Region Of Spacetime Research Articles

Soliton resolution for the Ostrovsky–Vakhnenko equation

We consider the Cauchy problem of the Ostrovsky–Vakhnenko (OV) equation expressed in the new variables (y,τ)q3−q(logq)yτ−1=0 with Schwartz initial data q0(y)>0 which supports smooth and single-valued solitons. It is shown that the solution to the Cauchy problem for the OV equation can be characterized by a 3 × 3 matrix Riemann–Hilbert (RH) problem. Furthermore, by employing the ∂̄-steepest descent method to deform the RH problem into solvable models, we derive the soliton resolution for the OV equation across two space–time regions: y/τ>0 and y/τ<0. This result also implies that the N-soliton solutions of the OV equation in variables (y,τ) are asymptotically stable.

Existence of traversable wormholes in the minimally coupled gravity model

The objective of this study is to examine the possible existence of traversable wormhole geometries within the context of [Formula: see text] gravity. To meet this objective, we employ the Karmarkar condition to construct the shape function that aids in identifying the wormhole configurations. This developed function is found to satisfy the essential conditions and provides a link between two asymptotically flat spacetime regions. We then assume the Morris–Thorne line element that expresses the wormhole configuration and formulate the anisotropic gravitational equations for a particular minimal matter-spacetime coupled model of the modified theory. Afterward, we develop three solutions and determine their viability by analyzing whether they violate the null energy conditions. Different stability methods are applied to the resulting geometries to explore the acceptance of the considered modified model. We conclude that the developed wormhole structures potentially fulfill the required criteria and thus exist in this modified gravity under all choices of the matter Lagrangian density.

Data-driven two-dimensional stationary quantum droplets and wave propagations in the amended Gross–Pitaevskii equation with two potentials via deep neural networks learning

In this paper, we develop a systematic deep learning approach to solve two-dimensional stationary quantum droplets (QDs) and investigate their wave propagation in the two-dimensional amended Gross–Pitaevskii equation with Lee–Huang–Yang correction and two kinds of potentials. Firstly, we use the initial-value iterative neural network algorithm for two-dimensional stationary QDs of stationary equations. Then, the learned stationary QDs are used as the initial value conditions for physics-informed neural networks to explore their evolutions in the space-time region. Especially, we consider two types of potentials, one is the two-dimensional quadruple-well Gaussian potential and the other is the P T -symmetric harmonic-oscillator (HO)-Gaussian potential, which lead to spontaneous symmetry breaking and the generation of multi-component QDs. The used deep learning method can also be applied to study wave propagations of other nonlinear physical models.

Моделирование суточной вариации атмосферного электрического поля в турбулентном приземном слое

An electrodynamic model of the electric field dynamics behavior in the atmospheric surface layer due to the action of local factors is presented. The model was obtained by reducing the differential equations system of the electrode effect to the so-called total current equation, which is a second-order equation of parabolic type, considered in a two-dimensional space-time region. The total current equation allows us to connect the set of main factors influencing on the atmospheric surface layer electric field state: conduction current, turbulent current and current arising as a result of convective processes in the atmosphere with the so-called total current in the nearground layer, reflecting changes in the ionospheric potential. The described method provides significant advantages in research, since within the framework of one model it allows the formulation of various problems of electrodynamics of the surface layer and a comparative analysis of the influence on the behavior of the electric field in the surface layer of both individual factors and their combinations. Based on meteorological data at the Peak Cheget mountain station in the Elbrus region, a daily variation in the values of the turbulent diffusion coefficient was constructed. The resulting analytical dependence was used to solve the equation for the total current in the surface layer, provided that it is constant at the upper boundary of the turbulent electrode layer. Solutions obtained by the Fourier method describe the daily variation of the electric field strength depending on the degree of turbulent mixing in the atmosphere. The appearance of a time shift in daily extrema, a change in their amplitude, and the appearance of additional extrema depending on the elec-tric field values have been established. All of these effects are comparable to the global unitary variation and increase with increasing electric field.

