Compact stars with non-uniform relativistic polytrope.

This paper presents new relativistic composite polytropic models for compact stars by simultaneously solving Einstein field equations with the polytropic state equation to simulate the spherically symmetric, static matter distribution. Using a non-uniform polytropic index, we get the Tolman-Oppenheimer-Volkoff equation for the relativistic composite polytrope (CTOV). To analyze the star's structure, we numerically solve the CTOV equation and compute the Emden and mass functions for various relativistic parameters and polytropic indices appropriate for neutron stars. The calculation results show that, as the relativistic parameter approaches zero, we recover the well-known Lane-Emden equation from the Newtonian theory of polytropic stars; thus, testing the computational code by comparing composite Newtonian models to those in the literature yields good agreement. We compute composite relativistic models for the neutron star candidates Cen X-3, SAXJ1808.4-3658, and PSR J1614-22304. We compare the findings with various existing models in the literature. Based on the accepted models for PSR J1614-22304 and Cen X-3, the star's core radius is predicted to be between 50 and 60% percent of its total radius, while we found that the radius of the core of star SAXJ1808.4-3658 is around 30% of the total radius. Our findings show that the neutron star structure may be approximated by a composite relativistic polytrope, resulting in masses and radii that are quite consistent with observation.

On the relativity of magnitudes: Delboeuf's forgotten contribution to the 19th century problem of space.

Faced with the mathematical possibility of non-Euclidean geometries, 19th Century geometers were tasked with the problem of determining which among the possible geometries corresponds to that of our space. In this context, the contribution of the Belgian philosopher-mathematician, Joseph Delboeuf, has been unduly neglected. The aim of this essay is to situate Delboeuf's ideas within the context of the philosophies of geometry of his contemporaries, such as Helmholtz, Russell and Poincaré. We elucidate the central thesis, according to which Euclidean geometry is given special status on the basis of the relativity of magnitudes, we uncover its hidden history and show that it is defensible within the context of the philosophies of geometry of the epoch. Through this discussion, we also develop various ideas that have some relevance to present-day methods in gravitational physics and cosmology.

The Chemical Bond at the Bottom of the Periodic Table: The Case of the Heavy Astatine and the Super-Heavy Tennessine.

In this work, we study the chemical bond in molecules containing heavy and super-heavy elements according to the current state-of-the-art bonding models. An Energy Decomposition Analysis in combination with Natural Orbital for Chemical Valence (EDA-NOCV) within the relativistic four-component Dirac-Kohn-Sham (DKS) framework is employed, which allows to successfully include the spin-orbit coupling (SOC) effects on the chemical bond description. Simple halogen-bonded adducts ClX⋯L (X=At, Ts; L=NH3, Br-, H2O, CO) of astatine and tennessine have been selected to assess a trend on descending along a group, while modulating the ClX⋯L bond features through the different electronic nature of the ligand L. Interesting effects caused by SOC have been revealed: i) a huge increase of the ClTs dipole moment (which is almost twice as that of ClAt), ii) a lowering of the ClX⋯L bonding energy arising from different contributions to the ClX…L interaction energy strongly depending on the nature of L, iii) a quenching of one of the π back-donation components to the bond. In the ClTs(CO) adduct, the back-donation from ClTs to CO becomes the most important component. The analysis of the electronic structure of the ClX dimers allows for a clear interpretation of the SOC effects in these systems.

Eventive modal projection: the case of Spanish subjunctive relative clauses.

How do modal expressions determine which possibilities they range over? According to the Modal Anchor Hypothesis (Kratzer in The language-cognition interface: Actes du 19e congrès international des linguistes, Libraire Droz, Genève, 179-199, 2013), modal expressions determine their domain of quantification from particulars (events, situations, or individuals). This paper presents novel evidence for this hypothesis, focusing on a class of Spanish relative clauses that host verbs inflected in the subjunctive. Subjunctive in Romance is standardly taken to be licensed only in a subset of intensional contexts. However, in our relative clauses, subjunctive is exceptionally licensed in extensional contexts. At the same time, the interpretation of these relative clauses still involves modality, a type of modality that targets the goals of the agent of the main event. We argue that the pattern displayed by these relative clauses follows straightforwardly if subjunctive is associated with a modal operator that, like modal indefinites (Alonso-Ovalle and Menéndez-Benito in Journal of Semantics 35(1):1-41, 2017), can project its domain from a volitional event. Overall, our proposal supports the event-based analysis of mood (Kratzer in Evidential mood in attitude and speech reports. Talk delivered at the 1st Syncart Workshop, Siena, July 13, 2016; Portner and Rubinstein in Natural Language Semantics 28:343-393, 2020) and extends its application beyond attitudinal and modal complements.

(Re)Construction of Quantum Space-Time: Transcribing Hilbert into Configuration Space.

Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space, through which space-time becomes an epiphenomenon construed by internal observers.

Falling charge in a gravitational field and radiation reaction.

The Lorentz-Dirac equation is formulated and studied in flat Minkowski spacetime. A concise, novel derivation of the equation is presented. The problem is then enlarged to study radiation damping of an electron moving through a gravitational field. The equation of motion is obtained for this case as well. It is suggested the study of the problem might motivate experiments which could shed light on the recent work related to the emergence of space-time and its structure by means of quantum effects such as quantum entanglement.

