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This study introduces a novel approach to achieving nonreciprocal transmission by implementing time modulation to the bianisotropic metasurface. For the first time, we present the analytical solution of the excitation of anti-symmetric surface waves on penetrable metasurfaces depending on the excitation direction. Exploiting this finding, we numerically demonstrate asymmetric control of the transmission coefficient under a fast-time scale by employing solely time modulation. This approach lowers the complexity of the modulation scheme and implementation encountered in the space-time modulation technique. We develop and simulate a 3D unit cell model in the microwave domain, which forms a surface cavity that incorporates time-varying capacitors. The impedance transfer matrix method and harmonic balance numerical solutions are applied to the retrieved equivalent circuit for the numerical simulations. The results reveal optimized phase-coherent and incoherent nonreciprocal transmission at the significant isolation level (≥ 40 dB) for forward and backward transmissions. We discuss the consistency and discrepancies between numerical methods and consider the impact of the losses and nonlinearity on the metastructure performance. [ABSTRACT FROM AUTHOR]

In this paper, we address the lower bound and space-time decay rates for the compressible Hall-MHD equations under H 3 -framework in R 3. First of all, the lower bound of decay rate for the density, velocity and magnetic field converging to the constant equilibrium status in L 2 is (1 + t) − 3 4 ; the lower bound of decay rate for the first order spatial derivative of density and velocity converging to zero in L 2 is (1 + t) − 5 4 , and the k (∈ [ 1 , 3 ]) -th order spatial derivative of magnetic field converging to zero in L 2 is (1 + t) − 3 + 2 k 4 . Secondly, the lower bound of decay rate for time derivative of density and velocity converging to zero in L 2 is (1 + t) − 5 4 ; however, the lower bound of decay rate for time derivatives of magnetic field converging to zero in L 2 is (1 + t) − 7 4 . Finally, we address the decay rate of solution in weighted Sobolev space H γ 3. [ABSTRACT FROM AUTHOR]

This research studies primarily centers around a specific vacuum solution of the Einstein’s field equations with a negative cosmological constant, known as a type-D vacuum solution in Anti-de Sitter (AdS) background. The key finding of this study is that the determinant of the Ricci tensor (Rμν) possesses a nonzero value. This observation ensures that this vacuum spacetime can be investigated within the framework of Ricci-inverse gravity as well. In fact, it has demonstrated that this type-D vacuum solution serves as an exact solution in Ricci inverse gravity in the background of AdS space. Notably, the negative cosmological constant undergoes modification by the coupling constant within this context. Moreover, we show that this gravity theory permits the formation of closed time-like curves at a specific moment in time analogue to the general relativity case. Consequently, this theory introduces an intriguing time-machine model within the domain of Ricci-inverse gravity theory. [ABSTRACT FROM AUTHOR]

The Bogoliubov transformation connecting the standard inertial frame mode functions to the standard mode functions defined in the Rindler frame R 0, leads to the result that the inertial vacuum appears as a thermal state with temperature T 0 = a 0 / 2 π where a 0 is the acceleration parameter of R 0. We construct an infinite family of nested Rindler-like coordinate systems R 1 , R 2 , ... within the right Rindler wedge, with time coordinates τ 1 , τ 2 , ... , and acceleration parameters a 1 , a 2 , ... by shifting the origin along the inertial x -axis by amounts ℓ 1 , ℓ 2 , ⋯ . We show that, apart from the inertial vacuum, the Rindler vacuum of the frame Rn also appears to be a thermal state in the frame R n + 1 with the temperature a n + 1 / 2 π . In fact, the Rindler frame R n + 1 attributes to all the Rindler vacuum states of R 1 , R 2 , ... R n , as well as to the inertial vacuum state, the same temperature a n + 1 / 2 π . We further show that our result is discontinuous in an essential way in the coordinate shift parameters. For a Rindler frame Ri, this thermality turns on with smallest non-zero ℓ i allowed in the semiclassical framework and remains insensitive to (ℓ i , a i − 1) thereafter, indicating its universal Planckian origin. Similar structures can be introduced in the right wedge of any spacetime with bifurcate Killing horizon, like, for e.g. Schwarzschild spacetime. Apart from providing unsuppressed observables capturing Planck scale effects, these results have important implications for quantum gravity (QG) when flat spacetime is treated as the ground state of QG. Furthermore, a frame with the shift ℓ and the corresponding acceleration parameter a (ℓ) can be thought of as a Rindler frame which is instantaneously comoving with the Einstein's elevator moving with a variable acceleration. Our result suggests that the quantum temperature associated with such an Einstein's elevator is the same as that defined in the comoving Rindler frame. The implications of these results are wide ranging, from having a definitive signature of Planck shifts in the horizon to the existence of a new set of observers in black hole exterior having thermodynamic description of the horizon they perceive. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the concept of Symmetric Teleparallel Gravity and its extensions, mainly focusing on f(Q,T) modified gravity theories. These theories explore the replacement of the Levi–Civita connection in General Relativity with a general affine connection in flat spacetime, leading to the formulation of gravity based on non-metricity. We highlight the advantages of second-order field equations in f(Q) and f(Q,T) theories compared to higher-order equations in modified f(R) gravity. The inclusion of bulk viscosity in the model offers insights into the late-time behavior of the universe. In this regard, we study the spatially homogeneous and anisotropic universe with viscous fluid in the framework of the symmetric teleparallel gravity f(Q,T). We solve the field equations and obtain some cosmological parameters, including the deceleration parameter, equation of state parameter, Bulk viscous pressure and scale factor. In the following, we analyze the behavior of the cosmological parameters of the model with some figures and adjust our model parameters with recent data. [ABSTRACT FROM AUTHOR]

