Search Results (89)

We investigate pseudo-complex General Relativity (pcGR)—a coordinate-extended formulation of General Relativity (GR)—within the framework of Hořava-Lifshitz gravity, a regularized theory featuring anisotropic scaling. The pcGR framework bridges GR with modified gravitational theories through the introduction of a minimal length scale. Focusing on Schwarzschild black holes, we derive the Wheeler-deWitt equation, obtaining a quantized description of pcGR. Using perturbative methods and semi-classical approximations, we analyze the solutions of the equations and their physical implications. A key finding is the avoidance of the central singularity due to nonlinear interaction terms in the Hořava-Lifshitz action. Notably, extrinsic curvature (kinetic energy) contributions prove essential for singularity resolution, even in standard GR. Furthermore, the theory offers new perspectives on dark energy, proposing an alternative mechanism for its accumulation. Full article

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

An approach is presented to address singularities in general relativity using a complex Riemannian spacetime extension. We demonstrate how this method can be applied to both black hole and cosmological singularities, specifically focusing on the Schwarzschild and Kerr black holes and the Friedmann–Lemaître–Robertson–Walker (FLRW) Big Bang cosmology. By extending the relevant coordinates into the complex plane and carefully choosing integration contours, we show that it is possible to regularize these singularities, resulting in physically meaningful, singularity-free solutions when projected back onto real spacetime. The removal of the singularity at the Big Bang allows for a bounce cosmology. The approach offers a potential bridge between classical general relativity and quantum gravity effects, suggesting a way to resolve longstanding issues in gravitational physics without requiring a full theory of quantum gravity. Full article

This study investigates the trajectory-tracking control problem of a two-degree-of-freedom underwater manipulator operating in a complex disturbance environment. A dynamic model of the multi-link serial manipulator is first established. In this study, water resistance and additional mass forces acting on the manipulator are analyzed and calculated using differential analysis and the Morrison formula. To account for coupling between joints, the concept of equivalent gravity is introduced to precisely calculate the underwater manipulator’s buoyancy and gravity. As a result, a relatively accurate dynamic model of the underwater manipulator is established. To mitigate the influences of external disturbances and unmodeled parts on the manipulator, a finite-time extended state observer (FTESO) is designed to estimate system quantities that are difficult to measure directly. The robustness of the controller is enhanced using a feedforward compensation mechanism, and it is demonstrated that the observation error of the observer converges in finite time. Finally, a global fast terminal sliding mode controller (GFTSMC) is developed for trajectory tracking, integrated with the aforementioned observer, and designed to smooth and limit the controller’s output. The controller’s stability is proven using Lyapunov stability theory, and its effectiveness is verified through simulation-based comparison experiments. Full article

Grounded in the theory of new economic geography, this research develops a comprehensive theoretical framework to examine the spatial interaction mechanisms between the Green Finance Index and carbon emissions. Employing a range of econometric techniques—including three-dimensional kernel density estimation, spatial quantile regression, bivariate spatial autocorrelation analysis, and the spatial linkage equation model—the dynamic evolution, spatial pattern shifts, and mutual influences of green finance and carbon emissions in the middle and lower reaches of the Yellow River from 2003 to 2022 are systematically assessed. The findings indicate that (1) both carbon emissions and the Green Finance Index have experienced a trajectory of continuous growth, phased decline, and structural optimization, accompanied by a gradual shift in the regional center of gravity from coastal economic zones towards resource-intensive and traditional industry-concentrated areas; (2) significant spatial clustering is evident for both green finance and carbon emissions, demonstrating a strong spatial correlation and regional synergy effects; (3) a persistent negative spatial correlation exists between green finance and carbon emissions; and (4) green finance exerts a stable negative spatial spillover effect on carbon emissions, suggesting that the influence of green finance extends beyond localities to adjacent regions through spatial externalities, manifesting pronounced spatial transmission and linkage characteristics. By unveiling the bidirectional spatial association between green finance and carbon emissions, this study highlights the pivotal role of green finance in driving regional low-carbon transitions. The results provide theoretical insights for optimizing green finance policies within the Yellow River Basin and offer valuable international references for similar regional low-carbon development initiatives. Full article

