General Spacetime Research Articles

On the convergence of cosmographic expansions in Lemaître–Tolman–Bondi models

Abstract We study cosmographic expansions of the luminosity distance for a variety of Lemaître–Tolman–Bondi (LTB) models which we specify inspired by local large-scale structures of the Universe. We consider cosmographic expansions valid for general spacetimes and compare to the Friedmann–Lemaître–Robertson–Walker (FLRW) limit of the expansions as well as to its naive isotropic extrapolation to an inhomogeneous Universe. The FLRW expansions are often poor near the observer but become better at higher redshifts, where the light rays have reached the FLRW background. In line with this we find that the effective Hubble, deceleration and jerk parameters of the general cosmographic expansion are often very different from the global ΛCDM values, with deviations up to several orders of magnitude. By comparing with the naive isotropic extrapolation of the FLRW expansion, we assess that these large deviations are mainly due to gradients of the shear. Very close to the observer, the general cosmographic expansion is always best and becomes more precise when more expansion terms are included. However, we find that the convergence radius of the general cosmographic expansion is small for all studied models and observers and the general cosmographic expansion becomes poor for most of the studied observers already before a single LTB structure has been traversed. The small radius of convergence of the general cosmographic expansion has also been indicated by earlier work and may need careful attention before we can safely apply the general cosmographic expansion to real data.

Analysis of fracton-gravity stability

We study the stability of fracton gravity, a variant of linearized gravity where the gauge symmetry is restricted to longitudinal diffeomorphisms. These transformations can be connected to a spacetime generalization of dipole symmetry, hence the tag fracton. We find that fracton gravity features an instability in the spin-1 sector corresponding to solutions with growing amplitude. This dynamical instability can be removed by tuning the couplings of the theory. Nonetheless, the Hamiltonian for the spin-1 modes remains always unbounded from below when evaluated on the classical solutions. We find no other sources of instability in the spin-2 or spin-0 sectors. We analyze in detail the canonical formulation and the constraints arguing that neither auxiliary fields nor gauge-fixing conditions can be employed to remove the problematic vector modes or stabilize them. Published by the American Physical Society 2024

Enhancing GeoHealth: A step-by-step procedure for spatiotemporal disease mapping.

Cartography, or geographical visualization of disease is an essential aspect of the field of GeoHealth, yet there is limited guidance on the visualization of spatiotemporal disease maps. In order to adequately contribute to understanding disease outbreaks, disease maps should be crafted carefully and according to relevant cartographic guidelines. This article aims to increase the understanding of space-time visualization techniques that are relevant to the field of GeoHealth, by providing a step-by-step framework for the creation of space-time disease visualizations. This study introduces a systematic approach to spatiotemporal disease mapping by integrating operations from the Generalized Space Time Cube (GSTC) Framework with established cartographic symbology guidelines. This resulted in an overview table that contains both the relevant GSTC operations and cartographic guidelines, as well as a step-by-step procedure that guides users through the process of creating informative spatiotemporal disease maps. The practical application of this step-by-step procedure is demonstrated with an example using Dutch COVID-19 data. By providing a clear, practical step by step procedure, this study enhances the capacity of public health professionals, policymakers, and researchers to monitor, understand, and respond to the spatial and temporal dynamics of diseases.

Self-gravitating matter in stationary and axisymmetric black hole spacetimes

Abstract All black holes (BHs) in nature are expected to be described by the Kerr vacuum solution of general relativity. However, the Kerr BH interior contains several problematic features such as a Cauchy horizon, a curvature singularity, and a causality-violating region. Non-Kerr BH models, which are used to examine the genericity of these features, typically contain nontrivial matter content. When such self-gravitating matter is minimally-coupled to Einstein–Hilbert gravity, the Einstein equations can be directly used to investigate its physical properties. We examine here the properties of matter in a broad class of stationary and axisymmetric, geodesically-integrable BH spacetimes, and how they are linked to various features of the spacetime geometry. In these spacetimes, we find the matter to typically flow along timelike Killing orbits in the BH exterior, usually exhibiting differential rotation but sometimes additionally also non-rigid rotation. At a horizon, the matter rest-frame energy density, ε, and principal normal pressure, pn , are shown to necessarily satisfy p n = − ϵ , implying that only specific types of matter can thread stationary event horizons (e.g. electromagnetic fields but not massless real scalar fields). Furthermore, we introduce Boyer–Lindquist-like coordinates for the nonstationary regions in the BH interior, which show the matter to be comoving with the interior cosmology. We also obtain simple expressions for the expansions of the ingoing and outgoing zero angular momentum null congruences and comment on the light-focussing behavior of the cosmology. Finally, we verify above results explicitly by working with a representative set of well-known BH spacetimes which contain various types of matter—scalar fields, electromagnetic fields, anisotropic fluids. Some spacetimes have singularities while others have regular interiors. In the exterior, the matter satisfies the weak energy condition. The framework developed here can be extended to cover more general spacetimes.