In this paper, we consider a cosmological model of hyperbolic inflation involving two-scalar fields. By examining the Noether symmetries of the corresponding Lagrangian in the context of a spatially flat Friedmann–Lemaître–Robertson–Walker spacetime, we identify conserved quantities or first integrals corresponding to specific cases. These conserved quantities facilitate the derivation of novel solutions to the field equations, offering new perspectives on the dynamics of two-field inflationary models. [ABSTRACT FROM AUTHOR]

Formalisms for higher order quantum processes provide a theoretical formalisation of quantum processes where the order of agents' operations need not be definite and acyclic, but may be subject to quantum superpositions. This has led to the concept of indefinite causal structures (ICS) which have garnered much interest. However, the interface between these information-theoretic approaches and spatiotemporal notions of causality is less understood, and questions relating to the physical realisability of ICS in a spatiotemporal context persist despite progress in their information-theoretic characterisation. Further, previous work suggests that composition of processes is not so straightforward in ICS frameworks, which raises the question of how this connects with the observed composability of physical experiments in spacetime. To address these points, we compare the formalism of quantum circuits with quantum control of causal order (QC-QC), which models an interesting class of ICS processes, with that of causal boxes, which models composable quantum information protocols in spacetime. We incorporate the set-up assumptions of the QC-QC framework into the spatiotemporal perspective and show that every QC-QC can be mapped to a causal box that satisfies these set up assumptions and acts on a Fock space while reproducing the QC-QC's behaviour in a relevant subspace defined by the assumptions. Using a recently introduced concept of fine-graining, we show that the causal box corresponds to a fine-graining of the QC-QC, which unravels the original ICS of the QC-QC into a set of quantum operations with a well-defined and acyclic causal order, compatible with the spacetime structure. Our results also clarify how the composability of physical experiments is recovered, while highlighting the essential role of relativistic causality and the Fock space structure. [ABSTRACT FROM AUTHOR]

This paper studies the properties of weak solutions to a class of space-time fractional parabolic-elliptic Keller-Segel equations with logistic source terms in R n , n ≥ 2 . The global existence and L ∞ -bound of weak solutions are established. We mainly divide the damping coefficient into two cases: (i) b > 1 - α n , for any initial value and birth rate; (ii) 0 < b ≤ 1 - α n , for small initial value and small birth rate. The existence result is obtained by verifying the existence of a solution to the constructed regularization equation and incorporate the generalized compactness criterion of time fractional partial differential equation. At the same time, we get the L ∞ -bound of weak solutions by establishing the fractional differential inequality and using the Moser iterative method. Furthermore, we prove the uniqueness of weak solutions by using the hyper-contractive estimates when the damping coefficient is strong. [ABSTRACT FROM AUTHOR]

In this paper, we study rigidity aspects of Penrose's singularity theorem. Specifically, we aim to answer the following question: if a spacetime satisfies the hypotheses of Penrose's singularity theorem except with weakly trapped surfaces instead of trapped surfaces, then what can be said about the global spacetime structure if the spacetime is null geodesically complete? In this setting, we show that we obtain a foliation of MOTS which generate totally geodesic null hypersurfaces. Depending on our starting assumptions, we obtain either local or global rigidity results. We apply our arguments to cosmological spacetimes (i.e., spacetimes with compact Cauchy surfaces) and scenarios involving topological censorship. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of the semiconformal curvature tensor's symmetry on the base and fiber manifolds of a warped product manifold. It establishes that the fiber manifold of a warped product manifold has a constant sectional curvature, whereas the base manifold is semiconformally symmetric. Furthermore, the paper derives the specific forms of the semiconformal curvature tensor for both the base and fiber manifolds. Also, it is demonstrated that a semiconformally symmetric (flat) GRW space-time is a perfect fluid space-time and exhibits an irrotational velocity vector field. [ABSTRACT FROM AUTHOR]

This paper delivers the characterization of a pseudo B -symmetric spacetimes and we illustrate that a pseudo B -symmetric spacetime admitting Codazzi type of B -tensor represents a perfect fluid spacetime and if this spacetime admits the time-like convergence criterion, then the pseudo B -symmetric spacetime fulfills cosmic strong energy criterion and contains pure matter. Besides, we find in a pseudo B -symmetric spacetime with Codazzi type of B -tensor the electric part of the Weyl tensor vanishes and has Riemann and Weyl compatible vector fields. Furthermore, it is established that the chosen spacetime with Codazzi type of B -tensor is conformally flat and represents a Robertson–Walker spacetime. Also, we calculate the scale factor Ψ (t) for these spacetimes in a spatially flat Robertson–Walker spacetime. Finally, we study the impact of this spacetime under f (R) gravity scenario and deduce several energy conditions by considering a new model f (ℛ) = e (α ℛ) − ln (β ℛ) in which α and β are positive constants. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel curvature tensor called the -curvature tensor, which is formed by combining the Weyl tensor and the 2 -curvature tensor. It is proved that a semi-Riemannian manifold with traceless -curvature tensor is Einstein, while a -curvature flat semi-Riemannian manifold exhibits constant sectional curvature. We show that a space-time with traceless -curvature tensor or -curvature flat represents dark energy era. A semi-Riemannian manifold with divergence-free -curvature tensor is Weyl harmonic. In a space-time where the -curvature tensor is of divergence-free, both the isotropic pressure and energy density are constants. Under certain conditions, it is shown that a pseudo- -symmetric semi-Riemannian manifold reduces to a pseudo-Riemannian manifold. It is demonstrated that pseudo- -symmetric space-times can be regarded as generalized Robertson–Walker (GRW) space-times. Finally, a concrete example of pseudo- -symmetric semi-Riemannian manifolds is presented. [ABSTRACT FROM AUTHOR]