We extend a result by one of the authors, established for nonvacuum Einstein gravity, to minimally coupled k-essence scalar–tensor theories. First, we prove that in order to source a Kerr–Schild-type spacetime, the k-essence Lagrangian should be at most quadratic in the kinetic term. This is reduced to linear dependence when the Kerr–Schild null congruence is autoparallel. Finally, we show that solutions of the Einstein equations linearized in Kerr–Schild-type perturbations are also required to solve the full nonlinear system of Einstein equations, selecting once again k-essence scalar fields with linear Lagrangians in the kinetic term. The only other k-essence sharing the property of sourcing perturbative Kerr–Schild spacetimes, which are also exact, is the scalar field constant along the integral curves of the Kerr–Schild congruence, with the otherwise unrestricted Lagrangian. Full article

This paper presents a novel approach to solving the Yang–Mills existence and mass gap problem using quantum information theory. We develop a rigorous mathematical framework that reformulates the Yang–Mills theory in terms of quantum circuits and entanglement structures. Our method provides a concrete realization of the Yang–Mills theory that is manifestly gauge-invariant and satisfies the Wightman axioms. We demonstrate the existence of a mass gap by analyzing the entanglement spectrum of the vacuum state, establishing a direct connection between the mass gap and the minimum non-zero eigenvalue of the entanglement Hamiltonian. Our approach also offers new insights into non-perturbative phenomena such as confinement and asymptotic freedom. We introduce new mathematical tools, including entanglement renormalization for gauge theories and quantum circuit complexity measures for quantum fields. The implications of our work extend beyond the Yang–Mills theory, suggesting new approaches to quantum gravity, strongly coupled systems, and cosmological problems. This quantum information perspective on gauge theories opens up exciting new directions for research at the intersection of quantum field theory, quantum gravity, and quantum computation. Full article

We have investigated the Janis–Newman–Winicour spacetime through three fundamental tests of theories of gravity, namely, gravitational lensing, perihelion shift, and redshift due to gravitational force. Focusing initially on the circular motion of a massive particle within the equatorial plane, the analysis disregards external scalar field interactions. The Janis–Newman–Winicour (JNW) spacetime’s unique parameters, mass (M) and the scalar parameter (n), are examined, revealing an intriguing relationship between the innermost stable circular orbit position of the test particle and the scalar field parameter. The study also explores photon motion around a gravitational object in JNW spacetime, revealing the expansion of the photon sphere alongside a diminishing shadow, influenced by the external scalar field. Despite these complexities, gravitational bending of light remains consistent with general relativity predictions. The investigation extends to perihelion precession, where the trajectory of a massive particle in JNW spacetime exhibits eccentricity-dependent shifts, distinguishing it from Schwarzschild spacetime. Finally, oscillatory motion of massive particles in JNW spacetime is explored, providing analytical expressions for epicyclic frequencies using perturbation methods. The study concludes with the application of MCMC analyses to constrain the JNW spacetime parameters based on observational data. Full article

We revisit Weyl’s unified field theory, which arose in 1918, shortly after general relativity was discovered. As is well known, in order to extend the program of the geometrization of physics started by Einstein to include the electromagnetic field, H. Weyl developed a new geometry which constitutes a kind of generalization of Riemannian geometry. In this paper, our aim is to discuss Weyl’s proposal anew and examine its consistency and completeness as a physical theory. We propose new directions and possible conceptual changes in the original work. Among these, we investigate with some detail the propagation of gravitational waves, and the new features arising in this recent modified gravity theory, in which the presence of a massive vector field appears somewhat unexpectedly. We also speculate whether the results could be examined in the context of primordial gravitational waves. Full article

