General Spacetime Research Articles

Curvature properties of Nariai spacetimes

This paper is concerned with the study of the geometry of (charged) Nariai spacetime, a topological product spacetime, by means of covariant derivative(s) of its various curvature tensors. It is found that on this spacetime the condition [Formula: see text] is satisfied and it also admits the pseudosymmetric type curvature conditions [Formula: see text] and [Formula: see text]. Moreover, it is 4-dimensional Roter type, [Formula: see text]-quasi-Einstein and generalized quasi-Einstein spacetime. The energy–momentum tensor is expressed explicitly by some 1-forms. It is worthy to see that a generalization of such topological product spacetime proposes to exist with a class of generalized recurrent type manifolds which is semisymmetric. It is observed that the rank of [Formula: see text], [Formula: see text], of Nariai spacetime (NS) is 0 whereas in case of charged Nariai spacetime (CNS) it is 2, which exhibits that effects of charge increase the rank of Ricci tensor. Also, due to the presence of charge in CNS, it gives rise to the proper pseudosymmetric type geometric structures.

Different instances of time as different quantum modes: quantum states across space-time for continuous variables

Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in general relativity space-time is taken as a combinator, curved around mass. Here we present a unified approach on both space and time in quantum theory, and build quantum states across spacetime instead of only on spatial slices. We no longer distinguish measurements on the same system at different times with measurements on different systems at one time and construct spacetime states upon these measurement statistics. As a first step towards non-relativistic quantum field theory, we consider how to approach this in the continuous-variable multi-mode regime. We propose six possible definitions for spacetime states in continuous variables, based on four different measurement processes: quadratures, displaced parity operators, position measurements and weak measurements. The basic idea is to treat different instances of time as different quantum modes. They are motivated by the pseudo-density matrix formulation among indefinite causal structures and the path integral formalism. We show that these definitions lead to desirable properties, and raise the differences and similarities between spatial and temporal correlations. An experimental proposal for tomography is presented, construing the operational meaning of the spacetime states.

Gravity edges modes and Hayward term

We argue that corner contributions in gravity action (Hayward term) capture the essence of gravity edge modes, which lead to gravitational area entropies, such as the black hole entropy and holographic entanglement entropy. We explain how the Hayward term and the corresponding edge modes in gravity are explained by holography from two different viewpoints. One is an extension of AdS/CFT to general spacetimes and the other is the AdS/BCFT formulation. In the final part, we explore how gravity edge modes and its entropy show up in string theory by considering open strings stuck to a Rindler horizon.

On gauging finite subgroups

We study in general spacetime dimension the symmetry of the theory obtained by gauging a non-anomalous finite normal Abelian subgroup AA of a \GammaΓ-symmetric theory. Depending on how anomalous \GammaΓ is, we find that the symmetry of the gauged theory can be i) a direct product of G=\Gamma/AG=Γ/A and a higher-form symmetry \hat AÂ with a mixed anomaly, where \hat AÂ is the Pontryagin dual of AA; ii) an extension of the ordinary symmetry group GG by the higher-form symmetry \hat AÂ; iii) or even more esoteric types of symmetries which are no longer groups. We also discuss the relations to the effect called the H^3(G,\hat A)H3(G,Â) symmetry localization obstruction in the condensed-matter theory and to some of the constructions in the works of Kapustin-Thorngren and Wang-Wen-Witten.

New code for equilibriums and quasiequilibrium initial data of compact objects. IV. Rotating relativistic stars with mixed poloidal and toroidal magnetic fields

A new code for computing fully general relativistic solutions of strongly magnetized rapidly rotating compact stars is developed as a part of the COCAL (Compact Object CALculator) code. The full set of Einstein's equations, Maxwell's equations and magnetohydrodynamic equations are consistently solved assuming perfect conductivity, stationarity, and axisymmetry, and strongly magnetized solutions associated with mixed poloidal and toroidal components of magnetic fields are successfully obtained in generic (non-circular) spacetimes. We introduce the formulation of the problem and the numerical method in detail, then present examples of extremely magnetized compact star solutions and their convergence tests. It is found that, in extremely magnetized stars, the stellar matter can be expelled from the region of strongest toroidal fields. Hence we conjecture that a toroidal electro-vacuum region may appear inside of the extremely magnetized compact stars, which may seem like the neutron star becoming the strongest toroidal solenoid coil in the universe.