The principal aim of this paper is to find the expression of *-Bach tensors on (κ , μ) ′ -almost-Kenmotsu manifolds. It is shown that if the metric of a (κ , μ) ′ -almost-Kenmotsu manifold admits a generalized closed *-Bach soliton, then the metric is *-Bach flat under certain restrictions. We also prove that the metric of a generalized gradient *-Bach soliton on a (κ , μ) ′ -almost-Kenmotsu manifold is *-Bach flat, for a soliton function which is invariant under the Reeb vector field. Further, we characterize generalized *-Bach solitons with trace-free *-Bach tensors on (κ , μ) ′ -almost-Kenmotsu manifolds and results are verified by an example. As an application of these solitons, we study generalized almost-Bach solitons whose metrics are associated with the Lorentzian metric of the perfect fluid spacetimes. [ABSTRACT FROM AUTHOR]

Timelike sectional curvature bounds play an important role in spacetime geometry, both for the understanding of classical smooth spacetimes and for the study of Lorentzian (pre-)length spaces introduced by Kunzinger and Sämann [Ann. Global Anal. Geom. 54 (2018), pp. 399-447]. In the smooth setting, a bound on the sectional curvature of timelike planes can be formulated via the Riemann curvature tensor. In the synthetic setting, bounds are formulated by comparing various geometric configurations to the corresponding ones in constant curvature spaces. The first link between these notions in the Lorentzian context was established by Harris [Indiana Univ. Math. J. 31 (1982), pp. 289–308], which was instrumental in the proof of powerful results in spacetime geometry (see Beem et al. [ Toponogov splitting theorem for Lorentzian manifolds , Springer, Berlin, 1985; J. Differential Geom. 22 (1985), pp. 29–42]; Galloway and Ling [Gen. Relativity Gravitation 50 (2018), p. 7]). For general semi-Riemannian manifolds, the equivalence between sectional curvature bounds and synthetic bounds was established by Alexander and Bishop [Comm. Anal. Geom. 16 (2008), pp. 251–282]; however in this approach the sectional curvatures of both timelike and spacelike planes have to be considered. In this article, we fill a gap in the literature by proving the full equivalence between sectional curvature bounds on timelike planes and synthetic timelike bounds on strongly causal spacetimes. As an essential tool, we establish Hessian comparison for the time separation and signed distance functions. [ABSTRACT FROM AUTHOR]

Linking sensory-evoked traveling waves to underlying circuit patterns is critical to understanding the neural basis of sensory perception. To form this link, we performed simultaneous electrophysiology and two-photon calcium imaging through transparent NeuroGrids and mapped touch-evoked traveling waves and underlying microcircuit dynamics. In awake mice, both passive and active whisker touch elicited traveling waves within and across barrels, with a fast early component followed by a late wave that lasted hundreds of milliseconds poststimulus. Notably, late waves were modulated by perceived value and predicted behavioral choice in a two-whisker discrimination task. We found that the late wave feature was (i) modulated by motor feedback, (ii) differentially engaged a sparse ensemble reactivation pattern across layer 2/3, which a balanced-state network model reconciled via feedback-induced inhibitory stabilization, and (iii) aligned to regenerative layer 5 apical dendritic Ca2+ events. Our results reveal that translaminar spacetime patterns organized by cortical feedback support sparse touch-evoked traveling waves. [ABSTRACT FROM AUTHOR]

We investigate the cosmic evolution of the universe in context of f(R,G) gravity with homogeneous and isotropic background, where R represents the Ricci scalar, and G denotes the Gauss–Bonnet invariant. With the field equations of the f(R,G) gravity in the non-flat spacetime, we examine the characteristics of model with two distinct forms: f1(R,G) = μRnGm and f2(R,G) = β1R + β2μRnGm, where n, m, β1 and β2 are the model parameters. The power-law solutions for the field equations are obtained by constraining the model parameters by employing Bayesian analysis tools in conjunction with the Markov Chain Monte Carlo (MCMC) method. We constraint the parameters by utilizing the combined datasets (OHD+BAO+Pantheon) for open Friedmann–Lemaitre–Robertson–Walker (FLRW) model. The parameters of power-law solutions are determined as H0 = 70.76732−0.00088+0.00010 km/(s ⋅ Mpc) and q = −0.6478−0.000075+0.000091. The present dark energy model estimates H0 value higher than the ΛCDM model. This is one of the motivations to consider the f(R,G) gravity to describe dark energy era. The best-fit values of model parameters in an open model yield the power index of power-law solution as α = 2.394949−0.00060+.000089. In the present model, the joint analysis by incorporating data from OHD, BAO, and Pantheon datasets favors the open FLRW model with power-law solutions at the late times. The behavior of cosmological parameters has been studied to explore the evolution of dark energy. The equation of state parameter (ω ≃−1) supports the accelerated expansion of the Universe at late times. The energy conditions are also studied to test the cosmological viability of the model. [ABSTRACT FROM AUTHOR]

