and electric fields of spherically symmetric black holes have significant impact. Then, we also delve to study the weak gravitational lensing phenomenon. A comprehensive approach was employed to investigate this phenomenon and explore the angle of deflection of light rays near magnetically and electrically charged black holes. Full article

In this work, we elaborate further on a (3+1)-dimensional cosmological Running-Vacuum-type-Model (RVM) of inflation based on string-inspired Chern-Simons(CS) gravity, involving axions coupled to gravitational-CS(gCS) anomalous terms. Inflation in such models is caused by primordial-gravitational-waves(GW)-induced condensation of the gCS terms, which leads to a linear-axion potential. We demonstrate that this inflationary phase may be metastable, due to the existence of imaginary parts of the gCS condensate. These are quantum effects, proportional to commutators of GW perturbations, hence vanishing in the classical theory. Their existence is quantum-ordering-scheme dependent. We argue in favor of a physical importance of such imaginary parts, which we compute to second order in the GW (tensor) perturbations in the framework of a gauge-fixed effective Lagrangian, within a (mean field) weak-quantum-gravity-path-integral approach. We thus provide estimates of the inflation lifetime. On matching our results with the inflationary phenomenology, we fix the quantum-ordering ambiguities, and obtain an order-of-magnitude constraint on the String-Mass-Scale-to-Planck-Mass ratio, consistent with previous estimates by the authors in the framework of a dynamical-system approach to linear-axion RVM inflation. Finally, we examine the role of periodic modulations in the axion potential induced by non-perturbative effects on the slow-roll inflationary parameters, and find compatibility with the cosmological data. Full article

In this paper, we review some recent findings related to the Casimir effect. Initially, the thermal corrections to the vacuum Casimir energy density are calculated, for a quantum scalar field, whose modes propagate in the (3+1)-dimensional Euclidean spacetime, subject to a nontrivial compact boundary condition. Next, we analyze the Casimir effect induced by two parallel plates placed in a weak gravitational field background. Finally, we review the three-dimensional wormhole solutions sourced by the Casimir density and pressures associated with the quantum vacuum fluctuations of the Yang-Mills field. Full article

We calculate the metric of a self-gravitating and collapsing infinitely thin spherical shell in the weak-field and slow-motion limits, and we demonstrate that Birkhoff’s theorem is not consistent with the theory of the post-Newtonian approximation. More importantly, it is illustrated that performing a coordinate transformation in solving Einstein field equations may change the matter energy-momentum tensor, making the resultant solution not correspond to the original problem. Full article

It is already known that a simple nonlocal de Sitter gravity model, which we denote as $\sqrt{dS}$ gravity, contains an exact vacuum cosmological solution that mimics dark energy and dark matter and is in very good agreement with the standard model of cosmology. This success of $\sqrt{dS}$ gravity motivated us to investigate how it works at a lower-than-cosmic scale—galactic and the solar system. This paper contains our investigation of the corresponding Schwarzschild–de Sitter metric of the $\sqrt{dS}$ gravity model. To obtain an exact solution, it is necessary to solve the corresponding nonlinear differential equation, which is a very complicated and difficult problem. What we obtained is a solution to a linearized equation, which is related to space metrics far from the massive body, where the gravitational field is weak. The obtained approximate solution is of particular interest for examining the possible role of nonlocal de Sitter gravity $\sqrt{dS}$ in describing the effects in galactic dynamics that are usually attributed to dark matter. This solution was tested on the Milky Way and the spiral galaxy M33 and is in good agreement with observational measurements. Full article

