Search

The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and Huygens waves with the speed a 2 + b 2 at low-frequency, the singular kinetic wave and the remainder term decaying exponentially in space and time. In addition, we establish the pointwise space-time estimate of the global solution to the nonlinear relativistic Boltzmann equation with non-smooth initial data based on the Green's function. [ABSTRACT FROM AUTHOR]

The space–time perturbed fractional Gerdjikov–Ivanov equation is the main topic of this work, together with quintic nonlinearity and self-steepening, as it involves several intricate physical phenomena including nonlinearity, self-steepening and fractional calculus, where the fractional derivative is described by employing a conformable derivative. In addition, the governing equation is transformed into an integer-order ordinary differential equation by using an appropriate fractional complex transformation. Under certain restrictions, a direct algebraic method is employed to investigate the structures of chirp soliton solutions enfolding hyperbolic functional terms. The dynamic behaviour and bifurcation of equilibria of the system are thoroughly examined; chirp soliton solutions under specified constraints are investigated and the evolving profiles of the obtained solutions are visualized. Moreover, this research offers valuable perspectives on the behaviour of chirp solitons under specific conditions, which have practical applications in nonlinear physical systems and optical communication systems. The significant contribution of this work is the investigation and obtaining of novel chirp soliton solutions with hyperbolicfunctional terms under particular limitations using a novel approach. It further extends the prior approaches by treating difficult fractional differential equations from a fresh angle, offering new tools, and closely examining soliton solutions. [ABSTRACT FROM AUTHOR]

We consider the problem of preprocessing a weighted directed planar graph in order to quickly answer exact distance queries. The main tension in this problem is between space S and query time Q, and since the mid- 1990s all results had polynomial time-space tradeoffs, e.g., Q = ...(n/ √ S) or Q = ...(n5/2/S3/2). In this article we show that there is no polynomial tradeoff between time and space and that it is possible to simultaneously achieve almost optimal space n1+o(1) and almost optimal query time no(1). More precisely, we achieve the following space-time tradeoffs: n1+o(1) space and log2+o(1) n query time, n log2+o(1) n space and no(1) query time, n4/3+o(1) space and log1+o(1) n query time. We reduce a distance query to a variety of point location problems in additively weighted Voronoi diagrams and develop new algorithms for the point location problem itself using several partially persistent dynamic tree data structures. [ABSTRACT FROM AUTHOR]

PT Perkebunan Nusantara VIII (PTPN VIII) is a State-Owned Enterprise (BUMN). It operates in the plantation sector. The leading commodity is tea. The demand for tea produced by PTPN VIII is increasing. Thus, planning tea production is necessary. One of the production planning efforts is through forecasting based on previous data. Tea production data is time-series data. It contains seasonal elements and is dependent on other locations. We will analyze data with these criteria using space-time models, one of which is vector autoregressive (VAR). VAR models the relationship between observations on certain variables at one time. It also models the observation of the variable itself at previous times. Additionally, VAR models the relationship between observations and other variables at previous times. This paper explains how to forecast tea production. It uses the reconstituted VAR and Seasonal Autoregressive Moving Average (SARIMA) models. The results showed that the reconstituted VAR model was better than the SARIMA model in predicting tea production. The tea production prediction was at the Sedep and Santosa plantations in Bandung Regency.

Our aim in this paper is two-fold. We establish a novel geometric characterization of the Robertson–Walker (RW) spacetime and, along the process, we find a canonical form of the RW metric associated to an arbitrary timelike curve and an arbitrary space frame. A known characterization establishes that a spacetime foliated by constant curvature leaves whose orthogonal flow (the cosmological flow) is geodesic, shear-free, and with constant expansion on each leaf, is RW. We generalize this characterization by relaxing the condition on the expansion. We show it suffices to demand that the spatial gradient and Laplacian of the cosmological expansion on a single arbitrary timelike curve vanish. In General Relativity these local conditions are equivalent to demanding that the energy flux measured by the cosmological flow, as well as its divergence, are zero on a single arbitrary timelike curve. The proof allows us to construct canonically adapted coordinates to the arbitrary curve, thus well-fitted to an observer with an arbitrary motion with respect to the cosmological flow. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study geometrical aspects of an almost Ricci soliton on (wRs)4 perfect fluid spacetime obeying Einstein’s field equation. Among others, we first find the soliton constant and cosmological constant in terms of scalar curvature and potential vector field in (wRs)4 perfect fluid spacetime. Next, we discuss some physical phenomena related to dust fluid, dark fluid, and radiation era in (wRs)4 perfect fluid spacetime admitting an almost Ricci soliton with potential vector field as solenoidal vector field and basic vector field ρ under matter collineation condition. Further, we find an inequality for soliton constant when (wRs)4 perfect fluid spacetime obeys the timelike convergence condition. Finally, we obtain some results in a (wRs)4 perfect fluid spacetime whose metric represents an almost Ricci soliton when basic vector field and potential vector field both are torseforming vector field ρ. Also, for such spacetime we find the soliton constant in terms of cosmological constant, gravitational constant, energy density, and isotropic pressure. We also provide an example of (wRs)4 spacetime whose metric represents an almost Ricci soliton. [ABSTRACT FROM AUTHOR]