In this paper, we study the Lagrangian structure of Vlasov-Maxwell system, that is, by using a suitable notion of flow, we prove that if the densities ρ , j are integrable in spacetime, and the charge acceleration ∂ t j and ∂ t t j (or ∇ ∂ t j) are integrable functions in spacetime, then renormalized and distributional solutions of the system are the transport of the initial condition by its flow. We study more general vector fields, with wavelike structure in the sense that it has finite speed of propagation, generalizing the vector fields studied in [6]. The result is a extension of those obtained by Ambrosio, Colombo, and Figalli [2] for the Vlasov-Poisson system, and by the author and Marcon [5] for relativistic Vlasov-systems with quasistatic approximations of Maxwell's equations. [ABSTRACT FROM AUTHOR]

This paper obtains the matrix elements and characters of the discrete series unitary irreducible representations (UIRs) of the Sp(4, ℝ) group. With an isomorphic relationship to the two-fold covering of SO0(2, 3) (Sp(4, ℝ)∼SO0(2, 3) × ℤ2), this group holds particular importance as the kinematical/relativity group within the framework of (1 + 3-dimensional) anti-de Sitter spacetime. [ABSTRACT FROM AUTHOR]

After recalling the principles that allow spacetime to be considered by analogy as an elastic medium, we show how the modified gravity according to the MOND theory concerning the anomaly of the velocities of stars at the periphery of galaxies can be seen as a creep of space acting on the radius of galaxies that give a creep coefficient of φspace=a0aρlocalρmean−1. The values vary between 0.2 and 9 depending on the type of galaxy and density distribution. Considering the gravitational lensing effect of the ball cluster we obtain a creep coefficient φspace=1−pvpv with pv the percentage of visible matter and pDM the percentage of dark matter from the global mass (pv+pDM=1). The values vary between 0.66 and 4 for this cluster. This paper therefore raises the question, via these creep coefficients, of the possible granular nature of the vacuum and therefore of space fabric on the one hand and proposes another dark matter-free approach based on the creep of the texture of space to explain gravitational anomalies on the other hand. [ABSTRACT FROM AUTHOR]

This paper explores isotropic polytropes within the framework of the f(R,G) modified gravity theory. We derive the field equations that govern these systems and develop the Lane–Emden equations for both mass (baryonic) density and total energy density, utilizing two different polytropic equations of state. Our analysis shows that the constructed models feature positive and finite density and pressure, which decrease as expected towards the outer boundary, aligning with the typical behavior of self-gravitating objects. Additionally, the energy–momentum tensor meets the required energy conditions, confirming the physical viability of the models. The compactness factor remains below the critical limit, signifying stability and providing insights into gravitational redshift. Analysis of the sound speed confirms adherence to causality, while the adiabatic index indicates a degree of stiffness within the system. These findings advance our understanding of self-gravitating objects in f(R,G) gravity and lay the groundwork for future research in this field. [ABSTRACT FROM AUTHOR]

The focus of this paper is the examination of self-similar vector fields (SSVFs) within Bianchi type I spacetime utilizing the Rif tree approach. The paper employs a computer algorithm to convert the equations into a reduced involutive form, dividing the integration problem into multiple cases represented in a tree structure. These cases are subject to specific constraints on the metric functions. By employing these constraints, the set of equations governing self-similar symmetries is solved, yielding explicit expressions for the metrics and their associated self-similar vector fields. [ABSTRACT FROM AUTHOR]

This paper is the continuation of the groundwork laid in [A. Iram, A. A. Siddiqui and T. Feroze, Int. J. Mod. Phys. D 31(11) (2022) 2240006], where the Segre classification scheme was applied to categorize spherically symmetric static spacetime metrics into four possible Segre types [(1, 111)], [1, (111)], [(1, 1)(11)], or [1, 1(11)]. The solution for type [(1, 111)] leads to the Schwarzschild de-Sitter/anti de-Sitter metrics. The eigenvalue degeneracy in Segre types identifies the kind of matter distribution in space and aid in the consideration of novel solutions for the corresponding energy momentum tensor. We deal with an anisotropic distribution of matter correlated with electric field intensity for types [(1, 1)(11)] and [1, 1(11)]. The type [1, (111)] refers to ideal fluid characterized by uniformly distributed pressure. A comprehensive examination is conducted in scenarios where all physical and stability criteria are satisfied. Nevertheless, for type [(1, 1)(11)], the strong energy and causality prerequisites are breached due to negative pressure, suggesting the existence of dark energy where the attributes of standard matter cannot be met. Furthermore, the numerical test for models is conducted for the compact objects 4U 1538 − 52, PSR J1614 − 2230, 4U 1608 − 52, and EXO 1785 − 248. Each star’s density, pressure, and compactness factor are observed, showing the regularity at the origin. These observations impart that the discover models are plausible since they accurately represent the observable system. [ABSTRACT FROM AUTHOR]