If visible matter alone is present in the Universe, general relativity (GR) and its Newtonian weak field limit (WFL) cannot explain several pieces of evidence, from the largest to the smallest scales. The most investigated solution is the cosmological model $\mathsf{\Lambda }$ cold dark matter ($\mathsf{\Lambda }$CDM), where GR is valid and two dark components are introduced, dark energy (DE) and dark matter (DM), to explain the ∼70% and ∼25% of the mass–energy budget of the Universe, respectively. An alternative approach is provided by modified gravity theories, where a departure of the gravity law from $\mathsf{\Lambda }$CDM is assumed, and no dark components are included. This work presents refracted gravity (RG), a modified theory of gravity formulated in a classical way where the presence of DM is mimicked by a gravitational permittivity $ϵ\left(\rho \right)$ monotonically increasing with the local mass density $\rho$, which causes the field lines to be refracted in small density environments. Specifically, the flatter the system the stronger the refraction effect and thus, the larger the mass discrepancy if interpreted in Newtonian gravity. RG presented several encouraging results in modelling the dynamics of disk and elliptical galaxies and the temperature profiles of the hot X-ray emitting gas in galaxy clusters and a covariant extension of the theory seems to be promising. Full article

In this paper we use a modification of the Newtonian gravitational potential with a non-linear Yukawa-like correction, as it was proposed by C. Will earlier to obtain new bounds on graviton mass from the observed orbits of S-stars around the Galactic Center (GC). This phenomenological potential differs from the gravitational potential obtained in the weak field limit of Yukawa gravity, which we used in our previous studies. We also assumed that the orbital precession of S-stars is close to the prediction of General Relativity (GR) for Schwarzschild precession, but with a possible small discrepancy from it. This assumption is motivated by the fact that the GRAVITY Collaboration in 2020 and in 2022 detected Schwarzschild precession in the S2 star orbit around the Supermassive Black Hole (SMBH) at the GC. Using this approach, we were able to constrain parameter $\lambda$ of the potential and, assuming that it represents the graviton Compton wavelength, we also found the corresponding upper bound of graviton mass. The obtained results were then compared with our previous estimates, as well as with the estimates of other authors. Full article

The gravity and gradient anomalies contain valuable information about the underground geological structures at various depths. Deep and shallow buried source bodies are able to be identified through multi-scale field separation processes, and visual comprehensions of geological structures can be obtained via 3D density inversion techniques. In this study, we propose an improved 3D imaging strategy based on gravitational field separation using the preferential continuation filter. This strategy incorporates the relationship between spectral features and buried depths of source bodies, allowing for a one-step transformation from planar gravity and full-tensor gradient field observations to a 3D density structure in the wave-number domain. Synthetic tests validate the effectiveness and robustness of the gravity and gradient imaging approaches, highlighting their advantages in high vertical resolution and low computational requirements. Nonetheless, it should be noted that the imaging effects of horizontal gradients ${\Gamma }_{xx}$ and ${\Gamma }_{yy}$ are unsatisfactory due to their weak noise resistance. Thus, they are not suitable for real data applications. The other imaging approaches are further applied to recover the subsurface 3D density structure beneath the Weishan cone in Wudalianchi Volcanic Field, Northeastern China. Our results provide insights into the possible location and shape of the low-density magma chamber. Also, the potential presence of partial melts is inferred and supported from a gravity perspective. The primary advantage of these approaches is their ability to generate a reasonable geological model in scenarios with limited prior information and physical property constraints. As a result, they have significant practical value in the field of applied geophysics, including mineral exploration and volcanology studies. Full article

Light bending is one of the classical tests of general relativity and is a crucial aspect to be taken into account for accurate assessments of photon propagation. In particular, high-precision astrometry can constrain theoretical models of gravitation in the weak field limit applicable to the Sun neighborhood. We propose a concept for experimental determination of the light deflection close to the Sun in the ${10}^{-7}$ to ${10}^{-8}$ range, in a modern rendition of the 1919 experiment by Dyson, Eddington and Davidson, using formation flying to generate an artificial long-lasting eclipse. The technology is going to be demonstrated by the forthcoming ESA mission PROBA3. The experimental setup includes two units separated by 150 m and aligned to the mm level: an occulter and a small telescope (0.3 m diameter) with an annular field of view covering a region $0^{\circ }.7$ from the Sun. The design is compatible with a space weather payload, merging several instruments for observation of the solar corona and environment. We discuss the measurement conditions and the expected performance. Full article