The generalized STAR modelling with three-dimensional of spatial weight matrix in predicting the Indonesia peatland’s water level

The release rate of CO2 gas can be influenced by peatlands’ physical properties, such as water level and soil moisture, and rainfall. To anticipate the unstable condition which is when the peatland emit more carbon, we developed the Generalized Space Time Autoregressive (GSTAR) model in predicting these physical properties for the following weeks. As the innovation in modelling, the spatial weight matrix was based on three-dimensional coordinates with a modification on the height factor. The data we used are real-time data of water level on the peatlands in Pulang Pisau Regency, Central Kalimantan Province from 20 February 2021 to 18 March 2023. We then used Ordinary Kriging interpolation on the prediction results to create contour maps on different dates. There were empty data on several dates, especially from 24 March until 3 August 2022. To fill the empty data, we used linear interpolation and then we added white noise to the interpolation results. From the data, the water level has a downward trend pattern from around November to September and an upward trend pattern from October to November. Furthermore, we found that the best model for water level was GSTAR (2;0.1) with a modified matrix a=0.1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a=0.1$$\\end{document} and b=1.1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b=1.1$$\\end{document}. Based on the predicted water level, there is a risk of changes in the properties of the peatlands in several areas in Pulang Pisau Regency.

GPS observables in Newtonian spacetime or why we do not need ‘physical’ coordinate systems

Some authors have defended the claim that one needs to be able to define ‘physical coordinate systems’ and ‘observables’ in order to make sense of general relativity. Moreover, in Rovelli (Physical Review D,65(4), 044017 2002), Rovelli proposes a way of implementing these ideas by making use of a system of satellites that allows defining a set of ‘physical coordinates’, the GPS coordinates. In this article I oppose these views in four ways. First, I defend an alternative way of understanding general relativity which implies that we have a perfectly fine interpretation of the models of the theory even in the absence of ‘physical coordinate systems’. Second, I analyze and challenge the motivations behind the ‘observable’ view. Third, I analyze Rovelli’s proposal and I conclude that it does not allow extracting any physical information from our models that wasn’t available before. Fourth, I draw an analogy between general relativistic spacetimes and Newtonian spacetimes, which allows me to argue that as ‘physical observables’ are not needed in Newtonian spacetime, then neither are they in general relativity. In this sense, I conclude that the ‘observable’ view of general relativity is unmotivated.

Piecewise linear potentials for false vacuum decay and negative modes

We study bounce solutions and associated negative modes in the class of piecewise linear triangular-shaped potentials that may be viewed as approximations of smooth potentials. In these simple potentials, the bounce solution and action can be obtained analytically for a general spacetime dimension D. The eigenequations for the fluctuations around the bounce are universal and have the form of a Schrödinger-like equation with delta-function potentials. This Schrödinger equation is solved exactly for the negative modes whose number is confirmed to be one. The latter result may justify the usefulness of such piecewise linear potentials in the study of false vacuum decay. Published by the American Physical Society 2024

Gluonic evanescent operators: negative-norm states and complex anomalous dimensions

In this paper, we build on our previous work to further investigate the role of evanescent operators in gauge theories, with a particular focus on their contribution to violations of unitarity. We develop an efficient method for calculating the norms of gauge-invariant operators in Yang-Mills (YM) theory by employing on-shell form factors. Our analysis, applicable to general spacetime dimensions, reveals the existence of negative-norm states among evanescent operators. We also explore the one-loop anomalous dimensions of these operators and find complex anomalous dimensions. We broaden our analysis by considering YM theory coupled with scalar fields and we observe similar patterns of non-unitarity. The presence of negative-norm states and complex anomalous dimensions across these analyses provides compelling evidence that general gauge theories are non-unitary in non-integer spacetime dimensions.

Numerical conformal bootstrap with analytic functionals and outer approximation

This paper explores the numerical conformal bootstrap in general spacetime dimensions through the lens of a distinct category of analytic functionals, previously employed in two-dimensional studies. We extend the application of these functionals to a more comprehensive backdrop, demonstrating their adaptability and efficacy in general spacetime dimensions above two. The bootstrap is implemented using the outer approximation methodology, with computations conducted in double precision. The crux of our study lies in comparing the performance of this category of analytic functionals with conventional derivatives at crossing symmetric points. It is worth highlighting that in our study, we identified some novel kinks in the scalar channel during the maximization of the gap in two-dimensional conformal field theory. Our numerical analysis indicates that these analytic functionals offer a superior performance, thereby revealing a potential alternative paradigm in the application of conformal bootstrap.