Physically accessible and inaccessible quantum correlations of Dirac fields in Schwarzschild spacetime

In this study, we investigate the influence of Hawking decoherence on the quantum correlations of Dirac fields between Alice and Bob. Initially, they share a Gisin state near the Schwarzschild black hole (SBH) in an asymptotically flat region. Then, Alice remains stationary in this region, while Bob hovers near the event horizon (EH) of the SBH. We expect that Bob, using his excited detector, will detect a thermal Fermi-Dirac particle distribution. We assess the quantum correlations in the evolved Gisin state using quantum consonance and uncertainty-induced non-locality across physically accessible, physically inaccessible, and spacetime regions. Our investigation examines how these measures vary with Hawking temperature, Dirac particle frequency, and the parameters of the initial Gisin state. Additionally, we analyze the distribution of these quantum correlation measures across all possible regions, noting a redistribution towards the physically inaccessible region. Our findings demonstrate that Hawking decoherence reduces the quantum correlations of Dirac fields in the physically accessible region, with the extent of reduction depending on the initial state parameters. Moreover, as Hawking decoherence intensifies in the physically inaccessible and spacetime regions, the quantum correlations of Dirac fields reemerge and ultimately converge to specific values at infinite Hawking temperature. These results contribute to our understanding of quantum correlation dynamics within the framework of relativistic quantum information (RQI).

Entanglement membrane in exactly solvable lattice models

Entanglement membrane theory is an effective coarse-grained description of entanglement dynamics and operator growth in chaotic quantum many-body systems. The fundamental quantity characterizing the membrane is the entanglement line tension. However, determining the entanglement line tension for microscopic models is in general exponentially difficult. We compute the entanglement line tension in a recently introduced class of exactly solvable yet chaotic unitary circuits, so-called generalized dual-unitary circuits, obtaining a nontrivial form that gives rise to a hierarchy of velocity scales with vE&lt;vB. For the lowest level of the hierarchy, L¯2 circuits, the entanglement line tension can be computed entirely, while for the higher levels the solvability is reduced to certain regions in spacetime. This partial solvability enables us to place bounds on the entanglement velocity. We find that L¯2 circuits saturate certain bounds on entanglement growth that are also saturated in holographic models. Furthermore, we relate the entanglement line tension to temporal entanglement and correlation functions. We also develop methods of constructing generalized dual-unitary gates, including constructions based on complex Hadamard matrices that exhibit additional solvability properties and constructions that display behavior unique to local dimension greater than or equal to three. Our results shed light on entanglement membrane theory in microscopic Floquet lattice models and enable us to perform nontrivial checks on the validity of its predictions by comparison to exact and numerical calculations. Moreover, they demonstrate that generalized dual-unitary circuits display a more generic form of information dynamics than dual-unitary circuits. Published by the American Physical Society 2024

Linearized gravity and soft graviton theorem in de Sitter spacetime

We study the linearized gravity theory in the Newman-Unti gauge in the near horizon region of the de Sitter spacetime. The linearized Einstein equation involves the cosmological constant. The near horizon symmetry consists of near horizon supertranslation and near horizon superrotation. We compute the near horizon supertranslation charge and find the proper near horizon falloff conditions that uncover a soft graviton theorem from the Ward identity of the near horizon supertranslation. Published by the American Physical Society 2024

Dynamics and collision of particles in modified black-bounce geometry

In the present work, we first regularize a black hole spacetime in modified gravity (MOG) in the presence of the scalar-tensor-vector (STV) field, called the Schwarzschild MOG black hole, under the transformation r2→r2+a2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r^2 \\rightarrow r^2 + a^2$$\\end{document}, known as the Simpson–Visser (SV) spacetime (where a is regularization or black-bounce parameter). The spacetime can represent a black hole and a wormhole. We analyze horizon properties and calculate the effective mass of the spacetime. Also, we find black hole-wormhole regions in black-bounce and MOG parameter spacetime. We also analyze scalar invariants of spacetime, such as the Ricci scalar, the square of the Ricci tensor, and the Kretchmann scalar. We study test particle motion in the SV-MOG spacetime by considering the interaction between the particle and the STV field. We investigate how the STV fields change the innermost stable circular orbits (ISCOs), energy, and angular momentum of the test particle’s ISCO. It is shown that the ISCO decreases in the presence of the black bounce parameter and increases in the STV field. We also study the collisions of test particles and analyze how the MOG and black-bounce parameters influence the critical angular momentum of colliding particles and their center of mass energy.

The Interplay of Fantasy and Physics in King’s The Dark Tower: The Gunslinger: A Physicist’s Perspective

