Search Results (140)

The paper outlines the hybrid framework of spin hydrodynamics, combining classical kinetic theory with the Israel–Stewart method of introducing dissipation. The local equilibrium expressions for the baryon current, the energy–momentum tensor, and the spin tensor of particles with spin 1/2 following the Fermi–Dirac statistics are obtained and compared with the earlier derived versions where the Boltzmann approximation was used. The expressions in the two cases are found to have the same form, but the coefficients are shown to be governed by different functions. The relative differences between the tensor coefficients in the Fermi–Dirac and Boltzmann cases are found to grow exponentially with the baryon chemical potential. In the proposed formalism, nonequilibrium processes are studied including mathematically possible dissipative corrections. Standard conservation laws are applied, and the condition of positive entropy production is shown to allow for the transfer between the spin and orbital parts of angular momentum. Full article

The primary objective of this paper is to derive a non-relativistic system of equations for a spin-2 particle in the presence of an external Coulomb field, solve these equations, and determine the corresponding energy spectra. We begin with the known radial system of 39 equations formulated for a free spin-2 particle and modify it to incorporate the effects of the Coulomb field. By eliminating the 28 components associated with vector and rank-3 tensor fields, we reduce the system to a set of 11 second-order equations related to scalar and symmetric tensor components. In accordance with parity constraints, this system naturally groups into two subsystems consisting of three and eight equations, respectively. To perform the non-relativistic approximation, we employ the method of projective operators constructed from the matrix ${\Gamma }^0$ of the original matrix equation. This approach allows us to derive two non-relativistic subsystems corresponding to the parity restrictions, comprising two and three coupled differential equations. Through a linear similarity transformation, we further decouple these into five independent equations with a Schrödinger-type non-relativistic structure, leading to explicit energy spectra. Special attention is given to the case of the minimal quantum number of total angular momentum, $j=0$, which requires separate consideration. Full article

We investigate the evolution of future trapping horizons through the dynamics of the Misner–Sharp mass using ingoing Eddington–Finkelstein coordinates. Our analysis shows that an integral formulation of Hayward’s first law governs much of the evolution of general spherically symmetric spacetimes. To account for the accretion backreaction, we consider a near-horizon approximation, which yields first-order corrections of a Vaidya-dark energy form. We further propose a systematic perturbative scheme to study these effects for an arbitrary background. As an application, we analyze an accreting Reissner–Nordström black hole and demonstrate the horizon shifts produced. Finally, we compute accretion-induced corrections to an extremal configuration. It is shown that momentum influx and energy density produce distinct effects: the former forces the splitting of the extremal horizon, while the latter induces significant displacements in its position, computed up to first-order perturbative corrections. These results highlight how different components of the stress–energy tensor significantly affect horizon geometry, with potential implications for broader areas of research, including black-hole thermodynamics. Full article

In this paper, we introduce and conduct a comprehensive study of pseudo-Schouten symmetric manifolds ${\left(PSS\right)}_n$. We establish necessary and sufficient conditions for such a manifold to be Einstein and quasi-Einstein, respectively. Next, we examine pseudo-Schouten symmetric spacetimes within the framework of general relativity. Furthermore, we investigate their role in relativistic spacetime models by considering Einstein’s field equations with and without a cosmological constant. We also show that pseudo-Schouten symmetric spacetimes satisfying Einstein’s equations with a quadratic Killing energy–momentum tensor or a Codazzi-type energy–momentum tensor cannot have non-zero constant scalar curvature. Finally, the existence of pseudo-Schouten symmetric spacetime is shown by constructing an explicit non-trivial example. Full article

It has been known for over 100 years that there is a discrepancy between Maxwell’s electrodynamics and the idea of a classical electron as the “atom” of electricity. This incompatibility is known under the terms 4/3 problem of the classical electron and radiation reaction force and was circumvented in the currently most successful theories, the quantum field theories, by limit value considerations, by the mutual subtraction of infinities, i.e., by purely mathematical methods that eliminate obvious contradictions but are not really based on an intuitive understanding of its physical causes. The actual origin of the problems mentioned lies in the instability of the classical electron. Stabilization cannot be achieved within the framework of Maxwell’s electrodynamics. This raises the question of what a minimal change to the fundamentals of electrodynamics should look like, which contains Maxwell’s theory as a limiting case. A detailed analysis of the 4/3 problem points to models that fulfill these requirements. Full article

The pairing of non-relativistic and relativistic Lagrangians within the context of fluid mechanics, advancing methodologies for constructing Poincare-invariant Lagrangians, is explored. Through leveraging symmetries and Noether’s theorem in an inverse framework, three primary cases are investigated: potential flow, barotropic flow expressed in terms of Clebsch variables, and an extended Clebsch Lagrangian incorporating thermodynamic effects. To ensure physical correctness, the eigenvalue relation of the energy–momentum tensor, together with velocity normalisation, are applied as key criteria. The findings confirm that the relativistic Lagrangians successfully reduce to their non-relativistic counterparts in the limit $c\to \infty$. These results demonstrate a systematic approach that enhances the relationship between symmetries and variational formulations, providing the advantage of deriving Lagrangians that unify non-relativistic and relativistic theories. Full article

