Space-time Structure Research Articles

The Birth of the Universe as a Result of the Change of the Metric Signature

In this paper, I discuss the idea that the birth of our Universe may be a result of a quantum transition from a physical continuum with the Euclidean signature to a Lorentzian spacetime. A similar idea was expressed by Andrei D. Sakharov At the classical level, the idea was studied by George F. R. Ellis and his collaborators, who explored if solutions to the classical Einstein equation exist which admit a change of metric signature. The present paper aims at examining possible realizations of this idea at the level of quantum gravity, in the framework of the Wheeler–DeWitt theory and in the extended phase space approach to quantization of gravity. I intend to answer the questions: to answer the questions: Does the Hartle–Hawking wave function imply such a realization? How can this idea be realized in the extended phase space approach to quantum gravity, where the change of signature is described by imposing special conditions on g00-component of the metric in different regions of the physical continuum? The conclusion is that the idea can be realized from a formal mathematical point of view, but it can hardly help in understanding how spacetime structure and time itself appeared from a timeless continuum.

Nearest Neighbor Method for Discriminating Aftershocks and Duplicates When Merging Earthquake Catalogs

Early aftershocks contain important information about the physics of earthquake occurrence and postseismic relaxation processes. However, the standard catalogs of early aftershocks are usually incomplete. Many events can be missed in the main shock coda, some of which are strong enough due to the extremely high noise level. Under these conditions, the process of event identification becomes largely stochastic. Due to different network configurations and record processing methods, different agencies may register/miss different events, thus merging catalogs can improve the completeness of the aftershock sequence. When merging catalogs, the problem of identifying duplicates (records related to the same seismic event) arises. The main difficulty is discriminating aftershocks and duplicates, since both are events close in space and time. The problem is analogous to the problem of discriminating aftershocks and independent events. The solution methods are usually similar too. In this paper, we apply the nearest neighbor method modified for our problem. This method has become widespread in recent years in the problem of identifying aftershocks, and a probabilistic metric in the space of network errors in determining the epicenters and times of seismic events. It is applied for automatic identification of duplicates when merging catalogs of aftershocks for the Tohoku earthquake. An analysis of the space-time structure of duplicates and aftershocks shows their significant difference, which makes it possible to successfully solve the problem. In a sample from the global Advanced National Seismic System (ANSS) catalog (M> 4), were found more than 700 events missed by the Japan Meteorological Agency (JMA) seismic network, which is one of the best in the world. Among the misses, there are several events with M> 6 in the first hours after the main shock. Duplicate identification reliability is >97%. The method can be used to improve the completeness of aftershock sequences. The reliable identification of duplicates allows, in addition, to study the correspondence of the magnitudes determined by different agencies. Therefore the present method is an effective tool for creating merged catalogs of earthquakes with a uniform magnitude.

Geodesically complete black holes in Lorentz-violating gravity

We present a systematic study of the geometric structure of non-singular spacetimes describing black holes in Lorentz-violating gravity. We start with a review of the definition of trapping horizons, and the associated notions of trapped and marginally trapped surfaces, and then study their significance in frameworks with modified dispersion relations. This leads us to introduce the notion of universally marginally trapped surfaces, as the direct generalization of marginally trapped surfaces for frameworks with infinite signal velocities (Hořava-like frameworks), which then allows us to define universal trapping horizons. We find that trapped surfaces cannot be generalized in the same way, and discuss in detail why this does not prevent using universal trapping horizons to define black holes in Hořava-like frameworks. We then explore the interplay between the kinematical part of Penrose’s singularity theorem, which implies the existence of incomplete null geodesics in the presence of a focusing point, and the existence of multiple different metrics. This allows us to present a complete classification of all possible geometries that neither display incomplete physical trajectories nor curvature singularities. Our main result is that not all classes that exist in frameworks in which all signal velocities are realized in Hořava-like frameworks. However, the taxonomy of geodesically complete black holes in Hořava-like frameworks includes diverse scenarios such as evaporating regular black holes, regular black holes bouncing into regular white holes, and hidden wormholes.