The paper deals with an extensive study of Weyl integrable gravity theory in the background of flat FLRW space-time model, considering both classical and quantum cosmology. Noether symmetry approach has been used not only to simplify the evolution equations but also to obtain analytic solution from them. The classical solution has been analyzed from observational view point. Finally, canonical quantization programme has been complemented by the Noether symmetry analysis. [ABSTRACT FROM AUTHOR]

We give a complete classification of topological field theories with reflection structure and spin-statistics in one and two spacetime dimensions. Our answers can be naturally expressed in terms of an internal fermionic symmetry group G, which is different from the spacetime structure group. Fermionic groups encode symmetries of systems with fermions and time-reversing symmetries. We show that 1-dimensional topological field theories with reflection structure and spin-statistics are classified by finite-dimensional Hermitian representations of G. In spacetime dimension 2 we give a classification in terms of strongly G-graded stellar Frobenius algebras. Our proofs are based on the cobordism hypothesis. Along the way, we develop some useful tools for the computation of homotopy fixed points of 2-group actions on bicategories. [ABSTRACT FROM AUTHOR]

A new mechanism based on space-time noncommutativity has shown to produce anisotropy and an axial-like interaction, yielding leptonic asymmetry for fermionic particles propagating in a noncommutative curved FRW universe. As a byproduct, an analytical expression of this asymmetry for ultra-relativistic particles, such as neutrinos, is derived explicitly. Constraints and bounds from the cosmological parameters are also discussed. [ABSTRACT FROM AUTHOR]

We propose a new framework for spherical charged compact objects admitting conformal motion in five-dimensional spacetime. The outer spacetime is considered as Reissner-Nordström to obtain matching conditions. The behavior of model characteristics like stress, pressure, and surface tension for the specific density profile is investigated by using Einstein's Maxwell field equations in a five-dimensional framework. For the proposed solution, all physical parameters behave very well even for variations in electric charge parameters. The existence of charged compact stars is also predicted by this study. [ABSTRACT FROM AUTHOR]

In this study, we explore a topologically charged higher-dimensional traversable defect wormhole, with a specific emphasis on five dimensions. Particularly noteworthy is the fact that the matter–energy distribution attributed to this charged wormhole configuration adheres to the weak energy condition, thus presenting an instance of a five-dimensional wormhole supported by non-exotic matter. Furthermore, our analysis shows that scalar quantities related to space-time curvature and parameters associated with the matter–energy distribution remain finite at the wormhole throat. Moreover, they diminish as distance extends toward infinity, indicating the asymptotic flatness inherent in our model. [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(αℛ) −ln(βℛ) in which α and β are positive constants. [ABSTRACT FROM AUTHOR]

We have discussed the Dirac equation in Schwarzschild spacetime using pseudo-supersymmetric quantum mechanics and have obtained the partner Hamiltonian of the initial Hamiltonian operator. We demonstrate that the partner metric tensors, corresponding to these Hamiltonians, can be derived using the intertwining relations inherent in pseudo-supersymmetric approaches. We have seen that the Schwarzschild metric may be expanded into Schwarzschild–Tangherlini metric using the aspects of pseudo-supersymmetry. Furthermore, we have derived approximate solutions for the radial component within the framework of N = 2 supersymmetry with the corresponding radial potential graphs presented. Subsequently, our discussion extends to the quasinormal modes, focusing particularly on the asymptotic limits as r approaches ± ∞ . [ABSTRACT FROM AUTHOR]

Let H : O↦H(O) be a local net of real Hilbert subspaces of a complex Hilbert space ℋ on the family 풪 of double cones of the spacetime ℝd+1 (d odd), covariant with respect to a positive energy, unitary representation U of the Poincaré group 풫+↑, with the Bisognano–Wichmann property for the wedge modular group. We set an upper bound on the local entropy SH(ϕ||C) of a vector ϕ ∈ℋ in a given region C ⊂ ℝd+1 that depends only on U and the PCT anti-unitary canonically associated with H. A similar result holds for local, Möbius covariant nets of standard subspaces on the circle. We compute the entropy increase with respect to the dual net and illustrate this bound for the nets associated with the U(1)-current derivatives. [ABSTRACT FROM AUTHOR]

As part of our study, we investigate gradient Schouten harmonic solutions to sequential warped product manifolds. The main contribution of our work is an explanation of how it is possible to express gradient Schouten harmonic solitons on sequential warped product manifolds. Our analysis covers both sequential generalized Robertson–Walker spacetimes and sequential static spacetimes using gradient Schouten harmonic solitons. Studies conducted previously can be generalized from this study. [ABSTRACT FROM AUTHOR]