Short time PM2.5 prediction model for Beijing-Tianjin-Hebei region based on Generalized Space Time Autoregressive (GSTAR)

In recent years, with the rapid development of China’s economy and urbanization, the irrational industrial structure, large energy consumption, and increased car ownership have made China’s air pollution increasingly serious, especially in Beijing-Tianjin-Hebei, Yangtze River Delta, and the Pearl River Delta. As the primary pollutant affecting the air quality in the Beijing-Tianjin-Hebei region, the accurate prediction of PM2.5 concentration is of great significance for predicting heavy pollution weather, formulating the start-up mechanism of emergency plan and optimizing the production of enterprises. This study used the online hourly data of conventional pollutants from 80 national control stations in Beijing, Tianjin and Hebei from May 1, 2015 to May 31, 2019. Considering the influence of time and space, the GSTAR model of PM2.5 prediction is established. Comparing the prediction results of GSTAR model with ARMA and STAR, the validity of GSTAR model is verified by applying relevant accuracy evaluation indicators.

PEMODELAN GENERALIZED SPACE TIME AUTOREGRESSIVE (GSTAR) SEASONAL PADA DATA CURAH HUJAN EMPAT KABUPATEN DI PROVINSI JAWA TENGAH

In many applications, several time series data are recorded simultaneously at a number of locations. Time series data from nearby locations often to be related by spatial and time. This data is called spatial time series data. Generalized Space Time Autoregressive (GSTAR) model is one of space time models used to modeling and forecasting spatial time series data. This study applied GTSAR model to modeling volume of rainfall four locations in Jepara Regency, Kudus Regency, Pati Regency, and Grobogan Regency. Based on the smallest RMSE mean of forecasting result, the best model chosen by this study is GSTAR (11)-I(1)12 with the inverse distance weighted. Based on GSTAR(11)-I(1)12 with the inverse distance weighted, the relationship between the location shown on rainfall Pati Regency influenced by the rainfall in other regencies. Keywords: GSTAR, RMSE, Rainfall

Separability of the Klein-Gordon equation for rotating spacetimes obtained from Newman-Janis algorithm

In the literature, the Newman-Janis algorithm (NJA) has been widely used to construct stationary and axisymmetric spacetimes to describe rotating black holes. In addition, it has been recently shown that the general stationary and axisymmetric spacetime generated through NJA allows the complete separability of the null geodesic equations. In fact, the Hamilton-Jacobi equation in this spacetime is also separable if one of the metric functions is additively separable. In this work, we further study the conditions for a separable Klein-Gordon equation in such a general spacetime. The relations between the NJA spacetime and other parameterized axially symmetric spacetimes in the literature are also discussed.

Transfer matrix method for the analysis of space-time-modulated media and systems

Space-time modulation adds another powerful degree of freedom to the manipulation of classical wave systems. It opens the door for complex control of wave behavior beyond the reach of stationary systems, such as nonreciprocal wave transport and realization of gain media. Here we generalize the transfer matrix method and use it to create a general framework to solve wave propagation problems in time-varying acoustic, electromagnetic, and electric circuit systems. The proposed method provides a versatile approach for the study of general space-time varying systems, which allows any number of time-modulated elements with arbitrary modulation profile, facilities the investigation of high order modes, and provides an interface between space-time modulated systems and other systems.

An analytical approach to obtain exact solutions of some space-time conformable fractional differential equations

In this paper, the sine-Gordon expansion method is used to obtain analytical solutions of the conformable space-time generalized reaction Duffing model and conformable space-time Eckhaus equation with the aid of symbolic computation. These equations can be reduced into ordinary differential equations (ODEs) using a suitable wave transformation with a predicted polynomial-type solution.