This research paper aims to redefine the complexity factor in f(R,G) gravity and the appearance of electric charge, where R is the Ricci scalar and G is the Gauss–Bonnet term. In this context, we intend to analyze the splitting of the Riemann tensor after considering the anisotropic distribution of the charged fluid related to the spherically symmetric spacetime. We interpret YTF as the complexity factor among all the determined structural scalars that encompasses the characteristics of anisotropic pressure and the effective representation of the energy density. The correction terms associated with modified theory are considered to calculate some significant results related to the Weyl scalar, Tolman mass, and the complexity factor (CF). Moreover, the expression for CF is established by using the structure scalars determined in our paper, and the diminishing complexity restraint is utilized to determine the solutions for the various models. The celestial object having non-uniform energy density and anisotropic pressure asserts the maximum intricacy. But, if the effects of non-uniform energy density and anisotropic distribution of pressure are eradicated due to the presence of dark source terms associated with modified gravity then these fluids may not exhibit any complexity. Consequently, it is revealed that the constituents of effective and electromagnetic parts directly influence the structure scalars and CF. [ABSTRACT FROM AUTHOR]

The notion of Unchanged Direction (UD) motion in an arbitrary Galilean spacetime is introduced providing a mathematical framework for the intuitive notion that “proper acceleration does not change its direction”. Given a prescribed scalar acceleration, the corresponding initial value problem is analyzed and used to characterize the UD trajectories as the projected curves on the spacetime of the integral curves of a smooth vector field defined on a certain fiber bundle. This key fact allows us to prove a result on the completeness of inextensible UD motions, that can be physically interpreted saying that observers which obey a UD motion live forever. Concretely, it is shown that a UD observer in a globally synchronizable Galilean spacetime can be extended if there exists a complete spatially conformally Leibnizian field of observers with conformal factor and gravitational field bounded along finite times. Finally, another completeness result is presented in the case of the existence of a compact absolute spacelike leaf. [ABSTRACT FROM AUTHOR]

In this paper, we calculate the radiative correction to the Casimir energy for both massive and massless Lorentz-violating scalar fields confined between two membranes with rough surfaces in a (3+1)-dimensional spacetime. The computations are performed for four types of boundary conditions: Dirichlet, Neumann, Periodic, and Mixed. A crucial element of our approach involves the use of position-dependent counterterms to incorporate the influence of boundaries within the renormalization program. To manage the divergences that emerge in the Casimir energy calculations, we apply the Box Subtraction Scheme (BSS) along with the cutoff regularization technique. We present and discuss results for various degrees of membrane roughness, emphasizing the consistency of our findings with theoretical expectations. [ABSTRACT FROM AUTHOR]

This paper explores the cracking phenomenon within the framework of Rastall gravity, focusing on how local density perturbations influence the stability of stellar objects. To achieve this, we assumed an isotropic matter configuration and derived the field equations and equilibrium conditions for spherically symmetric spacetime in the context of Rastall gravity. Our analysis utilized the barotropic equation of state along with the Krori–Barua spacetime metric coefficients. The equilibrium state of the configuration was then subjected to local density perturbations to assess its stability. To validate our methodology, we analyzed several stellar objects, including 4U 1820-30, Her X-1, SAX J1808.4-3658, PSR J1614-2230, RX J1856-37, Vela X-1, and Cen X-3. The results demonstrate that cracking occurs in these stars for specific ranges of Rastall parameters. This study highlights the importance of the cracking approach as a powerful tool for conducting a detailed stability analysis of stellar structures. [ABSTRACT FROM AUTHOR]

Among the factors, such as emotions, that distort time perception, vestibular stimulation causes a contraction in subjective time. Unlike emotions, the intensity of vestibular stimulation can be easily and precisely modified, making it possible to study the quantitative relationship between stimulation and its effect on time perception. We hypothesized that the contraction of subjective time would increase with the vestibular stimulation magnitude. In the first experiment, participants sat on a rotatory chair and reproduced time intervals between the start and the end of whole-body passive rotations (40° or 80°; dynamic condition) or between two consecutive low-amplitude shakes (static condition). We also assessed reaction time under the same conditions to evaluate the attentional effect of the stimuli. As expected, duration reproduction in the 40° rotation was shorter than that observed in the static condition, but this effect was partly reversed for 80° rotations. In other words, vestibular stimulation shortens the perceived time interval, but this effect weakens with stronger stimulation. Attentional changes do not explain this unexpected result, as reaction time did not change between conditions. We hypothesized that the space-time interaction (i.e., spatially larger stimuli are perceived as lasting longer) could explain these findings. To assess this, in a second experiment participants were subjected to the same protocol but with three rotation amplitudes (30°, 60°, and 120°). The duration reproductions were systematically shorter for the lower amplitudes than for the higher amplitudes; so much so that for the highest amplitude (120°), the duration reproduction increased so that it did not differ from the static condition. Overall, the experiments show that whole-body rotation can contract subjective time, probably at the rather low level of the interval timing network, or dilate it, probably at a higher level via the space-time interaction. [ABSTRACT FROM AUTHOR]