The paper is devoted to the mathematical description of the whispering gallery waves modulated by amplitude and frequency. Space-time ray method for this problem is developed. [ABSTRACT FROM AUTHOR]

We consider quasiphotons, which are asymptotic solutions of the wave equation with a Gaussian-type localization around points moving along rays. We show in this note that well-known procedures of obtaining the formulas for quasiphotons lead to a complete class of quasiphotons described by the complex space-time ray method (STRM), in spite of the very restrictive normalizing condition. It is possible in the case of the constant velocity to derive formulas in explicit form for 3 × 3-matrices describing quasiphotons. (These matrices, in particular, can have all nonzero components). [ABSTRACT FROM AUTHOR]

Summary: Acoustic emission or scattering problems naturally involve uncertainties about the sound sources or boundary conditions. This article initiates the study of time domain boundary elements for such stochastic boundary problems for the acoustic wave equation. We present a space‐time stochastic Galerkin boundary element method which is applied to sound‐hard, sound‐soft and absorbing scatterers. Uncertainties in both the sources and the boundary conditions are considered using a polynomial chaos expansion. The numerical experiments illustrate the performance and convergence of the proposed method in model problems and present an application to a problem from traffic noise. [ABSTRACT FROM AUTHOR]

Some important problems in science do not have analytical solutions in four dimensions including QCD, but they are integrable in two dimensions. For many years, scientists have been trying to find a relation between two-dimensional and four-dimensional space-time to explain the real problem in four dimensions by accurately solving the appropriate model in two dimensions. In this paper, an interesting relation between g Y M 2 (generalized two-dimensional Yang–Mills) and Maxwell construction has been found, which can be a starting point for finding more relations between two-dimensional and four-dimensional space-time, so this paper can play an important role in the advancement of science. For this purpose, first, the large-N behavior of the quartic-cubic generalized two-dimensional Yang–Mills U(N) on a sphere is investigated for finite cubic couplings. It is shown that there are two phase transitions one of which is of third order, which is similar to previous papers, and the other one is of second order, which is a novel result. Second, g Y M 2 (for G (z) = z m + λ z n ; m = 4 , 6 ; n < m ) and Maxwell construction are compared with each other and a relationship between two-dimensional space-time, which is integrable, and four-dimensional space-time is obtained. [ABSTRACT FROM AUTHOR]

We expect the final theory of gravity to have more symmetries than we suspect and our research points in this direction. To start with, standard general coordinate invariance can be extended to complex holomorphic general coordinate transformations. This is possible by introducing a non-Riemannian measure of integration (NRMI) and where we avoid the nonholomorphic standard −g measure of integration. Second, locally signed coordinate transformations where the Jacobian changes sign locally but the Jacobian approaches one asymptotically should be symmetries of Nature. This is unlike globally signed transformations that produce a change of boundary conditions, like in the cases of global parity and global time reversal, which are not symmetries of Nature. The holomorphic extension can regularize the regions of spacetime where the Jacobian changes sign. Consequences for Quantum Gravity are discussed. [ABSTRACT FROM AUTHOR]

In this article, generalized Robertson Walker spacetimes are investigated in light of perfect fluid spacetimes. First, we establish that a perfect fluid spacetime with nonvanishing vorticity whose associated scalars are constant along the velocity vector field becomes a generalized Robertson Walker spacetime. Among others, it is also shown that a Ricci parallel perfect fluid spacetime is either a generalized Robertson Walker spacetime or a static spacetime. Finally, we acquire that in a conformally semisymmetric generalized Robertson Walker spacetime of dimension 4, the scalar curvature vanishes and the spacetime is locally isometric to the Minkowski spacetime, provided the electric part of the Weyl tensor vanishes. Moreover, it is established that the last result also holds in a conformally recurrent generalized Robertson Walker spacetime. [ABSTRACT FROM AUTHOR]

This article deals with the characterization of an almost pseudo symmetric spacetime and we illustrate that a conformally flat almost pseudo symmetric spacetime with nonzero constant scalar curvature represents a perfect fluid spacetime. Also, it is established that the chosen spacetime represents a spacetime of quasi constant sectional curvature and generalized Robertson-Walker spacetime. Besides, we find under what condition the spacetime represents radiation era and dust matter fluid. Further it is shown that under certain restriction in an almost pseudo symmetric spacetime, if the Ricci tensor is Killing, then it represents a static spacetime and it is vacuum. Lastly, we study the impact of this spacetime under f (R) gravity scenario and deduce several energy conditions. [ABSTRACT FROM AUTHOR]