The paper aims to explore the existence of many worlds and their interconnections in Stephen King’s The Dark Tower: The Gunslinger. It draws on theoretical physicist Brian Greene’s concept of parallel universes. It also draws on the theoretical concept of Albert Einstein and Nathan Rosen as they have discussed in ‘Einstein-Rosen Bridge Theory’. This theory is commonly known as wormholes that connect different regions of space-time, enabling the journey from one world to another and back. Greene's theoretical underpinnings, proposing a vast ensemble of universes with distinct properties, find expressions in the narrative. King's narrative, exemplified by, among others, Jake's revival in Mid-World after a presumed death in a New York car accident, explicitly embraces the idea of parallel universes, each with unique physical laws that influence the concepts such as life and death. The narrative unfolds across disparate worlds, echoing Greene’s theoretical mapping of parallel universes, each governed by its unique set of physical laws and realities. In the narrative, the exploration of multiverse concepts employs fiction's imaginative license to investigate interconnected universes and the potential for transcendent journeys through the cosmic fabric. The theoretical backdrop finds resonance in the novel where characters navigate within the four-dimensional continuum, mirroring the speculative nature of multiverse theories. By intertwining the world of fantasy with the hypotheses of physics, the paper discusses the connections between seemingly disparate realms. This perspective bridges literature and theoretical physics, offering a compelling exploration of the speculative landscapes of parallel universes.

Quantum state over time is unique

The conventional framework of quantum theory treats space and time in vastly different ways by representing temporal correlations via quantum channels and spatial correlations via multipartite quantum states—an imbalance absent in classical probability theory. Since Leifer and Spekkens [] called for a causally neutral formulation of quantum theory in their seminal work, numerous attempts have been made to rectify this asymmetry by proposing a dynamical description of a quantum system encapsulated by a static , without a definite consensus on which one is most appropriate. In this paper, we propose sets of operationally motivated axioms for quantum states over time alternative to the ones proposed by Fullwood and Parzygnat [], which we show is unable to induce a unique quantum state over time. Our proposed axioms are better suited to describe quantum states over any spacetime regions beyond two points. Through this reformulation, we prove that the Fullwood-Parzygnat state over time uniquely satisfies all these operational axioms, unifying the bipartite spacetime correlations of quantum systems. Published by the American Physical Society 2024

Exact pretransition effects in kinetically constrained circuits: Dynamical fluctuations in the Floquet-East model.

We study the dynamics of a classical circuit corresponding to a discrete-time version of the kinetically constrained East model. We show that this classical "Floquet-East" model displays pre-transition behavior which is a dynamical equivalent of the hydrophobic effect in water. For the deterministic version of the model, we prove exactly (i) a change in scaling with size in the probability of inactive space-time regions (akin to the "energy-entropy" crossover of the solvation free energy in water), (ii) a first-order phase transition in the dynamical large deviations, (iii) the existence of the optimal geometry for local phase separation to accommodate space-time solutes, and (iv) a dynamical analog of "hydrophobic collapse."

Particle detectors under chronological hazard

We analyze how the presence of closed timelike curves (CTCs) characterizing a time machine can be discerned by placing a local particle detector in a region of spacetime which is causally disconnected from the CTCs. Our study shows that not only can the detector tell if there are CTCs, but also that the detector can separate topological from geometrical information and distinguish periodic spacetimes without CTCs (like the Einstein cylinder), curvature, and spacetimes with topological identifications that enable time-machines.

Sharp estimates for distinguished random walks on affine buildings of type [formula omitted]

We study a distinguished random walk on affine buildings of type A˜r , which was already considered by Cartwright, Saloff-Coste and Woess. In rank r=2, it is the simple random walk and we obtain optimal global bounds for its transition density (same upper and lower bound, up to multiplicative constants). In the higher rank case, we obtain sharp uniform bounds in fairly large space–time regions which are sufficient for most applications.

On locational sensory individuals and spacetime

Perception not only registers property instances, but also connects with and attributes properties to individual entities—so‐called sensory individuals, or SIs. But what are SIs? The most‐discussed answers are: (i) SIs are ordinary material objects—cohesive, temporally persistent objects extended and bounded in space, and (ii) SIs are locations or regions in spacetime. I will argue for the object view of SIs on the grounds that its rival, the locational view, faces obstacles concerning the relationship between SIs and spacetime: it makes a mystery of perception's representation of SIs as occupying locations in and moving in ordinary spacetime.

Black holes, white holes, and near-horizon physics

Black and white holes play remarkably contrasting roles in general relativity versus observational astrophysics. While there is observational evidence for the existence of compact objects that are “cold, dark, and heavy”, which thereby are natural candidates for black holes, the theoretically viable time-reversed variants — the “white holes” — have nowhere near the same level of observational support. Herein we shall explore the theoretical possibility that the connection between black and white holes is much more intimate than commonly appreciated. We shall first construct “horizon penetrating” coordinate systems that differ from the standard curvature coordinates only in a small near-horizon region, thereby emphasizing that ultimately the distinction between black and white horizons depends only on near-horizon physics. We shall then construct an explicit model for a “black-to-white transition” where all of the nontrivial physics is confined to a compact region of spacetime — a finite-duration finite-thickness, (in principle arbitrarily small), region straddling the naïve horizon. Moreover we shall show that it is possible to arrange the “black-to-white transition” to have zero action — so that it will not be subject to destructive interference in the Feynman path integral. This then raises the very intriguing possibility that astrophysical black holes might be interpretable in terms of a quantum superposition of black and white horizons — a “gray” horizon.