Covariant cosmography: the observer-dependence of the Hubble parameter

The disagreement between low- and high-redshift measurements of the Hubble parameter is emerging as a serious challenge to the standard model of cosmology. We develop a covariant cosmographic analysis of the Hubble parameter in a general spacetime, which is fully model-independent and can thus be used as part of a robust assessment of the tension. Here our focus is not on the tension but on understanding the relation between the physical expansion rate and its measurement by observers — which is critical for model-independent measurements and tests. We define the physical Hubble parameter and its multipoles in a general spacetime and derive for the first time the covariant boost transformation of the multipoles measured by a heliocentric observer. The analysis is extended to the covariant deceleration parameter. Current cosmographic measurements of the expansion anisotropy contain discrepancies and disagreements, some of which may arise because the correct transformations for a moving observer are not applied. A heliocentric observer will detect a dipole, generated not only by a Doppler effect, but also by an aberration effect due to shear. In principle, the observer can measure both the intrinsic shear anisotropy and the velocity of the observer relative to the matter — without any knowledge of peculiar velocities, which are gauge dependent and do not arise in a covariant approach. The practical implementation of these results is investigated in a follow-up paper. We further show that the standard cosmographic relation between the Hubble parameter, the redshift and the luminosity distance (or magnitude) is not invariant under boosts and holds only in the matter frame. A moving observer who applies the standard cosmographic relation should correct the luminosity distance by a redshift factor — otherwise an incorrect dipole and a spurious octupole are predicted.

Cosmography of the local Universe by multipole analysis of the expansion rate fluctuation field

We establish a relationship between the multipoles of the expansion rate fluctuation field η, which capture in an accurate way deviations from isotropy in the redshift-distance relation, and the multipoles of the covariant cosmographic parameters—Hubble ℍ o , deceleration ℚ o , jerk 𝕁 o , and curvature ℝ o . These parameters, derived from the third-order expansion of the luminosity distance with respect to redshift in a generic spacetime, provide model-independent insight into the geometry and symmetries of the cosmic line element without requiring the Cosmological Principle. Moreover, we demonstrate that although this approach is fully nonperturbative and does not rely on concepts such as peculiar velocities, it has the potential to constrain the motion of the matter frame at the observer's position relative to the cosmic microwave background.We use two analytical axisymmetric models, motivated by observational evidence, to test the formalism and the effectiveness of the third-order expansion of the luminosity distance. These models also help to predict the precision with which future surveys, like the Zwicky Transient Facility, will constrain the covariant cosmographic parameters in the local (z < 0.1) Universe.

GLS estimation in python to forecast gross regional domestic product using generalized space–time autoregressive seemingly unrelated regression model

GLS estimation in python to forecast gross regional domestic product using generalized space–time autoregressive seemingly unrelated regression model

On the holographic dual of a topological symmetry operator

We study the holographic dual of a topological symmetry operator in the context of the AdS/CFT correspondence. Symmetry operators arise from topological field theories localized on a subspace of the boundary conformal field theory spacetime. We use bottom up considerations to construct the topological sector associated with their bulk counterparts. In particular, by exploiting the structure of entanglement wedge reconstruction we argue that the bulk counterpart has a nontopological world volume action, i.e., it describes a dynamical object. As a consequence, we find that there are no global p-form symmetries for p≥0 in asymptotically anti–de Sitter spacetimes, which includes the case of noninvertible symmetries. Provided one has a suitable notion of subregion-subregion duality, our argument for the absence of bulk global symmetries applies to more general spacetimes. These considerations also motivate us to consider for general QFTs (holographic or not) the notion of lower-form symmetries, namely, (−m)-form symmetries for m≥2. Published by the American Physical Society 2024

Towards bit threads in general gravitational spacetimes

The concept of the generalized entanglement wedge was recently proposed by Bousso and Penington, which states that any bulk gravitational region a possesses an associated generalized entanglement wedge E(a) ⊃ a on a static Cauchy surface M in general gravitational spacetimes, where E(a) may contain an entanglement island I(a). It suggests that the fine-grained entropy for bulk region a is given by the generalized entropy Sgen(E(a)). Motivated by this proposal, we extend the quantum bit thread description to general gravitational spacetimes, no longer limited to the AdS spacetime. By utilizing the convex optimization techniques, a dual flow description for the generalized entropy Sgen(E(a)) of a bulk gravitational region a is established on the static Cauchy surface M, such that Sgen(E(a)) is equal to the maximum flux of any flow that starts from the boundary ∂M and ends at bulk region a, or equivalently, the maximum number of bit threads that connect the boundary ∂M to the bulk region a. In addition, the nesting property of flows is also proved. Thus the basic properties of the entropy for bulk regions, i.e. the monotonicity, subadditivity, Araki-Lieb inequality and strong subadditivity, can be verified from flow perspectives by using properties of flows, such as the nesting property. Moreover, in max thread configurations, we find that there exists some lower bounds on the bulk entanglement entropy of matter fields in the region E(a) \\ a, particularly on an entanglement island region I(a) ⊂ (E(a) \\ a), as required by the existence of a nontrivial generalized entanglement wedge. Our quantum bit thread formulation may provide a way to investigate more fine-grained entanglement structures in general spacetimes.