Everything in our environment moves through both space and time, and to effectively act we must be aware of both spatial and temporal elements in relation to our own bodies. Thus, perceptions of space and time have an intimate relationship. Walsh's a theory of magnitude (ATOM) suggests that space and time perception rely on a general magnitude system and their relationship should be roughly symmetrical. Alternatively, metaphor theory, which is based on the philosophical work of Lakoff and Johnson, argues that we represent time using a spatial metaphor and thus the relationship should be asymmetrical (with space influencing time more than time influences space). A compelling line of evidence for metaphor theory comes from the work of Casasanto & Boroditsky. Cognition, 106(2), 579–593. (2008) who experimentally demonstrated this asymmetric effect. However, in our previous unpublished online replication attempt of this work, we found a roughly symmetrical relationship between space and time, more in line with the theoretical predictions of ATOM. Given this, we performed a registered replication of Casasanto & Boroditsky. Cognition, 106(2), 579–593. (2008) in both an online and laboratory environment. [ABSTRACT FROM AUTHOR]

We consider a massless and minimally coupled self interacting quantum scalar field in the inflationary de Sitter spacetime. The scalar potential is taken to be a hybrid of cubic and quartic self interactions, V (ϕ) = λ ϕ 4 / 4 ! + β ϕ 3 / 3 ! ( λ > 0 ). Compared to the earlier well studied β = 0 case, the present potential has a rolling down effect due to the ϕ 3 term, along with the usual bounding effect due to the ϕ 4 term. We begin by constructing the Schwinger–Dyson equation for the scalar Feynman propagator up to two loop, at O (λ) , O (β 2) , O (λ 2) and O (λ β 2) . Using this equation, we consider first the local part of the scalar self energy and compute the rest mass squared of the scalar field, dynamically generated via the late time non-perturbative secular logarithms, by resumming the daisy-like graphs. The logarithms associated here are sub-leading, compared to those associated with the non-local, leading terms. We also argue that unlike the quartic case, considering merely the one loop results for the purpose of resummation does not give us any sensible result here. We next construct the non-perturbative two particle irreducible effective action up to three loop and derive from it the Schwinger–Dyson equation once again. This equation is satisfied by the non-perturbative Feynman propagator. By series expanding this propagator, the resummed local part of the self energy is shown to yield the same dynamical mass as that of the above. We next use this equation to resum the effect of the non-local part of the scalar self energy in the Feynman propagator, and show that even though the perturbatively corrected propagator shows secular growth at late times, there exists one resummed solution which is vanishing for large spacelike separations, in qualitative agreement with the well known result found via the stochastic formalism. [ABSTRACT FROM AUTHOR]

The null-surface formulation (NSF) of general relativity differs markedly from the conventional approach. The conventional approach to general relativity is concerned with local fields such as the metric, whereas the NSF focuses on surfaces. The NSF has two distinct but mathematically equivalent interpretations: (a) Future-directed light rays leave a spacetime point and intersect future null-infinity. The resulting surface, known as a light-cone cut, encodes the properties of the spacetime; (b) The angular coordinates (Bondi coordinates) of null-infinity are used to label past light cones, thereby producing a family of null surfaces. These will satisfy the NSF field equations and a solution of these equations provides a description of spacetime. This paper features a new exact solution that, for the first time, directly links the two interpretations, thereby illustrating both approaches and demonstrating their equivalence. The solution and its properties are first explored in 2+1 dimensions, after which, the generalization to 3+1 is outlined. [ABSTRACT FROM AUTHOR]

We study a model of the neutron star in κ -deformed space-time in the presence of the cosmological constant (Λ ). The Einstein tensor and the energy-momentum tensor are generalized to κ -deformed space-time and we construct the field equations with the cosmological constant. Considering the interior of the star to be a perfect fluid as in the commutative case, we find the Tolman–Oppenheimer–Volkoff equations with the inclusion of the cosmological constant in κ -deformed space-time. The behavior of the maximum allowed mass of the star and its radius are studied with the variation in the cosmological constant as well as the deformation parameter. We see that the non-commutativity enhances the mass of the star and its maximum mass increases with a decrease in the cosmological constant. The maximum mass varies from 3.44 to 3.68 M ⊙ as Λ varies from 10 - 10 to 10 - 15 m - 2 . We also obtain the compactness factor and surface redshift of the star. We observe that the compactness of the star increases as the cosmological constant decreases, whereas the surface redshift of the star decreases with a decrease in the cosmological constant. The compactness factor and surface redshift corresponding to the maximum mass of the neutron star remains almost constant as Λ decreases. [ABSTRACT FROM AUTHOR]

In this paper we use the Homotopy analysis method to obtain an analytic approximation for the entire photon trajectory in the Schwarzschild spacetime. This is usually expressed exactly in terms of an elliptic integral. We compare our approximation with other formulae found in the literature, which were specifically obtained for the Schwarzschild solution. Unlike some of these formulae, our approximation can be applied and maintains a good accuracy for emission point close to the event horizon and also for emission angles close to and greater than π / 2 . We show that our method can easily be applied to other spherically symmetric solutions such as the Reissner-Nordström solution. Such an approximation would be useful when accurate determination of the light trajectories around compact objects is required without the need to revert to time consuming numerical integration of elliptic integrals. [ABSTRACT FROM AUTHOR]