We study h-almost conformal ω-Ricci–Bourguignon solitons and h-almost gradient conformal ω-Ricci–Bourguignon solitons in spacetimes of general relativity. At first, we provide an example of h-almost conformal ω-Ricci–Bourguignon soliton. Next, we prove that if a generalized Robertson–Walker spacetime admits an h-almost conformal ω-Ricci–Bourguignon soliton or an h-almost gradient conformal ω-Ricci–Bourguignon soliton, then it becomes a perfect fluid spacetime. Moreover, we have observed that a spacetime with h-almost conformal ω-Ricci–Bourguignon soliton whose potential vector field is a conformal vector field is an ω-Einstein manifold. [ABSTRACT FROM AUTHOR]

In this work, we investigate some extensions of the Kiselev black hole solutions in the context of f(핋,풯) gravity. By mapping the components of the Kiselev energy–momentum tensor into the anisotropic energy–momentum tensor and assuming a particular form of f(핋,풯), we obtain exact solutions for the field equations in this theory that carries dependence on the coupling constant and on the parameter of the equation of state of the fluid. We show that in this scenario of modified gravity some new structure is added to the geometry of spacetime as compared to the Kiselev black hole. We analyze the energy conditions, mass, horizons and the Hawking temperature considering particular values for the parameter of the equation of state. [ABSTRACT FROM AUTHOR]

The purpose of the article is to analyze an accurate numerical technique to solve a space-time fractional-order Fisher equation in the Caputo sense. For this purpose, the spectral collocation technique is used, which is based on the Vieta-Lucas approximation. By using the properties of Vieta-Lucas polynomials, this technique reduces the nonlinear equations into a system of ordinary differential equations (ODEs). The non-standard finite difference (NSFD) method converts this system of ODEs into algebraic equations which have been solved numerically. Moreover, the error estimate is investigated for the proposed method. To show the accuracy and efficiency of the technique, the obtained numerical results are compared with the analytical results and existing results of the particular forms of the considered fractional order models through error analysis. The important feature of this article is the exhibition of variations of the field variable for various values of spatial and temporal fractional order parameters for different particular cases. [ABSTRACT FROM AUTHOR]

Using Darmois-Israel-Sen junction conditions, and with help of Visser's cut-and-paste method, we study the dynamics of thin-shell wormholes that are made of two conformally Killing gravity (a.k.a Harada gravity) black holes. We check the energy conditions for different values of the new parameter that Harada introduced, as alternative for dark energy. We examine the radial acceleration to reveal the attractive and repulsive characteristics of the thin-shell wormhole throat. We consider the dynamics and stability of the wormhole around the static solutions of the linearized radial perturbations at the wormhole throat. Finally, we determine the regions of stability by applying the concavity test on the "speed of sound" as a function in the throat radius and other spacetime parameters, particularly the new Harada parameter. [ABSTRACT FROM AUTHOR]

In this work, the fractal continuum Maxwell law for the creep phenomenon is introduced. By mapping standard integer space-time into fractal continuum space-time using the well-known Balankin's approach to variable-order fractal calculus, the fractal version of Maxwell model is developed. This methodology employs local fractional differential operators on discontinuous properties of fractal sets embedded in the integer space-time so that they behave as analytic envelopes of non-analytic functions in the fractal continuum space-time. Then, creep strain ε (t) , creep modulus J (t) , and relaxation compliance G (t) in materials with fractal linear viscoelasticity can be described by their generalized forms, ε β (t) , J β (t)   and   G β (t) , where β = d i m S / d i m H represents the time fractal dimension, and it implies the variable-order of fractality of the self-similar domain under study, which are d i m S and d i m H for their spectral and Hausdorff dimensions, respectively. The creep behavior depends on beta, which is characterized by its geometry and fractal topology: as beta approaches one, the fractal creep behavior approaches its standard behavior. To illustrate some physical implications of the suggested fractal Maxwell creep model, graphs that showcase the specific details and outcomes of our results are included in this study. [ABSTRACT FROM AUTHOR]

In this paper, we find several teleparallel F (T , B) solutions for a Robertson–Walker (TRW) cosmological spacetime. We first set and solve the F (T , B) -type field equations for a linear perfect fluid. Using similar techniques, we then find new F (T , B) solutions for non-linear perfect fluids with a weak quadratic correction term to the linear equation of state (EoS). Finally, we solve for new classes of F (T , B) solutions for a scalar field source by assuming a power-law scalar field and then an exponential scalar field in terms of the time coordinate. For flat cosmological cases ( k = 0 cases), we find new exact and approximate F (T , B) solutions. For non-flat cases ( k = ± 1 cases), we only find new teleparallel F (T , B) solutions for some specific and well-defined cosmological expansion subcases. We conclude by briefly discussing the impact of these new teleparallel solutions on cosmological processes such as dark energy (DE) quintessence and phantom energy models. [ABSTRACT FROM AUTHOR]

Before we ask what the quantum gravity theory is, there is a legitimate quest to formulate a robust quantum field theory in curved spacetime (QFTCS). Several conceptual problems, especially unitarity loss (pure states evolving into mixed states), have raised concerns over several decades. In this paper, acknowledging the fact that time is a parameter in quantum theory, which is different from its status in the context of General Relativity (GR), we start with a "quantum first approach" and propose a new formulation for QFTCS based on the discrete spacetime transformations which offer a way to achieve unitarity. We rewrite the QFT in Minkowski spacetime with a direct-sum Fock space structure based on the discrete spacetime transformations and geometric superselection rules. Applying this framework to QFTCS, in the context of de Sitter (dS) spacetime, we elucidate how this approach to quantization complies with unitarity and the observer complementarity principle. We then comment on understanding the scattering of states in de Sitter spacetime. Furthermore, we discuss briefly the implications of our QFTCS approach to future research in quantum gravity. [ABSTRACT FROM AUTHOR]

