Past Horizon Research Articles

Smooth Gowdy-symmetric generalised Taub–NUT solutions with polynomial initial data

Abstract We consider smooth Gowdy-symmetric generalised Taub–NUT solutions, a class of inhomogeneous cosmological models with spatial three-sphere topology. They are characterised by existence of a smooth past Cauchy horizon and, with the exception of certain singular cases, they also develop a regular future Cauchy horizon. Several examples of exact solutions were previously constructed, where the initial data (in form of the initial Ernst potentials) are polynomials of low degree. Here, we generalise to polynomial initial data of arbitrary degree. Utilising methods from soliton theory, we obtain a simple algorithm that allows us to construct the resulting Ernst potential with purely algebraic calculations. We also derive an explicit formula in terms of determinants, and we illustrate the method with two examples.

Quadratic perturbations of the Schwarzschild black hole: the algebraically special sector

We investigate quadratic algebraically special perturbations (ASPs) of the Schwarzschild black hole. Their dynamics are derived from the expansion up to second order in perturbation of the most general algebraically special twisting vacuum solution of general relativity. Following this strategy, we present analytical expressions for the axial-axial, polar-polar and polar-axial source terms entering in the dynamical equations. We show that these complicated inhomogeneous equations can be solved analytically and we present explicit expressions for the profiles of the quadratic ASPs. As expected, they exhibit exponential growth both at the past and future horizons even in the non-linear regime. We further use this result to analyze the quadratic zero modes and their interpretation in terms of quadratic corrections to mass and spin of the Schwarzschild black hole. The present work provides a direct extension beyond the linear regime of the original work by Couch and Newman.

Smart Manufacturing and its Impact on Production Processes : A Review

This review paper aims to analyze the theoretical foundations of smart manufacturing and its impact on production processes, particularly in the domains of robotics and additive manufacturing, across past, present, and future time horizons. It also explores the potential of smart manufacturing to improve the precision of manufacturing processes, as well as the challenges it poses to the manufacturing sector. This overview will deepen our understanding of modern manufacturing practices. It's worth noting that some scientific developments and technological tools discussed here can be applied to a wider range of automated systems beyond the manufacturing sector. As such, this paper offers valuable insights for those involved in automated system design and implementation.

Infrared effects and the Unruh state

Detailed behaviors of the modes of quantized scalar fields in the Unruh state for various eternal black holes in two dimensions are investigated. It is shown that the late-time behaviors of some of the modes of the quantum fields and of the symmetric two-point function are determined by infrared effects. The nature of these effects depends upon whether there is an effective potential in the mode equation and what form this potential takes. Here, three cases are considered, one with no potential and two with potentials that are nonnegative everywhere and are zero on the event horizon of the black hole and zero at either infinity or the cosmological horizon. Specifically, the potentials are a delta function potential and the potential that occurs for a massive scalar field in Schwarzschild–de Sitter spacetime. In both cases, scattering effects remove infrared divergences in the mode functions that would otherwise arise from the normalization process. When such infrared divergences are removed, it is found that the modes that are positive frequency with respect to the Kruskal time on the past black hole horizon approach zero in the limit that the radial coordinate is fixed and the time coordinate goes to infinity. In contrast, when there is no potential and thus infrared divergences occur, the same modes approach nonzero constant values in the late-time limit when the radial coordinate is held fixed. The behavior of the symmetric two-point function when the field is in the Unruh state is investigated for the case of a delta function potential in certain asymptotically flat black hole spacetimes in two dimensions. The removal of the infrared divergences in the mode functions results in the elimination of terms that grow linearly in time.

Probing de Sitter from the horizon

In a QFT on de Sitter background, one can study correlators between fields pushed to the future and past horizons of a comoving observer. This is a neat probe of the physics in the observer’s causal diamond (known as the static patch). We use this observable to give a generalization of the quasinormal spectrum in interacting theories, and to connect it to the spectral density that appears in the Källén-Lehmann expansion of dS correlators. We also introduce a finite-temperature effective field theory consisting of free bulk fields coupled to a boundary. In matching it to the low frequency expansion of correlators, we find positivity constraints on the EFT parameters following from unitarity.