We present a systematic investigation of antilinear superoperators and their applications in studying open quantum systems, particularly focusing on quantum geometric invariance, entanglement distribution, and symmetry. We study several classes of antilinear superoperators, including antilinear quantum channels, antilinearly unital superoperators, antiunitary superoperators, and generalized Θ -conjugation. Using the Bloch representation, we present a systematic investigation of quantum geometric transformations in higher-dimensional quantum systems. By choosing different generalized Θ -conjugations, we obtain various metrics for the space of Bloch space-time vectors, including the Euclidean and Minkowskian metrics. Utilizing these geometric structures, we then investigate the entanglement distribution over a multipartite system constrained by quantum geometric invariance. The strong and weak antilinear superoperator symmetries of the open quantum system are also discussed. Additionally, Kramers' degeneracy and conserved quantities are examined in detail. [ABSTRACT FROM AUTHOR]

We introduce a new class of two-dimensional gravity models using ideas motivated by the Teleparallel Equivalent of General Relativity. This leads to a rather natural formulation of a theory that has close links with Jackiw–Teitelboim gravity. After introducing the theory and discussing its vacuum solutions, we present the Hamiltonian analysis. This implies the presence of a single dynamical degree of freedom, which is in sharp contrast to General Relativity, where there are no degrees of freedom in two spacetime dimensions. Our approach can be extended to various other lower-dimensional gravity theories and thus could be of wider interest. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of global in time small data solutions of semilinear Klein–Gordon equations in space-time with a static Schwarzschild radius in the expanding universe. [ABSTRACT FROM AUTHOR]

The Kerr-star spacetime is the extension over the horizons and in the negative radial region of the Kerr spacetime. Despite the presence of closed timelike curves below the inner horizon, we prove that the timelike geodesics cannot be closed in the Kerr-star spacetime. Since the existence of closed null geodesics was ruled out by the author in Sanzeni [arXiv:2308.09631v3 (2024)], this result shows the absence of closed causal geodesics in the Kerr-star spacetime. [ABSTRACT FROM AUTHOR]

In the context of hotly contested debates within critical urban theory, many scholars have recently attempted (both implicitly and explicitly) to move beyond the relational-dialectical concept of 'totality', taking up the notion of 'the constitutive outside' in its place. With this in view, this article seeks to (1) develop a critique of the ways in which the concept of the constitutive outside is deployed in these debates; and (2) to sketch another path forward – one that understands capitalist urbanisation as a distinctive moment in the evolution of a world-encompassing and internally related socio-spatial totality, while also attending to well-founded concerns among theorists of the constitutive outside regarding the question of difference and ascriptive hierarchisation. More precisely, this article will pursue a close reading of work on the constitutive outside in critical urban theory, suggesting that it effectively re-articulates longstanding and entrenched tenets of capitalist ideology, positing the image of a 'space-time of the other'. And it will conclude with a revised conceptualisation of totality for critical urban theory, building on Nancy Fraser's recent work on capitalism's racialised, gendered, and ecological 'hidden abodes'. [ABSTRACT FROM AUTHOR]

Topological quantum field theories (TQFTs) provide a general, minimal‐assumption language for describing quantum‐state preparation and measurement. They therefore provide a general language in which to express multi‐agent communication protocols, e.g., local operations, classical communication (LOCC) protocols. In the accompanying Part I, we construct LOCC protocols using TQFT, and show that LOCC protocols induce quantum error‐correcting codes (QECCs) on the agent‐environment boundary. Such QECCs can be regarded as implementing or inducing the emergence of spacetimes on such boundaries. Here connection between inter‐agent communication and spacetime is investigated, by exploiting different realizations of TQFT. The authors delved into TQFTs that support on their boundaries spin‐networks as computational systems: these are known as topological quantum neural networks (TQNNs). TQNNs, which have a natural representation as tensor networks, implement QECC. The HaPPY code is recognized to be a paradigmatic example. How generic QECCs, as bulk‐boundary codes, induce effective spacetimes is then shown. The effective spatial and temporal separations that take place in QECC enables LOCC protocols between spatially separated observers. The implementation of QECCs in BF and Chern‐Simons theories are then considered, and QECC‐induced spacetimes are shown to provide the classical redundancy required for LOCC. Finally, the topological M‐theory is considered as an implementation of QECC in higher spacetime dimensions. [ABSTRACT FROM AUTHOR]

In this paper, we explore a set of geometric properties of Mixed Super Quasi-Einstein (MSQE) manifolds and provide examples of both Riemannian and Lorentzian MSQE manifolds to demonstrate their existence. Furthermore, we examine MSQE spacetimes in the context of the space-matter tensor, discussing several related properties. Finally, we establish the existence of an MSQE spacetime through a nontrivial example. [ABSTRACT FROM AUTHOR]