Collapsing dust thin shells in Einstein\u2013Gauss\u2013Bonnet gravity

We investigate gravitational collapse of a spherically symmetric thin shell in the Einstein–Gauss–Bonnet (EGB) gravity. Under the recently proposed 4D limit, we find that the collapsing shell will be bounced back at a small radius, without forming a singularity. This bouncing behavior is similar to those of a test particle and a homogeneous spherical dust star, in accordance with the expectation that the Gauss–Bonnet term will modify the small scale behavior of the Einstein gravity. We analyze the causal structure of the dynamic spacetime that represents the bouncing process, finding that the thin shell has an oscillation behavior on the Penrose diagram, which means that the thin shell results in a novel type of black hole with respect to observers outside the event horizon that the collapse forms. We also find that the weak cosmic censorship conjecture holds in this model. Further implications of such a regular gravitational collapse are discussed.

Determination of Spatial-Temporal Characteristics of Sea Wind Waves

The nonlinearity of sea surface waves is an important property of them. Despite the fact that the nonlinearity is weak, it must be taken into account when solving many applied and fundamental problems. In this work, we study the effect of nonlinearity on the space-time structure of sea waves. The results of determining the spatial-temporal structure from the data of measurements by an array of wave sensors and from optical images of the sea surface are compared. It is shown that there is a discrepancy between the wave characteristics determined in different ways. Partially, but not completely, these discrepancies are explained by incomplete consideration of the directional spreading function.

Lattice construction of exotic invertible topological phases

In this paper, we provide state sum path integral definitions of exotic invertible topological phases proposed in the recent paper by Hsin, Ji, and Jian [arXiv:2105.09454 [cond-mat.str-el]. The exotic phase has time-reversal $(T)$ symmetry, and depends on a choice of the space-time structure called the Wu structure. The exotic phase cannot be captured by the classification of any bosonic or fermionic topological phases and thus gives a novel class of invertible topological phases. When the $T$ symmetry defect admits a spin structure, our construction reduces to a sort of the decorated domain wall construction, in terms of a bosonic theory with $T$ symmetry defects decorated with a fermionic phase that depends on a spin structure of the $T$ symmetry defect. By utilizing our path integral, we propose a lattice construction for the exotic phase that generates the ${\mathbb{Z}}_{8}$ classification of the $(3+1)$d invertible phase based on the Wu structure. This generalizes the ${\mathbb{Z}}_{8}$ classification of the $T$-symmetric $(1+1)$d topological superconductor proposed by Fidkowski and Kitaev. On oriented space-time, this $(3+1)$d invertible phase with a specific choice of Wu structure reduces to a bosonic Crane-Yetter TQFT which has a topological ordered state with a semion on its boundary. Moreover, we propose a subclass of $G$-SPT phases based on the Wu structure labeled by a pair of cohomological data in generic space-time dimensions. This generalizes the Gu-Wen subclass of fermionic SPT phases.

Nonreciprocal optical response in parity-breaking superconductors

Superconductivity, an emergence of a macroscopic quantum state, gives rise to unique electromagnetic responses leading to perfect shielding of magnetic field and zero electrical resistance. In this paper, we propose that superconductors with the space-inversion symmetry breaking host giant nonreciprocal optical phenomena, such as photocurrent generation and second harmonic generation. The nonreciprocal optical responses show divergent behaviors in the low-frequency regime and originate from two-fold indicators unique to parity-breaking superconductors, namely, the nonreciprocal superfluid density and the Berry curvature derivative. Furthermore, the mechanism and frequency dependence are closely tied to the preserved temporal symmetry in the superconductor. The relation is useful for probing the space-time structure of the superconducting symmetry. The indicators characterize the low-frequency property of nonreciprocal optical responses and hence quantify the performance of superconductors in nonreciprocal optics.

Possible Structure of a Local Space-Time of Charged Fermions

Possible Structure of a Local Space-Time of Charged Fermions

Ads to Ds Phase Transition Mediated by Thermalon in Einstein-Gauss-Bonnet Gravity from R\'{E}Nyi Statistics

In this work, we examine thermalon phase transition between AdS and dS vacua in Einstein-Gauss-Bonnet gravity by considering the R\'{e}nyi statistics. The thermalon changes the asymptotic structure of spacetimes via the bubble nucleation of spherical thin-shells which host a black hole in the interior. All relevant thermodynamical quantities are computed in terms of the R\'{e}nyi statistics in order to demonstrate the possible existence of the AdS to dS phase transition. In addition, we also comment on the behaviors of the phase transitions in the R\'{e}nyi statistics.

Spatial Attributes of Particles and Quantum Fields

According to the characteristics of manifold and the double helix structure of spacetime, four coordinate systems are established as reference frames. The grand parity principle and the general exclusion principle are proposed. The minimum action distance of electromagnetic force is obtained and the structure of intrinsic space of particle is studied. The stability of particle reaction, the reason for only three generations of leptons and the spatial significance of the electroweak equivalence are discussed by using the two principles and the four coordinate systems. The behavior of boson including condensation is described in terms of spatial structure. Finally, we suggest that symmetry between the field excited by charge and the field excited by mass should be further investigated.