It has been proven that in standard Einstein gravity, exotic matter (i.e., matter violating the pointwise and averaged Weak and Null Energy Conditions) is required to stabilize traversable wormholes. Quantum field theory permits these violations due to the quantum coherent effects found in any quantum field. Even reasonable classical scalar fields violate the energy conditions. In the case of the Casimir effect and squeezed vacuum states, these violations have been experimentally proven. It is advantageous to investigate methods to minimize the use of exotic matter. One such area of interest is extended theories of Einstein gravity. It has been claimed that in some extended theories, stable traversable wormholes solutions can be found without the use of exotic matter. There are many extended theories of gravity, and in this review paper, we first explore $f\left(R\right)$ theories and then explore some wormhole solutions in $f\left(R\right)$ theories, including Lovelock gravity and Einstein Dilaton Gauss–Bonnet (EdGB) gravity. For completeness, we have also reviewed ‘Other wormholes’ such as Casimir wormholes, dark matter halo wormholes, thin-shell wormholes, and Nonlocal Gravity (NLG) wormholes, where alternative techniques are used to either avoid or reduce the amount of exotic matter that is required. Full article

Since the development of Brans–Dicke gravity, it has become well-known that a conformal transformation of the metric can reformulate this theory, transferring the coupling of the scalar field from the Ricci scalar to the matter sector. Specifically, in this new frame, known as the Einstein frame, Brans–Dicke gravity is reformulated as General Relativity supplemented by an additional scalar field. In 1959, Hans Adolf Buchdahl utilized an elegant technique to derive a set of solutions for the vacuum field equations within this gravitational framework. In this paper, we extend Buchdahl’s method to incorporate the cosmological constant and to the scalar-tensor cases beyond the Brans–Dicke archetypal theory, thereby, with a conformal transformation of the metric, obtaining solutions for a version of Brans–Dicke theory that includes a quadratic potential. More specifically, we obtain synchronous solutions in the following contexts: in scalar-tensor gravity with massless scalar fields, Brans–Dicke theory with a quadratic potential, where we obtain specific synchronous metrics to the Schwarzschild–de Sitter metric, the Nariai solution, and a hyperbolically foliated solution. Full article

Most space shuttle fuel tanks use a center column to hold the Propellant Management Device (PMD). This paper analyzes the gas–liquid interface state in the tanks with a central column during microgravity experiments conducted in the Chinese Space Station. It launches an extended study to investigate the gas–liquid interface state under different gravity conditions. Using the perturbation method and boundary layer theory, we numerically calculated the morphology of the gas–liquid interface under varying gravity conditions based on the Young–Laplace equation. The results were then compared to those obtained from existing commercial software and were found to be consistent. Based on this, the study develops two types of calculation procedures. The first procedure generates the corresponding shape of the liquid surface by inputting the height of the liquid surface endpoints and the gravity level. The second procedure is based on the targeting method and generates the corresponding liquid surface by inputting the volume of the liquid in the storage tank and the gravity level. The procedures were used to analyze the variation of gas–liquid interface properties under different gravity conditions. This study offers theoretical support for liquid management in aerospace engineering fuel tanks. Full article