In this paper, we will discuss an alternative theory for the origin of dark matter and dark energy based on the new concept of tetrad gauge states of spacetime. The new tetrads already introduced new physics since it has been proved that local electromagnetic gauge transformations can boost the local tetrad fields in a four-dimensional curved Lorentz spacetime. It is within this context that we will present a different qualitative explanation for the so-called dark matter and dark energy and new possible topological solutions of a galactic nature for Einstein–Maxwell spacetimes in its relation to dark matter and new possible topological solutions of a cosmological nature for Einstein–Maxwell spacetimes in its relation to dark energy. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the existence of Ricci solitons and the nature of curvature inheritance as well as collineations on the Robinson–Trautman (briefly, RT) spacetime. It is shown that under certain conditions RT spacetime admits almost-Ricci soliton, almost- η -Ricci soliton, almost-gradient η -Ricci soliton. As a generalization of curvature inheritance [K. L. Duggal, Curvature inheritance symmetry in Riemannian spaces with applications to fluid space times, J. Math. Phys. 33(9) (1992) 2989–2997] and curvature collineation [G. H. Katzin, J. Livine and W. R. Davis, Curvature collineations: A fundamental symmetry property of the space-times of general relativity defined by the vanishing Lie derivative of the Riemann curvature tensor, J. Math. Phys. 10(4) (1969) 617–629], in this paper, we introduce the notion of generalized curvature inheritance and examine if RT spacetime admits such a notion. It is shown that RT spacetime also realizes the generalized curvature (resp., Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) inheritance. Finally, several conditions are obtained, under which RT spacetime possesses curvature (resp., Ricci, conharmonic, Weyl projective) inheritance as well as curvature (resp., Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) collineation, and we have also introduced the concept of generalized Lie inheritance and showed that RT spacetime realizes such a notion. [ABSTRACT FROM AUTHOR]

The ontology behind quantum mechanics has been the subject of endless debate since the theory was formulated some 100 years ago. It has been suggested, at one time or another, that the objects described by the theory may be individual particles, waves, fields, ensembles of particles, observers, and minds, among many other possibilities. I maintain that these disagreements are due in part to a lack of precision in the use of the theory's various semantic designators. In particular, there is some confusion about the role of representation, reference, and denotation in the theory. In this article, I first analyze the role of the semantic apparatus in physical theories in general and then discuss the corresponding ontological implications for quantum mechanics. Subsequently, I consider the extension of the theory to quantum fields and then analyze the semantic changes of the designators with their ontological consequences. In addition to the classical arguments to rule out a particle ontology in the case of non-relativistic quantum field theory, I show how the existence of black holes makes the proposal of a particle ontology in general spacetimes unfeasible. I conclude by proposing a provisional pluralistic ontology of fields and spacetime and discussing some prospects for possible future ontological economies. [ABSTRACT FROM AUTHOR]

In the framework of the functional renormalization group and of the perturbative, algebraic approach to quantum field theory (pAQFT), in D’Angelo et al. [Ann. Henri Poinc. 25 (2024) 2295–2352] it has been derived a Lorentzian version of a flow equation à la Wetterich, which can be used to study nonlinear, quantum scalar field theories on a globally hyperbolic spacetime. In this work, we show that the realm of validity of this result can be extended to study interacting scalar field theories on globally hyperbolic manifolds with a timelike boundary. By considering the specific examples of half-Minkowski spacetime and of the Poincaré patch of Anti-de Sitter, we show that the form of the Lorentzian Wetterich equation is strongly dependent on the boundary conditions assigned to the underlying field theory. In addition, using a numerical approach, we are able to provide strong evidences that there is a qualitative and not only a quantitative difference in the associated flow and we highlight this feature by considering Dirichlet and Neumann boundary conditions on half-Minkowski spacetime. [ABSTRACT FROM AUTHOR]

SO(1,d + 1) is the isometry group of (d + 1)-dimensional de Sitter spacetime (dSd+1) and the conformal group of ℝd. This note gives a pedagogical introduction to the representation theory of SO(1,d + 1), from the perspective of de Sitter quantum field theory and using tools from conformal field theory. Topics include (1) the construction and classification of all unitary irreducible representations (UIRs) of SO(1, 2) and SL(2, ℝ), (2) the construction and classification of all UIRs of SO(1,d + 1) that describe integer-spin fields in dSd+1, (3) a physical framework for understanding these UIRs, (4) the definition and derivation of Harish-Chandra group characters of SO(1,d + 1) and (5) a comparison between UIRs of SO(1,d + 1) and SO(2,d). [ABSTRACT FROM AUTHOR]