The wormhole model with an exponential shape function in the Finslerian framework

This paper aims to study the wormhole model with an exponential shape function within the framework of Finsler geometry. By considering anisotropic energy-momentum tensor, we have analyzed the wormhole solution of the gravitational field equation in the Finslerian context. To investigate the viability of the Finslerian wormhole solution, we have discussed the energy conditions and the nature of the parameters like radial and transverse equation-of-state parameters and density. The force due to the contribution of gravity is examined along with the anisotropic force and hydrostatic force to verify whether the obtained exact Finslerian wormhole solution is in equilibrium or not. Further, we have observed that the solution is feasible and physically interesting for analyzing wormholes in the Finslerian structure of space-time.

Light-Cone Coordinate System in General Relativity

If there exists a null gradient field in 3 + 1 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is helpful for simplifying and solving the Einstein’s field equation. This light-cone coordinate system has wonderful properties and has been used widely in astrophysics to calculate parameters. We discuss the structure of space-time with light-cone coordinate system in detail. We show how to construct the light-cone coordinate system and obtain the conditions of its existence, and then explain their geometrical and physical meanings.

Macrocausality implies Lorenz group:a physics-related comment on guts's results

It is known that, in the space-time of Special Relativity, causalityimplies Lorenz group, i.e., if we know which events can causally influenceeach other, then, based on this information, we can uniquely reconstruct theaffine structure of space-time. When the two events are very close, quantumeffects, with their probabilistic nature, make it difficult to detect causality. So,the following question naturally arises: can we uniquely reconstruct the affinestructure if we only know causality for events which are sufficiently far awayfrom each other? Several positive answers to this question were provided ina recent paper by Alexander Guts. In this paper, we describe a very simpleanswer to this same question.

Дискурс “Pax Yalta” (к вопросу о пространственно-временной модели власти М. Фуко)

Subject of the article: spatial-temporal characteristics of power in the philoso­phical theory of M. Foucault. The main methodological strategy of the study: the analysis of the Yalta world in the framework of the Fukian space-time theory of power. However, the theoretical developments of M. Foucault are used to study the features of the Yalta world not as a final solution to the problem. The realities of the Yalta world serve as a platform for conducting an experiment aimed at finding out the epistemological possibilities of the classical Fukian the­ory of power. For a better understanding of the space-time structures of power that M. Foucault uses (but rarely reveals and describes in detail), the concepts of “chronotopicity of power” and “topochronicity of power” are introduced. The conclusion is made about total processality as the ontic basis of power in M. Foucault. This gives Pax Yalta the status of a third between the episteme of power and the dispositive of power. In a series of changes of the Fukian chronotopes of power (“Shepherd”, “Policeman”) Pax Yalta has a special charac­ter. From the point of view of the topos, the Yalta world is a fact of the devel­oped chronotope “Policeman” characteristic of the New Time. But from the point of view of temporality, the Yalta Myrrh is a fact that makes it related to the Middle Ages (the chronotope “Shepherd”). The gap between the topos and the chronos of power explains many of the paradoxes of the modern world and international relations in particular. And the ontic processality of the power says that the revealed imbalance is characteristic of the period of formation of a new system of power, possibly in the format of a higher synthesis, which will be car­ried out outside of public international law. Its basis is a sense (perception) of the correctness of a certain model of time and space of power, which will end (and not begin) with international legal procedures.

ИЗУЧЕНИЕ УСЛОВИЙ ВОЗНИКНОВЕНИЯ СЛОЖНЫХ РЕЖИМОВ ДИНАМИКИ В БЫСТРО-МЕДЛЕННОЙ МОДЕЛИ МИГРАЦИОННО СВЯЗАННЫХ СООБЩЕСТВ

The paper deals with the study of dynamics of fast-slow system consisting of two non-identical communities «predator – prey» coupled by migration. We study the mechanisms that lead to the complex space-time structures in the case of a weak coupling between very different communities. The community dynamics in this case is non-synchronous or partially synchronous.