Let {Ptα}t>0 be the fractional semigroup equipped with the integral kernel {Ptα}t>0 on a complete doubling metric measure space ( M , d, μ) supporting the weak Poincaré inequality. Our aim is to characterize such a measure ν on M × (0 , ∞) that f ↦ ∫ M p t α d w α (⋅ , y) f (y) d μ (y) is bounded from the Newton–Sobolev spaces and the Lebesgue space into the Lebesgue space L q (M × (0 , ∞) , ν) respectively, where the kernel Ptα satisfies certain two-sided estimate obtained from the assumption on the heat kernel pt. Preliminary results including estimates, involving the variational p-capacity and the non-tangential maximal function are provided. For the extension of Lebesgue spaces, a new Lp-capacity associated to the semigroup {Ptα}t>0 is introduced. Then some basic properties of the Lp-capacity, including its dual form, the Lp-capacity of fractional parabolic balls, and capacitary strong type inequalities, are established. Meanwhile, we also obtain the space-time estimate for the semigroup {Ptα}t>0. [ABSTRACT FROM AUTHOR]

This paper primarily lies in presenting an α -robust analysis of finite element method for space-time fractional diffusion equation. To this end, we firstly develop finite element approximation to fractional Laplacian and provide a d-dimensional fast Fourier transform (FFT)-based fast algorithm to derive spatial discretization of space-time fractional diffusion problem. Then we study the α -robust stability and error analyses of full discrete scheme of space-time fractional diffusion problem using L1 scheme on graded temporal meshes. Different from current many existing works, the established stability and error bounds will not blow-up under energy norm as α → 1 - , and the present error analysis illustrates that a choice of time mesh graded factor γ = (2 - α) / α shall yield an optimal rate of convergence O (N - (2 - α)) in temporal direction, where N is the number of temporal meshes. Eventually, some numerical tests are given to show the efficiency and α -robust behavior of the proposed scheme. [ABSTRACT FROM AUTHOR]

Space-time wave packets (STWPs) are a new class of pulsed optical beams with many unique and intriguing attributes, including propagation invariance and tunable group velocity in linear optical media. STWPs are a form of spatiotemporally structured light, so their synthesis poses challenges that are not shared by conventional monochromatic structured light fields. We present here a detailed description of the synthesis of STWPs that are localized along one transverse dimension and uniform along the other; i.e. space-time light sheets. We also describe the main characterization schemes needed for benchmarking the unique properties of space-time light sheets. [ABSTRACT FROM AUTHOR]

We prove the stability of entropy solutions of nonlinear conservation laws with respect to perturbations of the initial datum, the space-time dependent flux and the entropy inequalities. Such a general stability theorem is motivated by the study of problems in which the flux P[u](t, x, u) depends possibly non-locally on the solution itself. For these problems we show the conditional existence and uniqueness of entropy solutions. Moreover, the relaxation of the entropy inequality allows to treat approximate solutions arising from various numerical schemes. This can be used to derive the rate of convergence of the recent particle method introduced in Radici and Stra (SIAM J Math Anal 55(3):2001–2041, 2023. https://doi.org/10.1137/21M1462994) to solve a one-dimensional model of traffic with congestion, as well as recover already known rates for some other approximation methods. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating the behavior of charged compact stars in the f (R , ϕ , X) theory of gravity, where R denotes the Ricci Scalar, ϕ is a scalar potential, and X is a kinetic term. For this purpose, we consider spherically symmetric spacetime with Bardeen geometry as exterior spacetime to investigate various properties of compact stars, including energy density and pressure components. Matching conditions are used to find model parameters. We present a detailed analysis, including a discussion of equations of state parameters, and stability criteria. In this analysis, we discuss the energy conditions to check the viability of our model. Furthermore, an equilibrium condition can be visualized through the modified Tolman–Oppenheimer–Volkov equation. It is concluded that Bardeen's geometry supports the existence of compact stars in the background of the f (R , ϕ , X) theory of gravity. [ABSTRACT FROM AUTHOR]

First, we prove that a Ricci symmetric spacetime is a perfect fluid spacetime if and only if it is a generalized Robertson–Walker spacetime. Consequently, we establish that under certain constraints on the associated scalar, such a spacetime turns into a static spacetime and is classified under Petrov classification I , D , or O. Also, we notice that a semi-symmetric as well as pseudo-Ricci symmetric generalized Robertson–Walker spacetime is a perfect fluid spacetime. We examine conformally flat generalized Robertson–Walker spacetime as a solution of f (ℛ ∗) -gravity theory and describe the physical relevance. For the model f (ℛ ∗) = ln (ℛ ∗) − exp (− ℛ ∗) , numerous energy conditions in terms of associated scalars are investigated. This model agrees with the current investigations which states that the Cosmos is in an accelerating phase. [ABSTRACT FROM AUTHOR]