The Janis–Newman–Winicour spacetime corresponds to a static spherically symmetric solution of Einstein equations with the energy momentum tensor of a massless quintessence field. It is understood that the spacetime describes a naked singularity. The solution has two parameters, b and s. To our knowledge, the exact physical meaning of the two parameters is still unclear. In this paper, starting from the Janis–Newman–Winicour naked singularity solution, we first obtain a wormhole solution by a complex transformation. Then, letting the parameter s approach infinity, we obtain the well-known exponential wormhole solution. After that, we embed both the Janis–Newman–Winicour naked singularity and its wormhole counterpart in the background of a de Sitter or anti-de Sitter universe with the energy momentum tensor of massive quintessence and massive phantom fields, respectively. To our surprise, the resulting quintessence potential is actually the dilaton potential found by one of us. It indicates that, by modulating the parameters in the charged dilaton black hole solutions, we can obtain the Janis–Newman–Winicour solution. Furthermore, a charged wormhole solution is obtained by performing a complex transformation on the charged dilaton black hole solutions in the background of a de Sitter or anti-de Sitter universe. We eventually find that s is actually related to the coupling constant of the dilaton field to the Maxwell field and b is related to a negative mass for the dilaton black holes. A negative black hole mass is physically forbidden. Therefore, we conclude that the Janis–Newman–Winicour naked singularity solution is not physically allowed. [ABSTRACT FROM AUTHOR]

Quantum field theory (QFT) in Rindler spacetime is a gateway to understanding unitarity and information loss paradoxes in curved spacetime. Rindler coordinates map Minkowski spacetime onto regions with horizons, effectively dividing accelerated observers into causally disconnected sectors. Employing standard quantum field theory techniques and Bogoliubov transformations between Minkowski and Rindler coordinates yields entanglement between states across these causally separated regions of spacetime. This results in a breakdown of unitarity, implying that information regarding the entangled partner may be irretrievably lost beyond the Rindler horizon. As a consequence, one has a situation of pure states evolving into mixed states. In this paper, we introduce a novel framework for comprehending this phenomenon using a recently proposed formulation of direct-sum quantum field theory (DQFT), which is grounded in superselection rules formulated by the parity and time reversal ( P T ) symmetry of Minkowski spacetime. In the context of DQFT applied to Rindler spacetime, we demonstrate that each Rindler observer can, in principle, access pure states within the horizon, thereby restoring unitarity. However, our analysis also reveals the emergence of a thermal spectrum of Unruh radiation. This prompts a reevaluation of entanglement in Rindler spacetime, where we propose a novel perspective on how Rindler observers may reconstruct complementary information beyond the horizon. Furthermore, we revisit the implications of the Reeh-Schlieder theorem within the framework of DQFT. Lastly, we underscore how our findings contribute to ongoing efforts aimed at elucidating the role of unitarity in quantum field theory within the context of de Sitter and black hole spacetimes. [ABSTRACT FROM AUTHOR]

This article proposes a methodology to identify rhetorical energies that form within the diegetic timeline of movies and to translate these to creative sculpting of spacetime designs. In turn, the narrative manipulation of rhetorical spacetime correlates with that of the audience's emotional states. I achieved this by indexing fictional spacetime with movie barcodes to create a visual compression of sequential film frames into one solid image. I also discuss how patterns of spatial and temporal arrangement within the selected film trailer occurs. I utilise the short form movie trailer The Monster (2020) as my case study as it is a work that I co-directed. Essentially, I propose a method to show how temporal designs of a fictional dimension may be sculpted and intensified. For comparative purposes, I discuss a related study on Alejandro G. Iñárritu’s The Revenant (2015). I conclude that the spacetime relationships of the timeline exhibit a propensity to result in dramaturgic tension patterns. [ABSTRACT FROM AUTHOR]

We consider goal-oriented adaptive space-time finite-element discretizations of the regularized parabolic p-Laplace problem on completely unstructured simplicial space-time meshes. The adaptivity is driven by the dual-weighted residual (DWR) method since we are interested in an accurate computation of some possibly nonlinear functionals at the solution. Such functionals represent goals in which engineers are often more interested than the solution itself. The DWR method requires the numerical solution of a linear adjoint problem that provides the sensitivities for the mesh refinement. This can be done by means of the same full space-time finite element discretization as used for the primal non-linear problems. The numerical experiments presented demonstrate that this goal-oriented, full space-time finite element solver efficiently provides accurate numerical results for different functionals. [ABSTRACT FROM AUTHOR]

In this work, we consider Anderson acceleration for numerical solutions of nonlinear time dependent partial differential equations discretized by space–time spectral methods, where classical fixed-point methods converge slowly or even diverge. Specifically, we apply Anderson acceleration with finite window size w to speed up fixed-point methods in solving nonlinear reaction diffusion, nonlinear Schrödinger and Navier Stokes equations. We focus on studying the influence of the window size w on the number of iterations to numerical convergence. Numerical results show the high efficiency of Anderson acceleration in solving a variety of nonlinear time dependent problems discretized by space–time spectral methods, and a small value of w is enough to achieve good performance. [ABSTRACT FROM AUTHOR]