Entropic Alternatives to Initialization

Local entropic loss functions provide a versatile framework to define architecture-aware regularization procedures. Besides the possibility of being anisotropic in the synaptic space, the local entropic smoothening of the loss function can vary during training, thus yielding a tunable model complexity. A scoping protocol where the regularization is strong in the early-stage of the training and then fades progressively away constitutes an alternative to standard initialization procedures for deep convolutional neural networks, nonetheless, it has wider applicability. We analyze anisotropic, local entropic smoothenings in the language of statistical physics and information theory, providing insight into both their interpretation and workings. We comment some aspects related to the physics of renormalization and the spacetime structure of convolutional networks.

FORMATION OF THE OBJECT IDENTIFICATION ZONE WITH LASER INFORMATION-MEASURING SYSTEMS AT SHORT DISTANCES

The optimization of the methods for the formation of the spatial-energy distribution of the probing radiation power and the processing the receiving signal by the locating laser information-measuring systems (LIMS), taking into account the spatial-temporal structure, is carried out, and the analysis of the existing methods of their processing is carried out too. An assessment of the integral criteria for the LIMS functioning when operating in conditions of interference has been made. The calculation of the parameters of the LIMS main links was carried out, taking into account the correlation between the resolution of the optical system and the capabilities of object detection, recognition and classification. A method was developed for the formation of the probing radiation density distribution and the receiving signal processing, taking into account its space-time structure, which made it possible to determine the optimal duration of the laser probe pulse. The determined duration makes it possible to eliminate errors in measuring the parameters of an object's movement under the influence of a combination of destabilizing factors and a lack of signal processing time, which will ensure the accuracy of the target detection and recognition.

Tolman-Ehrenfest-Klein law in non-Riemannian geometries

Heat always flows from hotter to a colder temperature until thermal equilibrium be finally restored in agreement with the usual (zeroth, first and second) laws of thermodynamics. However, Tolman and Ehrenfest demonstrated that the relation between inertia and weight uniting all forms of energy in the framework of general relativity implies that the standard equilibrium condition is violated in order to maintain the validity of the first and second law of thermodynamics. Here we demonstrate that the thermal equilibrium condition for a static self-gravitating fluid, besides being violated, is also heavily dependent on the underlying spacetime geometry (whether Riemannian or non-Riemannian). As a particular example, a new equilibrium condition is deduced for a large class of Weyl and f(R) type gravity theories. Such results suggest that experiments based on the foundations of the heat theory (thermal sector) may also be used for confronting gravity theories and prospect the intrinsic geometric nature of the spacetime structure.

Spacetime structure of (3+1)D color fields in high energy nuclear collisions

We perform an analytic calculation of the color fields in heavy-ion collisions by considering the collision of longitudinally extended nuclei in the dilute limit of the Color Glass Condensate effective field theory of high-energy QCD. Based on general analytic expressions for the color fields in the future light cone, we evaluate the rapidity profile of the transverse pressure within a simple specific model of the nuclear collision geometry and compare our results to 3+1D classical Yang-Mills simulations.

Extraction of Human Motion Information from Digital Video Based on 3D Poisson Equation

Based on the 3D Poisson equation, this paper extracts the features of the digital video human body action sequence. By solving the Poisson equation on the silhouette sequence, the time and space features, time and space structure features, shape features, and orientation features can be obtained. First, we use the silhouette structure features in three-dimensional space-time and the orientation features of the silhouette in three-dimensional space-time to represent the local features of the silhouette sequence and use the 3D Zernike moment feature to represent the overall features of the silhouette sequence. Secondly, we combine the Bayesian classifier and AdaBoost classifier to learn and classify the features of human action sequences, conduct experiments on the Weizmann video database, and conduct multiple experiments using the method of classifying samples and selecting partial combinations for training. Then, using the recognition algorithm of motion capture, after the above process, the three-dimensional model is obtained and matched with the model in the three-dimensional model database, the sequence with the smallest distance is calculated, and the corresponding skeleton is outputted as the results of action capture. During the experiment, the human motion tracking method based on the university matching kernel (EMK) image kernel descriptor was used; that is, the scale invariant operator was used to count the characteristics of multiple training images, and finally, the high-dimensional feature space was mapped into the low-dimensional to obtain the feature space approximating the Gaussian kernel. Based on the above analysis, the main user has prior knowledge of the network environment. The experimental results show that the method in this paper can effectively extract the characteristics of human body movements and has a good classification effect for bending, one-foot jumping, vertical jumping, waving, and other movements. Due to the linear separability of the data in the kernel space, fast linear interpolation regression is performed on the features in the feature space, which significantly improves the robustness and accuracy of the estimation of the human motion pose in the image sequence.