Chiral anomalies in black hole spacetimes

We study the properties of chiral anomalies in a wide class of spacetimes which possess a principal Killing-Yano tensor. This class includes metrics of charged rotating black holes as a special physically important case. The spacetimes which admit a principal Killing-Yano tensor possess a number of remarkable properties. In particular, such spacetimes have two commuting Killing vectors and a Killing tensor responsible for their hidden symmetries. We calculate the gravitational and electromagnetic contributions to the axial anomaly currents in the spacetime of a charged rotating black hole, and demonstrate that the equation for the chiral anomaly current has special solutions which respect both explicit and hidden symmetries. Two of these solutions have the form of currents propagating along two principal null directions, which are null eigenvectors of the Riemann tensor. These solutions describe chiral currents for the incoming and outgoing polarization fluxes. It is demonstrated that these principal chiral currents can be written explicitly in the form which contains the off-shell metric coefficients and their derivatives. We discuss conditions where the principle chiral anomaly current is regular at the horizon and the axes of symmetry. We demonstrate that for states where the current vanishes at the past horizon and at the past null infinity, there exist chirality fluxes at both the future horizon and future infinity. The latter is directly related to the polarization asymmetry of Hawking radiation for massless spinning particles. We also calculate the Chern-Simons currents for both gravitational and electromagnetic chiral anomalies in the black hole spacetime, and discuss the properties of the chirality fluxes associated with these currents.

Predictive Modeling for Early Hyperglycemia Detection in Type 2 Diabetes

Type 2 Diabetes (T2D) is characterized by a combination of defects in insulin action and impairment in insulin secretion. Deficient insulin action causes people with Type 2 Diabetes to have difficulty controlling their blood glucose concentration (BGC) and experience periods of high (hyperglycemia) and low (hypoglycemia) BGC. Continuous glocuse monitoring (CGM) sensors and machine learning algorithms can automate the process of meal size estimation, improve the accuracy of the carbohydrate estimations, and reduce the involvement of the subject. The aim of this project was to use dynamic Partial Least Squares (PLS) regression to model blood glucose data from CGM devices and optimize the model parameters for best accuracy of the predictive modelling. The parameters were optimized by explicit enumeration and grid search approach to minimize the mean square error (MSE), and the lowest MSE was obtained with the number of latent variables as 5 and past horizon as 5 (25 minutes). Future research will develop the logic inference using the first- and second-order derivatives of the predicition curve that will sound the alarms based on the predicitions made in the current work.

The Unruh state for massless fermions on Kerr spacetime and its Hadamard property

We give a rigorous definition of the Unruh state in the setting of massless Dirac fields on slowly rotating Kerr spacetimes. In the black hole exterior region, we show that it is asymptotically thermal at Hawking temperature on the past event horizon. Furthermore, we demonstrate that in the union of the exterior and interior regions, the Unruh state is pure and Hadamard. The main ingredients are the Hafner-Nicolas scattering theory, new microlocal estimates for characteristic Cauchy problems and criteria on the level of square-integrable solutions.

Language about the future on social media as a novel marker of anxiety and depression: A big-data and experimental analysis.

Anxiety and depression negatively impact many. Studies suggest depression is associated with future time horizons, or how "far" into the future people tend to think, and anxiety is associated with temporal discounting, or how much people devalue future rewards. Separate studies from linguistics and economics have shown that how people refer to future time predicts temporal discounting. Yet no one-that we know of-has investigated whether future time reference habits are a marker of anxiety and/or depression. We introduce the FTR classifier, a novel classification system researchers can use to analyse linguistic temporal reference. In Study 1, we used the FTR classifier to analyse data from the social-media website Reddit. Users who had previously posted popular contributions to forums about anxiety and depression referenced the future and past more often than controls, had more proximal future and past time horizons, and significantly differed in their linguistic future time reference patterns: They used fewer future tense constructions (e.g. will), fewer high-certainty constructions (certainly), more low-certainty constructions (could), more bouletic modal constructions (hope), and more deontic modal constructions (must). This motivated Study 2, a survey-based mediation analysis. Self-reported anxious participants represented future events as more temporally distal and therefore temporally discounted to a greater degree. The same was not true of depression. We conclude that methods which combine big-data with experimental paradigms can help identify novel markers of mental illness, which can aid in the development of new therapies and diagnostic criteria.

Tuning of subspace predictive controls

Data-driven predictive control has recently gained increasing attention, as it makes it possible to design constrained controls directly from a set of data, without requiring an intermediate identification step. In this paper, we focus on a Subspace Predictive Control (SPC) scheme, with the aim of clarifying the sensitivity of the final closed-loop performance to its main hyperparameters, namely the length of the past horizon and the regularization penalties. Moreover, by delving deep into the structural properties of the control problem formulation, we provide a set of guidelines for the choice of such hyperparameters. The effectiveness of the resulting overall tuning strategy is assessed on two benchmark examples.