The main aim of this article is to modify the space-time fractionalKdV equations using the Bessel operator. The triple Laplace transform decomposition method (TLTDM) is proposed to find the solution for a time-fractional singular KdV coupled system of equations. Three problems are discussed to check the accuracy and illustrate the effectiveness of this technique. The results imply that our method is very active and easy to utilize while analyzing the manner of nonlinear fractional differential equations appearing in the joint field of science and mathematics. Moreover, this method is fast convergent if we compare it with the existing techniques in the literature. [ABSTRACT FROM AUTHOR]

We show that, given any static spacetime whose spatial slices are asymptotically Euclidean (or, more generally, asymptotically conic) manifolds modeled on the large end of the Schwarzschild exterior, there exist stationary solutions to the Klein–Gordon equation having Schwartz initial data. In fact, there exist infinitely many independent such solutions. The proof is a variational argument based on the long range nature of the effective potential. We give two sets of test functions which serve to verify the hypothesis of the variational argument. One set consists of cutoff versions of the hydrogen bound states and is used to prove the existence of eigenvalues near the hydrogen spectrum. [ABSTRACT FROM AUTHOR]

The diurnal cycle is an important mode of climatic variability associated with different aspects of micro, meso and large scale meteorological phenomena. Thus, we performed a study of the space-time variability of the diurnal cycle of precipitation with hourly sampling and covering all regions of Brazil. The dataset was collected during the period of 13-year, from 1st January 2008 to 31th December 2020. We used data from 411 rain gauges installed in automatic weather stations. To evaluate regional aspects, we conducted a cluster analysis with different configurations (4, 5 and 6 groups). We identified a considerable heterogeneity in the hour of maximum precipitation in Brazil and three main types of diurnal cycle were observed: (i) maximum precipitation at mid- to late afternoon associated with strong local convection activity; (ii) diurnal cycle with intense precipitation during nighttime at the Amazon basin, the coast of Northeast Brazil and the Southern region; (iii) semidiurnal cycles with low precipitation rate at the Northeast Brazil. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of source recovery in a dynamical system utilizing space-time samples. This is a specific issue within the broader field of dynamical sampling, which involves collecting samples from solutions to a differential equation across both space and time with the aim of recovering critical data, such as initial values, the sources, the driving operator, or other relevant details. Our focus in this study is the recovery of unknown, stationary sources across both space and time, leveraging space-time samples. This research may have significant applications; for instance, it could provide a model for strategically placing devices to measure the number of pollutants emanating from factory smokestacks and dispersing across a specific area. Space-time samples could be collected using measuring devices placed at various spatial locations and activated at different times. We present necessary and sufficient conditions for the positioning of these measuring devices to successfully resolve this dynamical sampling problem. This paper provides both a theoretical foundation for the recovery of sources in dynamical systems and potential practical applications. [ABSTRACT FROM AUTHOR]

Evaluation metrics for prediction error, model selection and model averaging on space–time data are understudied and poorly understood. The absence of independent replication makes prediction ambiguous as a concept and renders evaluation procedures developed for independent data inappropriate for most space–time prediction problems. Motivated by air pollution data collected during California wildfires in 2008, this manuscript attempts a formalization of the true prediction error associated with spatial interpolation. We investigate a variety of cross-validation (CV) procedures employing both simulations and case studies to provide insight into the nature of the estimand targeted by alternative data partition strategies. Consistent with recent best practice, we find that location-based cross-validation is appropriate for estimating spatial interpolation error as in our analysis of the California wildfire data. Interestingly, commonly held notions of bias-variance trade-off of CV fold size do not trivially apply to dependent data, and we recommend leave-one-location-out (LOLO) CV as the preferred prediction error metric for spatial interpolation. [ABSTRACT FROM AUTHOR]

Evaluating program reliability against software faults involves the work of analyzing program failure against software faults as behavior on failures is fundamental for assessing reliability. Similar failure behavior reflects similar reliability assessment against software faults of same time–space distribution. Since program failure is determined by fault manifestations, working on similarities on fault manifestations helps figuring out failures in similarity as well. In this paper, we propose a novel method to characterize program behavior by defining fine-grained runtime states at assembly-level of code, aiming to capture the very first abnormal manifestation—first-error—after software fault being activated during program run. Failure prediction model and measurement is presented based on similarities reflected by the runtime behaviors obtained. Fault injection experiments are conducted to verify the prediction measurement by utilizing software faults of Orthogonal Defect Classification to inject and MiBench programs to perform. Over 15 000+ times of fault injection by considering type and location of fault were conducted into each program in order to quantify and analyze the sensitivity on first-error and similarity on failure accordingly. The results show that programs having particular structural features (e.g. massive operations with regards to calculations, nested function-calls, case structures and loop structures, etc.) are well characterized toward first-error behaviors by extracting fine-grained states. Similarities on first-error sensitivity can be represented better for these programs as well. Same trend is seen on failure behavior and its prediction measurement. [ABSTRACT FROM AUTHOR]