Two extensions of the variational method with explicit energy functionals (EEFs) with respect to the spin-orbit force were performed. In this method, the energy per nucleon of nuclear matter is explicitly expressed as a functional of various two-body distribution functions, starting from realistic nuclear forces. The energy was then minimized by solving the Euler–Lagrange equation for the distribution functions derived from the EEF. In the first extension, an EEF of symmetric nuclear matter at zero temperature was constructed using the two-body central, tensor, and spin-orbit nuclear forces. The energy per nucleon calculated using the Argonne v8’ two-body nuclear potential was found to be lower than those calculated using other many-body methods, implying that the energy contribution caused by the spin-orbit correlation, whose relative orbital angular momentum operator acts on other correlations, is necessary. In a subsequent extension, the EEF of neutron matter at zero temperature, including the spin-orbit force, was extended to neutron matter at finite temperatures using the method by Schmidt and Pandharipande. The thermodynamic quantities of neutron matter calculated using the Argonne v8’ nuclear potential were found to be reasonable and self-consistent. Full article

We explore the equivalence between the low-energy dynamics of strained graphene and a quantum mechanical framework for the 2D Dirac equation in flat space with a deformed momentum operator. By considering some common forms of the anisotropic Fermi velocity tensor emerging from the elasticity theory, we associate such tensor forms with a deformation of the momentum operator. We first explore the bound states of charge carriers in a background uniform magnetic field in this framework and quantify the impact of strain in the energy spectrum. Then, we use a quadrature algebra formula as a mathematical tool to analyze the impact of the deformation attached to the momentum operator and identify physical consequences of such deformation in terms of energy modifications due to the applied strain. Full article

In this work, we obtained exact solutions of Einstein’s field equations for plane symmetric cosmological models by assuming that they admit conformal motion. The space-time geometry of these solutions is found to be nonsingular, non-vacuum and conformally flat. We have shown that in the case of a perfect fluid, these solutions have an energy-momentum tensor possessing dark energy with negative pressure and the energy equation of state is $\rho +p=0$. We have shown that a fluid has acceleration, rotation, shear-free, vanishing expansion, and rotation. In the case of a cosmic string cloud, we found that the tension density and particle density decrease as the fluid moves along the direction of the strings, then vanish at infinity. We shown that the exact conformal solution for a static plane symmetric model reduces to the well-known anti-De Sitter space-time. We obtained that the space-time under consideration admits a conformal vector field orthogonal to the 4-velocity vector and does not admits a vector parallel to the 4-velocity vector. Some physical and kinematic properties of the resulting models are also discussed. Full article

According to general relativity, the cosmological redshift may be caused by other mechanisms than the source moving away from the observer. It can occur on a global scale, similar to the gravitational redshift near massive stars. In principle, these are differences in the time-dependent global metric field between the source in the past and the observer in the present. In this paper we attempt a new interpretation of the simple solution of Einstein’s equations within a fully conformal metric for the case of a time-independent energy-momentum tensor. The scaling factor here acts identically on all four space-time coordinates and the speed of light is independent of the conformal time. The fully conformal metric is interpreted here as a universal geometric background which is scale invariant and acts universally on all objects, including gauges and clocks, regardless of their dimensions and internal interactions. The associated scale invariant exponential expansion is thus only relative and all observers at different times are completely equal. The model introduces the concept of the appearent age of the universe, which is the limiting consequence of time dilation into the past, and corresponds to the present value of the age of the universe H⁻¹ according to the standard model. This appearent age is the same for all observers, and the Hubble constant is thus a true universal constant, invariant to time translations. The motivation of this work was to test the possibility of the above cosmological redshift mechanism in confrontation with astrophysical data. Probably the most important consequence is the generalized formulation and interpretation of the Hubble-Lemaître law z(r) = (e^Hr/c − 1), which shows good agreement with astrophysical data even for the most distant supernovae. Confronting the conformal metric model with some astrophysical data shows an interesting agreement with the observed spatial distribution of astrophysical sources such as γ-ray bursts and quasars. On a cosmological scale, the above fully conformal metric naturally determines the global energy density, spatial flatness, and solves the horizon problem and Olbers’ paradox in infinite spacetime. Full article

Power consumption (PC) data are fundamental for optimizing energy use and managing industrial operations. However, with the widespread adoption of data-driven technologies in the energy sector, maintaining the integrity and quality of these data has become a significant challenge. Missing or incomplete data, often caused by equipment failures or communication disruptions, can severely affect the accuracy and reliability of data analyses, ultimately leading to poor decision-making and increased operational costs. To address this, we propose a Robust Momentum-Enhanced Non-Negative Tensor Factorization (RMNTF) model, which integrates three key innovations. First, the model utilizes adversarial loss and $L_2$ regularization to enhance its robustness and improve its performance when dealing with incomplete data. Second, a sigmoid function is employed to ensure that the results remain non-negative, aligning with the inherent characteristics of PC data and improving the quality of the analysis. Finally, momentum optimization is applied to accelerate the convergence process, significantly reducing computational time. Experiments conducted on two publicly available PC datasets, with data densities of 6.65% and 4.80%, show that RMNTF outperforms state-of-the-art methods, achieving an average reduction of 16.20% in imputation errors and an average improvement of 68.36% in computational efficiency. These results highlight the model’s effectiveness in handling sparse and incomplete data, ensuring that the reconstructed data can support critical tasks like energy optimization, smart grid maintenance, and predictive analytics. Full article