The mutual influences of the electric field, rotation, and heat transmission find applications in controlled drug delivery systems, precise microfluidic manipulation, and advanced materials’ processing techniques due to their ability to tailor fluid behavior and surface morphology with enhanced precision and efficiency. Capillary instability has widespread relevance in various natural and industrial processes, ranging from the breakup of liquid jets and the formation of droplets in inkjet printing to the dynamics of thin liquid films and the behavior of liquid bridges in microgravity environments. This study examines the swirling impact on the instability arising from the capillary effects at the boundary of Rivlin–Ericksen and viscous liquids, influenced by an axial electric field, heat, and mass transmission. Capillary instability arises when the cohesive forces at the interface between two fluids are disrupted by perturbations, leading to the formation of characteristic patterns such as waves or droplets. The influence of gravity and fluid flow velocity is disregarded in the context of capillary instability analyses. The annular region is formed by two cylinders: one containing a viscous fluid and the other a Rivlin–Ericksen viscoelastic fluid. The Rivlin–Ericksen model is pivotal for comprehending the characteristics of viscoelastic fluids, widely utilized in industrial and biological contexts. It precisely characterizes their rheological complexities, encompassing elasticity and viscosity, critical for forecasting flow dynamics in polymer processing, food production, and drug delivery. Moreover, its applications extend to biomedical engineering, offering insights crucial for medical device design and understanding biological phenomena like blood flow. The inside cylinder remains stationary, and the outside cylinder rotates at a steady pace. A numerically analyzed quadratic growth rate is obtained from perturbed equations using potential flow theory and the Rivlin–Ericksen fluid model. The findings demonstrate enhanced stability due to the heat and mass transfer and increased stability from swirling. Notably, the heat transfer stabilizes the interface, while the density ratio and centrifuge number also impact stability. An axial electric field exhibits a dual effect, with certain permittivity and conductivity ratios causing perturbation growth decay or expansion. Full article

This study derives space travel pricing by Walrasian Equilibrium, which is logical reasoning from the general relativity theory (GRT), the accounting equation, and economic supply and demand functions. The Cobb–Douglas functions embed the endogenous space factor as new capital to form the space travel firm’s production function, which is also transformed into the consumer’s utility function. Thus, the market equilibrium occurs at the equivalence of supply and demand functions, like the GRT, which presents the equivalence between the spatial geometric tensor and the energy–momentum tensor, explaining the principles of gravity and the motion of space matter in the spacetime framework. The mathematical axiomatic set theory of the accounting equation explains the equity premium effect that causes a short-term accounting equation inequality, then reaches the equivalence by suppliers’ incremental equity through the closing accounts process of the accounting cycle. On the demand side, the consumption of space travel can be assumed as a value at risk (VaR) investment to attain the specific spacetime curvature in an expected orbit. Spacetime market equilibrium is then achieved to construct the space travel pricing model. The methodology of econophysics and the analogy method was applied to infer space travel pricing with the model of profit maximization, single-mindedness, and envy-free pricing in unit-demand markets. A case study with simulation was conducted for empirical verification of the mathematical models and algorithm. The results showed that space travel pricing remains associated with the principle of market equilibrium, but needs to be extended to the spacetime tensor of GRT. Full article

In the next decades, both space agencies and private competitors are targeting the lunar environment as a scientific and technological resource for future space missions. In particular, the confirmed existence of water-ice deposits in the vicinity of the poles (predominantly the south pole) makes polar or near-polar low lunar orbits attractive for the purpose of designing space missions that could search for suitable Lunar base sites. However, traveling very-low-altitude orbits is very challenging, as they are strongly perturbed by the Moon’s gravity field as well as third- and fourth-body effects due to the Earth and the Sun. Several studies demonstrate that these orbits are expected to impact the lunar surface in a few months. Therefore, the definition and implementation of an effective station-keeping strategy represents a crucial issue in order to extend satellites’ lifetime. In this paper, a feedback nonlinear control law is employed in order to perform corrective maneuvers aimed at keeping the state of the satellite within acceptable margins. The satellite is assumed to be equipped with a steerable and throttleable low-thrust propulsion system. The control law is based on the Lyapunov stability theory and does not require any reference path to track, with a considerable decrease in the computational cost. The proposed real-time control law includes control saturation, related to the maximum available thrust magnitude, and is developed employing modified equinoctial elements, in order to avoid singularities and extend its range of application. Finally, the strategy at hand is tested in the presence of all the relevant perturbations (i.e., harmonics of the selenopotential, third- and fourth-body effects) in order to show its effectiveness and efficiency. Full article