The Sasa–Satsuma equation with high-order discrete spectra in space-time solitonic regions: soliton resolution via the mixed ∂¯ -Riemann–Hilbert problem

In this paper, we investigate the Cauchy problem of the Sasa–Satsuma (SS) equation with initial data belonging to the Schwartz space. The SS equation is one of the integrable higher-order extensions of the nonlinear Schrödinger equation and admits a 3 × 3 Lax representation. With the aid of the ∂¯ -nonlinear steepest descent method of the mixed ∂¯ -Riemann–Hilbert problem, we give the soliton resolution and long-time asymptotics for the Cauchy problem of the SS equation with the existence of second-order discrete spectra in the space-time solitonic regions.

Non-minimal coupling, negative null energy, and effective field theory

The non-minimal coupling of scalar fields to gravity has been claimed to violate energy conditions, leading to exotic phenomena such as traversable wormholes, even in classical theories. In this work we adopt the view that the non-minimal coupling can be viewed as part of an effective field theory (EFT) in which the field value is controlled by the theory’s cutoff. Under this assumption, the average null energy condition, whose violation is necessary to allow traversable wormholes, is obeyed both classically and in the context of quantum field theory. In addition, we establish a type of "smeared" null energy condition in the non-minimally coupled theory, showing that the null energy averaged over a region of spacetime obeys a state dependent bound, in that it depends on the allowed field range. We finally motivate our EFT assumption by considering when the gravity plus matter path integral remains semi-classically controlled.

Micro-cosmos model of a nucleon

This study explores the age-old quest to construct a geometric model of a quantum particle. While static classical particle models have largely been dismissed, the focus has now shifted to intricate dynamic models that hold the promise of reconciling general relativity with quantum mechanics. We propose that matter particles can be described as radiation confined within dynamically curved spacetime regions, without the need for quantization of space and time, and using standard field equations and natural Planck units. Specifically, we investigate a cyclic or oscillating radiation-dominated micro-cosmos undergoing repeated bouncing. Our methodology employs integration, with carefully defined initial conditions. The results include several observable properties characteristic of quantum particles. We calculate the total mass, revealing a compelling inverse proportionality between mass and radius identical with the de Broglie relationship. Applying this model to protons, we discover a profound and surprisingly simple relationship between the proton’s radius and mass expressed in Planck units. This enables a definition of the proton radius that aligns remarkably well with the 2018 CODATA value. Furthermore, our analysis demonstrates that the radial density profile of the proton (or nucleon), averaged over a cycle time, increases toward the center. The problem of embedding the micro-cosmos within a background spacetime is also described. These results underscore the relevance of general relativity in the domain of nuclear physics. Moreover, the model offers a fresh perspective that can stimulate new ideas in the ongoing quest to unify general relativity with quantum physics.

Crossed product algebras and generalized entropy for subregions

An early result of algebraic quantum field theory is that the algebra of any subregion in a QFT is a von Neumann factor of type III_{1}1, in which entropy cannot be well-defined because such algebras do not admit a trace or density states. However, associated to the algebra is a modular group of automorphisms characterizing the local dynamics of degrees of freedom in the region, and the crossed product of the algebra with its modular group yields a type II_∞∞ factor, in which traces and hence von Neumann entropy can be well-defined. In this work, we generalize recent constructions of the crossed product algebra for the TFD to, in principle, arbitrary spacetime regions in arbitrary QFTs, formally paving the way to the study of entanglement entropy without UV divergences. In contrast to previous works, we emphasize that this construction is independent of gravity. In this sense, the crossed product construction represents a refinement of Haag’s assignment of nets of observable algebras to spacetime regions by providing a natural construction of a type II factor. We present several concrete examples: a QFT in Rindler space, a CFT in an open ball of Minkowski space, and arbitrary boundary subregions in AdS/CFT. In the holographic setting, we provide a novel argument for why the bulk dual must be the entanglement wedge, and discuss the distinction arising from boundary modular flow between causal and entanglement wedges for excited states and disjoint regions.

On Penrose’s Analogy between Curved Spacetime Regions and Optical Lenses

On Penrose’s Analogy between Curved Spacetime Regions and Optical Lenses