In this paper, we give some classification of conformally harmonic Z -recurrent spacetime in the context of F (R) -gravity theory based on its scalar curvature and obtained the expression for energy density and isotopic pressure. Their behaviors along with EoS parameter are analyzed by considering two F (R) -gravity models. Moreover, the energy conditions for the considered models are studied and found to support the accelerated expansion of the universe. [ABSTRACT FROM AUTHOR]

Mining traffic congestion dynamics presents difficulties in data structure and spatiotemporal analysis. Existing studies mainly provide insights from a supply perspective, with a restricted examination of why congestion occurs and how travel demands affect congestion. This study introduces an innovative framework to mine congestion dynamics from the perspective of human mobility. In human mobility modeling, we refine the conventional origin-destination representation of activity flow by introducing "path flow" (PF) which considers space-time paths and movement patterns. In congestion scenarios, congestion-related path flow (CPF) and congested path sub-flow (CPSF) are extended to track individuals' congestion exposure and explore the correlations between congestion and human mobility. To finely classify congestion-related travel demands, a Bayesian inference approach, incorporating destination and spatiotemporal heterogeneities, is developed to deduce trip purposes. The experiments conducted in Wuhan demonstrate the availability and importance of PF in spatiotemporal dynamics analysis of human mobility. Interestingly, we find that 1) the job-housing relationship is imbalanced, with massive residents opting for cross-district living and working; 2) individuals tend to visit tertiary hospitals on weekends and secondary medical facilities with less congestion on weekdays. Notably, path flow can promote the fine-grained modeling of human mobility and provide theoretical support for many urban issues. [ABSTRACT FROM AUTHOR]

The article "Modern Challenges to Pastoral Faithfulness" discusses the extreme challenges faced by pastors in the modern era, including burnout, scandalous sin, and temptations to leave the ministry. It highlights the impact of technological revolution, discord among believers, sexual immorality, Generation Z's worldview, and the importance of maintaining pastoral vitality. The text emphasizes the need for pastors to persevere through prayer, reliance on God, and adherence to the gospel amidst societal and technological challenges. [Extracted from the article]

The time efficiency and spatial accessibility of emergency resources during transportation are critical factors in evaluating the utility and emergency capacity of the railway emergency rescue network, distinguishing it from other transportation networks. Analyzing the spatiotemporal accessibility of the railway emergency rescue network provides insights into the spatial and temporal dynamics of emergency transport, which are essential for optimizing the structure and configuration of the emergency rescue transport network. This paper employs the classical travel time budget model to assess the spatiotemporal accessibility of resource allocation within the emergency rescue network under varying demand scenarios. Furthermore, the improved DEMATEL (Decision-Making Trial and Evaluation Laboratory) method is utilized to evaluate the existing capability of resource allocation points in identifying spatiotemporal accessibility, effectively addressing the inherent uncertainty in resource allocation states. As a result, the spatiotemporal accessibility capability identified using the classical travel time budget model proves to be more reasonable and accurate. Finally, the feasibility and validity of the model are confirmed through a comparative analysis using actual data from the Xi'an Railway Bureau. [ABSTRACT FROM AUTHOR]

In this work, we study a hypersurface immersed in specific types of cylindrically symmetric static space-times, then we identify the gauge fields of the Lagrangian that minimizes the area beside the Noether symmetries. We show that these symmetries are part of the Killing algebra of cylindrically symmetric static space-times. By using Noether's theorem, we construct the conserved vector fields for the minimal hypersurface. [ABSTRACT FROM AUTHOR]

The stable Gaussian radial basis function (RBF) interpolation is applied to solve the time and space-fractional Schrödinger equation (TSFSE) in one and two-dimensional cases. In this regard, the fractional derivatives of stable Gaussian radial basis function interpolants are obtained. By a method of lines, the computations of the TSFSE are converted to a coupled system of Caputo fractional ODEs. To solve the resulting system of ODEs, a high-order finite difference method is proposed, and the computations are reduced to a coupled system of nonlinear algebraic equations, in each time step. Numerical illustrations are performed to certify the ability and accuracy of the new method. Some comparisons are made with the results in other literature. [ABSTRACT FROM AUTHOR]

In this article, we experimentally generate a vortex space-time (ST) wave packet carrying orbital angular momentum (OAM) and confirm that the OAM of the beam survives after propagating either in the presence of a line obstruction or across a thin scattering medium. A comparison of our findings with both Bessel and standard Gaussian beams carrying OAM reveals that ST-OAM wave packets exhibit a significantly higher mean Pearson's correlation coefficient compared to these other beams. In addition, we employ a standard 3-mm thick glass microscope slide as a waveguide and find that the OAM belonging to ST wave packets remains protected after propagation. Our findings have potential utility in communication applications, sensing, imaging, and optical trapping. [ABSTRACT FROM AUTHOR]

The application of DFT precoding in mitigating peak-to-average power ratio (PAPR) issues in optical wireless communication systems under power constraints is well established. However, the channel spatial diversity for multiusers needs to be considered. This paper proposes a joint DFT and spacetime precoding technique to support multiple users and mitigate the PAPR for optical wireless communication systems when OFDM modulation is used. In our study, we introduce the weighted Bussgang theorem as an alternative method for evaluating the communication performance of hard-clipped systems due to the transmitted power constraint. Our numerical results demonstrate the effectiveness of this approach in analyzing SNR and BER performance. [ABSTRACT FROM AUTHOR]