White hole cosmology and Hawking radiation from quantum cosmological perturbations

The spacetime inside the white hole is like an anisotropic cosmological background with the past singularity playing the role of a big bang singularity. The scale factor along the extended spatial direction is contracting while the scale factor along the two-sphere is expanding. We consider an eternal Schwarzschild manifold and study quantum cosmological perturbations generated near the white hole singularity which propagate towards the past event horizon and to the exterior of the black hole. It is shown that an observer deep inside the white hole and an observer far outside the black hole both share the same vacuum. We calculate the Hawking radiation associated to these quantum white hole perturbations as measured by an observer in the exterior of the black hole. Furthermore, we also consider the Hawking radiation for the general case where the initial cosmological perturbations deep inside the white hole are in a ``nonvacuum'' state yielding to a deviation from Planck distribution. This analysis suggests that if the black hole is not entirely black (due to Hawking radiation) then the white hole is not entirely white either.

Rindler bulk reconstruction and subregion duality in AdS/CFT

In this paper, we study the AdS-Rindler reconstruction. The CFT operators naively given by the holographic dictionary for the AdS-Rindler reconstruction contain tachyonic modes, which are inconsistent with the causality and unitarity of the CFT. Therefore, the subregion duality and the entanglement wedge reconstruction do not hold. We also find that the tachyonic modes in the AdS-Rindler patch lead to arbitrary high-energy or trans-Planckian modes in the global AdS. It means that the mode expansion of the Rindler patch is sensitive to the UV limit of the theory, that is, quantum gravity. In addition, the tachyonic modes are related to the existence of null geodesics connecting the past and future horizons.

No Page curves for the de Sitter horizon

We investigate the fine-grained entropy of the de Sitter cosmological horizon. Starting from three-dimensional pure de Sitter space, we consider a partial reduction approach, which supplies an auxiliary system acting as a heat bath both at mathcal{I} + and inside the static patch. This allows us to study the time-dependent entropy of radiation collected for both observers in the out-of-equilibrium Unruh-de Sitter state, analogous to black hole evaporation for a cosmological horizon. Central to our analysis in the static patch is the identification of a weakly gravitating region close to the past cosmological horizon; this is suggestive of a relation between observables at future infinity and inside the static patch. We find that in principle, while the meta-observer at mathcal{I} + naturally observes a pure state, the static patch observer requires the use of the island formula to reproduce a unitary Page curve. However, in practice, catastrophic backreaction occurs at the Page time, and neither observer will see unitary evaporation.

Continuity and Change in Political Culture: Israel and Beyond edited

How are political meanings created? How are they maintained and changed? How do they shape political realities? This book addresses these important yet often neglected questions through the themes of continuity and change in conflict and peace, challenges to democracy, and national memory. As a tribute to the scholarship of Myron J. Aronoff, the contributors of the 10 chapters that make up the book offer nuanced analyses of the political culture in Israel, Palestine, the United States, the Basque Autonomous Region of Spain, and Poland. The topics of the chapters range from political science to literature and visual arts. As its title suggests, Continuity and Change weaves the various topics, case studies, and perspectives together through an underlying temporal motif. Interestingly, the book starts with the future horizon, as Yael S. Aronoff discusses possible solutions to the Israeli-Palestinian conflict. The second chapter, by Saliba Sarsar, adds the past horizon, analyzing the political implications of the historical memories of the Holocaust and Al-Nakba. It invites readers to engage with the past in order to rethink a collective identity that does not exclude the Other. The next two chapters, by Nadav G. Shelef and Yossi Beilin, discuss two pathways (and their limitations) to bridge the past and the present horizons: denationalization and trust building.

On the duality of Schwarzschild–de Sitter spacetime and moving mirror

The Schwarzschild–de Sitter (SdS) metric is the simplest spacetime solution in general relativity with both a black hole event horizon and a cosmological event horizon. Since the Schwarzschild metric is the most simple solution of Einstein’s equations with spherical symmetry and the de Sitter metric is the most simple solution of Einstein’s equations with a positive cosmological constant, the combination in the SdS metric defines an appropriate background geometry for semi-classical investigation of Hawking radiation with respect to past and future horizons. Generally, the black hole temperature is larger than that of the cosmological horizon, so there is heat flow from the smaller black hole horizon to the larger cosmological horizon, despite questions concerning the definition of the relative temperature of the black hole without a measurement by an observer sitting in an asymptotically flat spacetime. Here we investigate the accelerating boundary correspondence of the radiation in SdS spacetime without such a problem. We have solved for the boundary dynamics, energy flux and asymptotic particle spectrum. The distribution of particles is globally non-thermal while asymptotically the radiation reaches equilibrium.

Horizons and correlation functions in 2D Schwarzschild-de Sitter spacetime

Two-dimensional Schwarzschild-de Sitter is a convenient spacetime in which to study the effects of horizons on quantum fields since the spacetime contains two horizons, and the wave equation for a massless minimally coupled scalar field can be solved exactly. The two-point correlation function of a massless scalar is computed in the Unruh state. It is found that the field correlations grow linearly in terms of a particular time coordinate that is good in the future development of the past horizons, and that the rate of growth is equal to the sum of the black hole plus cosmological surface gravities. This time dependence results from additive contributions of each horizon component of the past Cauchy surface that is used to define the state. The state becomes the Bunch-Davies vacuum in the cosmological far field limit. The two point function for the field velocities is also analyzed and a peak is found when one point is between the black hole and cosmological horizons and one point is outside the future cosmological horizon.