Landauer Principle and the Second Law in a Relativistic Communication Scenario.

The problem of formulating thermodynamics in a relativistic scenario remains unresolved, although many proposals exist in the literature. The challenge arises due to the intrinsic dynamic structure of spacetime as established by the general theory of relativity. With the discovery of the physical nature of information, which underpins Landauer's principle, we believe that information theory should play a role in understanding this problem. In this work, we contribute to this endeavour by considering a relativistic communication task between two partners, Alice and Bob, in a general Lorentzian spacetime. We then assume that the receiver, Bob, reversibly operates a local heat engine powered by information, and seek to determine the maximum amount of work he can extract from this device. As Bob cannot extract work for free, by applying both Landauer's principle and the second law of thermodynamics, we establish a bound on the energy Bob must spend to acquire the information in the first place. This bound is a function of the spacetime metric and the properties of the communication channel.

A comparison between the deflection angles of massive and massless particles in the Schwarzschild space-time and their consequences on black hole shadows

In this paper, we present comparisons of the deflection angles of massless and massive particles in the Schwarzschild space-time. For the case of photons in a general static space-time, we construct a spatial 3D equation of motion for their path that leads to an implicit formula for the deflection angle. We then compare our results with well-known results of the literature in the Schwarzschild space-time. For the case of massive particles, we calculate the deflection angle only in the Schwarzschild space-time. The end result is that as the velocity of any massive particle diminishes, the deflection angle increases. To show the relevance of these comparisons, we constructed different black hole shadows for massive particles in order to be compared with a shadow made by photons.

Visualisation of counter-rotating dust disks using ray tracing methods

Physical aspects of stationary axisymmetric vacuum spacetimes given by exact solutions of the Einstein equations are discussed via ray tracing. A detailed study of the spacetime generated by a disk of counter-rotating dust is presented. The spacetime is given in explicit form in terms of hyperelliptic theta functions. The numerical approach to ray tracing is set up for general stationary axisymmetric spacetimes and tested at the well-studied example of the Kerr solution. Similar features as in the case of a rotating black hole, are explored in the case of a dust disk. The effect of the central redshift varying between a Newtonian disk and the ultrarelativistic disk, where the exterior of the disk can be interpreted as the extreme Kerr solution, and the transition from a single component disk to a static disk is explored. Frame dragging, as well as photon spheres, are discussed.

Quantum Mechanics, Fields, Black Holes, and Ontological Plurality

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.

Higher-order derivative of local times for space–time anisotropic Gaussian random fields

Let X={X(t),t∈RN} be a centered space–time anisotropic Gaussian random field values in Rd. Under some general conditions, the existence and smoothness (in the sense of Meyer-Watanabe) of the higher-order derivative of the local times of X(t) are studied. Moreover, we show that the derivatives of the local time of X(t) is jointly continuous on Rd×[0,1]N. The existing results on local times of fractional Brownian motion and other Gaussian random fields are extended to higher-order derivative of local times of more general space–time anisotropic Gaussian random fields.

Towards Cosmography of the Local Universe

Anisotropies in the distance-redshift relation of cosmological sources are expected due to large-scale inhomogeneities in the local Universe. When the observed sources are tracing a large-scale matter flow in a general spacetime geometry, the distance-redshift relation with its anisotropies can be described with a geometrical prediction that generalises the well-known Friedmann-Lemaître-Robertson-Walker result. Furthermore, it turns out that a finite set of multipole coefficients contain the full information about a finite-order truncation of the distance-redshift relation of a given observer. The multipoles of the distance-redshift relation are interesting new cosmological observables that have a direct physical interpretation in terms of kinematical quantities of the underlying matter flow. Using light cones extracted from N-body simulations we quantify the anisotropies expected in a Λ cold dark matter cosmology by running a Markov chain Monte Carlo analysis on the observed data. In this observational approach the survey selection implements an implicit smoothing scale over which the effective rest frame of matter is fitted. The perceived anisotropy therefore depends significantly on the redshift range and distribution of sources. We find that the multipoles of the expansion rate, as well as the observer’s velocity with respect to the large-scale matter flow, can be determined robustly with our approach.