Hamiltonian formalism and gauge-fixing conditions for cosmological perturbation theory

We apply the Dirac procedure for constrained systems to the Arnowitt–Deser–Misner formalism linearized around the Friedmann–Lemaitre universe. We explain and employ some basic concepts such as Dirac observables, Dirac brackets, gauge-fixing conditions, reduced phase space, physical Hamiltonian and physical dynamics. In particular, we elaborate on the key concept which is the canonical isomorphism between different gauge-fixing surfaces. We apply our formalism to describe the reduced phase space of cosmological perturbations in some popular in the literature gauges. Our formalism is first developed for the universe with a single fluid and then extended to the multi-fluid case. The obtained results are a starting point for complete quantization of the cosmological perturbations and the cosmological background. Our approach may be used in future to derive the reduced phase space of higher order perturbations and in more generic cosmological spacetimes.

Tsallis, Rényi and Sharma-Mittal holographic and new agegraphic dark energy models in D-dimensional fractal universe

In this work, we explore the accelerated expansion of the Universe through a non-linear interaction of newly proposed dark energy models (namely Tsallis holographic dark energy (HDE), Renyi HDE, Sharma Mittal HDE, Tsallis new agegraphic dark energy (NADE), Renyi NADE and Sharma-Mittal NADE) with cold dark matter in the background of flat D -dimensional fractal Universe. The effect of IR cutoffs including the Hubble radius and Granda-Oliveros (GO) on the properties of the considered dark energy models have been investigated in this context. The cosmological parameters such as equation of state (EoS) parameter, squared speed of sound and $ \omega_{d}$ - $ \omega^{\prime}_{d}$ cosmological plane during the cosmic evolution have been calculated. Analyzing the behavior of such cosmological parameters graphically, it is found that the considered HDE and NADE models can lead to the late time accelerated expansion in the presence of interaction between two dark sectors of the Universe in more general space-time. This result is similar to the standard interacting HDE model with Hubble cutoff in FRW Universe.

Hypergeometric representation of one-loop Higgs decay to two photons

In this paper, we derive hypergeometric function representation of one-loop contributing to Higgs decay to two photons in the standard model and its extensions. The calculations are performed at general space–time dimension d. For the first time, analytic results are published for form factors that are valid in arbitrary space–time dimension. Moreover, we confirm against analytic results in previous computations that have been available in space–time dimension d = 4 – 2ϵ at ϵ0 expansions.

On conformal blocks, crossing kernels and multi-variable hypergeometric functions

In this note, we present an alternative representation of the conformal block with external scalars in general spacetime dimensions in terms of a finite summation over Appell fourth hypergeometric function F4. We also construct its generalization to the non-local primary exchange operator with continuous spin and its corresponding Mellin representation which are relevant for Lorentzian spacetime. Using these results we apply the Lorentzian inversion formula to compute the so-called crossing kernel in general spacetime dimensions, the resultant expression can be written as a double infinite summation over certain Kampé de Fériet hypergeometric functions with the correct double trace operator singularity structures. We also include some complementary computations in AdS space, demonstrating the orthogonality of conformal blocks and performing the decompositions.

Momentum space approach to crossing symmetric CFT correlators. Part II. General spacetime dimension

Our previous work [1] constructed, in three-dimensional momentum space, a manifestly crossing symmetric basis for scalar conformal four-point functions, based on the factorization property proposed by Polyakov. This work extends this construction to general dimensional conformal field theory. To facilitate the treatment of symmetric traceless tensors, we exploit techniques of spherical harmonics in general dimensions.

Revisiting the second post-Minkowskian eikonal and the dynamics of binary black holes

In this paper we study the two-body gravitational scattering of massive scalars with different masses in general spacetime dimensions. We focus on the Regge limit (eikonal regime) of the resulting scattering amplitudes and discuss how to extract the classical information representing the scattering of two black holes. We derive the leading eikonal and explicitly show the resummation of the first leading energy contribution up to second order in Newton's gravitational constant. We also calculate the subleading eikonal showing that in general spacetime dimensions it receives a non-trivial contribution from the box integral. From the eikonal we extract the two-body classical scattering angle between the two black holes up to the second post-Minkowskian order (2PM). Taking various probe-limits of the two-body scattering angles we are able to show agreement between our results and various results in the literature. We highlight that the box integral also has a log-divergent (in energy) contribution at subsubleading order which violates perturbative unitarity in the ultra-relativistic limit. We expect this term to play a role in the calculation of the eikonal at the 3PM order.