Purpose in Life: A Reconceptualization for Very Late Life

Across disciplines, we have long sought to understand the factors that contribute to purpose in life. Theorists have posited that having life goals, feeling productive, and remaining active are essential contributing elements to purpose in life (Crumbaugh & Maholick, 1969; Rowe & Kahn, 1997; Ryff, 1989). While these factors can undoubtedly contribute to purpose in life, they may not fully explain purpose in life for older adults in very late life (85 years old and older) who have long past and short future time horizons. In this presentation, we explore the concept of purpose in life for older adults in very late life and how current measures may not fully or accurately apply to this group. We examine the two most commonly used measures of purpose in life, the Purpose in Life Test (Crumbaugh & Maholick, 1964, 1969) and the Ryff Purpose Subscale (Ryff, 1989; Ryff & Keyes, 1995), and identify specific items that should be reconsidered for use with older adults in very late life. We then reconceptualize purpose in life for the oldest old based on several foundational theories, including Socioemotional Selectivity Theory, the Theory of Gerotranscendence, and Terror Management Theory. Stemming from this analysis, we posit that purpose in life in very life consists of three domains – the very long past, the very near future, and the transcendental post-mortem. Based upon this reconceptualization, we recommend the development of new measures of purpose of life in very late life that capture these three domains.

Static and radiating dyonic black holes coupled to conformally invariant electrodynamics in higher dimensions

We investigate the complete family of (aligned) Robinson-Trautman spacetimes sourced by conformally invariant non-linear electrodynamics in $D$ dimensions in the presence of an arbitrary cosmological constant. After presenting general features of the solutions (which exist only in even dimensions), we discuss in more detail some particular subclasses. Static metrics contain dyonic black holes with various possible horizon geometries (K\"ahler if there is a magnetic field, including flat branes) and different asymptotics. In addition, there exist also time-dependent solutions (not possible in the $D>4$ linear theory) which may represent white hole evaporation by emission of electromagnetic radiation (or a time-reversed picture of black hole formation). For those, we comment on a quasi-local characterization of possible past horizons. Finally, we briefly discuss the special case of stealth solutions. In an appendix, a theory-independent result on the redundancy of the gravity part of the field equations for Robinson-Trautman spacetimes is further obtained.

Quantum field theory with boundary conditions at the horizons

A procedure to derive a unitary evolution law for a quantised black hole has been proposed by the author. The proposal implies several assumptions, which seem almost unavoidable to this author. We start off with the question how to describe the energy eigenstates of a black hole. The background metric required for this cannot be the Vaidya metric let alone the metric proposed by Hawking, who included the effect of the final evaporation of the black hole. This however leads to the formation if firewalls at both the future and the past event horizon, unless one anticipates the effects that the firewalls have. These effects can be handled as new boundary conditions at the horizons, describing the flow of the participating particles. It is subsequently explained how these boundary conditions must involve the antipodes of the outside world. Imposing unitarity and continuity then automatically leads to a unique, unitary evolution operator. We exhibit the resulting, quite coherent picture.

Gravitational-wave echoes from spinning exotic compact objects: Numerical waveforms from the Teukolsky equation

We present numerical waveforms of gravitational-wave echoes from spinning exotic compact objects (ECOs) that result from binary black hole coalescence. We obtain these echoes by solving the Teukolsky equation for the ${\ensuremath{\psi}}_{4}$ associated with gravitational waves that propagate toward the horizon of a Kerr spacetime, and process the subsequent reflections of the horizon-going wave by the surface of the ECO, which lies right above the Kerr horizon. The trajectories of the infalling objects are modified from Kerr geodesics, such that the gravitational waves propagating toward future null infinity match those from merging black holes with comparable masses. In this way, the corresponding echoes can be used to approximate to those from nonspinning comparable-mass mergers. For boundary conditions at the ECO surface, we adopt recent work using the membrane paradigm, which relates ${\ensuremath{\psi}}_{0}$ associated with the horizon-going wave and ${\ensuremath{\psi}}_{4}$ of the wave that leaves the ECO surface. We obtain ${\ensuremath{\psi}}_{0}$ of the horizon-going wave from ${\ensuremath{\psi}}_{4}$ using the Teukolsky-Starobinsky relation. The echoes we obtain turn out to be significantly weaker than those from previous studies that generate echo waveforms by modeling the ringdown part of binary black hole coalescence waveforms as originating from the past horizon.