The star matter composed of nucleons deep inside compact stars, such as neutron stars, is believed to be very dense, such that various types of new concepts and physical phenomena are naturally expected due to the nontrivial strong correlations between hadrons. The possibility of revealing the hidden scale symmetry in dense baryonic matter has been discussed recently, to uncover the pseudo-conformal phase in dense star matter. In the pseudo-conformal phase, the trace of the energy–momentum tensor becomes density-independent, and the speed of sound approaches the conformal velocity in scale symmetric matter. Interestingly, it is also observed that the effective nucleon mass becomes a density-independent finite quantity, which can be identified as the chiral invariant mass of the parity doublet model, indicating that the parity doubling is an emergent phenomenon. In this paper, we will discuss how parity-doubling symmetry emerges inside the core of a compact star as a consequence of the interplays between $\omega$ vector mesons and nucleons (or dilaton, $\chi$, equivalently) and between the chiral symmetry and the scale symmetry. Full article

We analyze Hayward black holes (BHs) with a negative cosmological constant surrounded by a cloud of strings, which we designate Hayward–Letelier AdS BHs. These solutions can be obtained by coupling the Einstein equations with nonlinear electrodynamics and the energy–momentum tensor of clouds of strings. We show that these solutions are no longer regular and have a curvature singularity at the center. In turn, we analyze the thermodynamics associated with these BHs by establishing the form of the Smarr formula and the first law of thermodynamics. We derive the expressions for the thermodynamic quantities such as pressure, temperature, heat capacity, Gibbs free energy, and isothermal compressibility. We explore the phase structure of these solutions by analyzing the behavior of the heat capacity and Gibbs free energy. These solutions exhibit a first-order phase transition, similar to van der Waals fluids. We also check the behavior of the thermodynamic quantities near the critical points and calculate the values of the critical exponents. This illustrates a robust analogy between our solutions and van der Waals fluids. Full article

We present a review of the Semi-Symmetric Metric Gravity (SSMG) theory, representing a geometric extension of standard general relativity, based on a connection introduced by Friedmann and Schouten in 1924. The semi-symmetric connection is a connection that generalizes the Levi-Civita one by allowing for the presence of a simple form of the torsion, described in terms of a torsion vector. The Einstein field equations are postulated to have the same form as in standard general relativity, thus relating the Einstein tensor constructed with the help of the semi-symmetric connection, with the energy–momentum tensor. The inclusion of the torsion contributions in the field equations has intriguing cosmological implications, particularly during the late-time evolution of the Universe. Presumably, these effects also dominate under high-energy conditions, and thus SSMG could potentially address unresolved issues in general relativity and cosmology, such as the initial singularity, inflation, or the ⁷Li problem of the Big-Bang Nucleosynthesis. The explicit presence of torsion in the field equations leads to the non-conservation of the energy–momentum tensor, which can be interpreted within the irreversible thermodynamics of open systems as describing particle creation processes. We also review in detail the cosmological applications of the theory, and investigate the statistical tests for several models, by constraining the model parameters via comparison with several observational datasets. Full article

The propagation speeds of excitations are a crucial input in the modeling of interacting systems of particles. In this paper, we assume the microscopic physics is described by a kinetic theory for massless particles, which is approximated by a generalized relaxation time approximation (RTA) where the relaxation time depends on the energy of the particles involved. We seek a solution of the kinetic equation by assuming a parameterized one-particle distribution function (1-pdf) which generalizes the Chapman–Enskog (Ch-En) solution to the RTA. If developed to all orders, this would yield an asymptotic solution to the kinetic equation; we restrict ourselves to an approximate solution by truncating the Ch-En series to the second order. Our generalized Ch-En solution contains undetermined space-time-dependent parameters, and we derive a set of dynamical equations for them by applying the moments method. We check that these dynamical equations lead to energy–momentum conservation and positive entropy production. Finally, we compute the propagation speeds for fluctuations away from equilibrium from the linearized form of the dynamical equations. Considering relaxation times of the form $\tau ={\tau }_0{(-{\beta }_{\mu }{p}^{\mu })}^{-a}$, with $-\infty <a<2$, where ${\beta }_{\mu }=u_{\mu }/T$ is the temperature vector in the Landau frame, we show that the Anderson–Witting prescription $a=1$ yields the fastest speed in all scalar, vector and tensor sectors. This fact ought to be taken into consideration when choosing the best macroscopic description for a given physical system. Full article