Surface theory: the classical, the quantum, and the holographic

Motivated by the power of subregion/subregion duality for constraining the bulk geometry in gauge/gravity duality, we pursue a comprehensive and systematic approach to the behavior of extremal surfaces under perturbations. Specifically, we consider modifications to their boundary conditions, to the bulk metric, and to bulk quantum matter fields. We present a unified framework for treating such perturbations for classical extremal surfaces, classify some of their stability properties, and develop new technology to extend our treatment to quantum extremal surfaces, culminating in an ‘equation of quantum extremal deviation’. Part of the power of this formalism is due to its ability to map geometric statements into the language of elliptic operators; to illustrate, we show that various a priori disparate bulk constraints all follow from basic consistency of subregion/subregion duality. These include familiar properties such as (smeared) versions of the quantum focusing conjecture and the generalized second law, as well as new constraints on (i) metric and matter perturbations in spacetimes close to vacuum and (ii) the bulk stress tensor in generic (not necessary close to vacuum) spacetimes. This latter constraint is highly reminiscent of a quantum energy inequality.

A priori estimates for a relativistic liquid with free surface boundary

We prove energy estimates for a relativistic free liquid body with sufficiently small fluid velocity in a general Lorentz spacetime. These estimates control Sobolev norms of the fluid velocity and enthalpy in the interior as well as Sobolev norms of the second fundamental form on the boundary. These estimates are generalizations of the energy estimates of Christodoulou and Lindblad [D. Christodoulou and H. Lindblad, On the motion of the free surface of a liquid, Commun. Pure Appl. Math. 53(12) (2000) 1536–1602] and rely on elliptic estimates which only require bounds for the second fundamental form of the time slices of the free boundary.

Particle motion around generic black holes coupled to non-linear electrodynamics

We study spherically symmetric magnetically charged generic black hole solutions of general relativity coupled to non-linear electrodynamics (NED). For characteristic values of the generic spacetime parameters we give the position of horizons in dependence on the charge parameter, demonstrating separation of the black hole and no-horizon solutions, and possibility of existence of solutions containing three horizons. We show that null, weak and strong energy conditions are violated when the outer horizon is approaching the center. We study effective potentials for photons and massive test particles and location of circular photon orbits (CPO) and innermost stable circular orbit (ISCO). We show that the unstable photon orbit can become stable, leading to the possibility of photon capture which affects on silhouette of the central object. The position of ISCO approaches the horizon with increasing charge parameter q and the energy at ISCO decreases with increasing charge parameter. We investigate this phenomenon and summarize for a variety of the generic spacetime parameters the upper estimate on the spin parameter of the Kerr black which can be mimicked by the generic charged black hole solutions.

Impacts of Neighbors on Local Tax Rates: A Space–Time Dynamic Panel Data Analysis

This article explores the spatiotemporal pattern in the local tax system of Extremadura, a region in the southwest of Spain. Using the most relevant tax in terms of revenues at the local level in Spain, the property tax on urban land, a very general space–time dynamic panel data model with spatial and time period fixed effects, has been estimated to explore different types of strategic tax interactions among local governments. The empirical analysis uses a balanced panel database covering 383 municipalities from Extremadura for the period 2006–2015 to estimate the reaction of tax policy in a given municipality to its own past, to changes in tax policy in other municipalities, and to (direct and indirect) changes in some control variables. The results show that nominal local property tax rates are affected by tax policy inertia from the own municipality and neighboring municipalities and two observed municipal characteristics, whereas effective tax rates depend on tax policy inertia from the own municipality and property tax policies from neighboring municipalities and five observed municipal characteristics. In both cases, local spillover effects are not significant at standard statistical levels.