From conformal infinity to equations of motion: conserved quantities in general relativity.

This paper describes conservation laws in general relativity (GR) dating back to the mass-energy conservation of Bondi and Sachs in the early 1960s but using 2-spinor techniques. The notion of conformal infinity is employed, and the highly original ideas of E. T. Newman are discussed in relation to twistor theory. The controversial NP constants are introduced, and their meaning is considered in a new light related to the problem of equations of motion in GR. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.

At the interface of asymptotics, conformal methods and analysis in general relativity.

This is an introductory article for the proceedings associated with the Royal Society Hooke discussion meeting of the same title which took place in London in May 2023. We review the history of Penrose's conformal compactification, null infinity and a number of related fundamental developments in mathematical general relativity from the last 60 years. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.

Calculation of asymptotic charges at the critical sets of null infinity.

The asymptotic structure of null and spatial infinities of asymptotically flat spacetimes plays an essential role in discussing gravitational radiation, gravitational memory effect, and conserved quantities in General Relativity (GR). Bondi, Metzner and Sachs (BMS) established that the asymptotic symmetry group for asymptotically simple spacetimes is the infinite-dimensional BMS group. Given that null infinity is divided into two sets: past null infinity [Formula: see text] and future null infinity [Formula: see text], one can identify two independent symmetry groups: [Formula: see text] at [Formula: see text] and [Formula: see text] at [Formula: see text]. Associated with these symmetries are the so-called BMS charges. A recent conjecture by Strominger suggests that the generators of [Formula: see text] and [Formula: see text] and their associated charges are related via an antipodal reflection map near spatial infinity. To verify this matching, an analysis of the gravitational field near spatial infinity is required. This task is complicated due to the singular nature of spatial infinity for spacetimes with non-vanishing ADM mass. Different frameworks have been introduced in the literature to address this singularity, e.g. Friedrich's cylinder, Ashtekar-Hansen's hyperboloid and Ashtekar-Romano's asymptote at spatial infinity. This paper reviews the role of Friedrich's formulation of spatial infinity in the investigation of the matching of the spin-2 charges on Minkowski spacetime and in the full GR setting. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.

Analytic and conformal scattering in general relativity.

This paper is about two important trends of scattering theory in general relativity: time-dependent spectral analytic scattering and conformal scattering. The former was initiated by Jonathan Dimock and Bernard Kay in the mid-1980s and is based on spectral and functional analysis. The latter was proposed by Roger Penrose in 1965 and then constructed for the first time by Gerard Friedlander in 1980 by putting together Penrose's conformal method and another analytic approach to scattering: the Lax-Phillips theory due to Peter Lax and Ralph Phillips. We shall review the history of the two approaches and explain their general principles. We shall also explore an important question: 'can the tools of one approach be used to obtain a complete construction in the other?' This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.

Balance laws as test of gravitational waveforms.

Gravitational waveforms play a crucial role in comparing observed signals with theoretical predictions. However, obtaining accurate analytical waveforms directly from general relativity (GR) remains challenging. Existing methods involve a complex blend of post-Newtonian theory, effective-one-body formalism, numerical relativity and interpolation, introducing systematic errors. As gravitational wave astronomy advances with new detectors, these errors gain significance, particularly when testing GR in the nonlinear regime. A recent development proposes a novel approach to address this issue. By deriving precise constraints-or balance laws-directly from full nonlinear GR, this method offers a means to evaluate waveform quality, detect template weaknesses and ensure internal consistency. Before delving into the intricacies of balance laws in full nonlinear GR, we illustrate the concept using a detailed mechanical analogy. We will examine a dissipative mechanical system as an example, demonstrating how mechanical balance laws can gauge the accuracy of approximate solutions in capturing the complete physical scenario. While mechanical balance laws are straightforward, deriving balance laws in electromagnetism and GR demands a rigorous foundation rooted in mathematically precise concepts of radiation. Following the analogy with electromagnetism, we derive balance laws in GR. As a proof of concept, we employ an analytical approximate waveform model, showcasing how these balance laws serve as a litmus test for the model's validity. This article is part of the theme issue 'The particle-gravity frontier'.

From Black Holes Entropy to Consciousness: The Dimensions of the Brain Connectome.

It has been shown that the theory of relativity can be applied physically to the functioning brain, so that the brain connectome should be considered as a four-dimensional spacetime entity curved by brain activity, just as gravity curves the four-dimensional spacetime of the physical world. Following the most recent developments in modern theoretical physics (black hole entropy, holographic principle, AdS/CFT duality), we conjecture that consciousness can naturally emerge from this four-dimensional brain connectome when a fifth dimension is considered, in the same way that gravity emerges from a 'flat' four-dimensional quantum world, without gravitation, present at the boundaries of a five-dimensional spacetime. This vision makes it possible to envisage quantitative signatures of consciousness based on the entropy of the connectome and the curvature of spacetime estimated from data obtained by fMRI in the resting state (nodal activity and functional connectivity) and constrained by the anatomical connectivity derived from diffusion tensor imaging.

Perspectives on the insidious nature of pain metaphor: we literally need to change our metaphors.

Metaphorical language is used to convey one thing as representative or symbolic of something else. Metaphor is used in figurative language but is much more than a means of delivering "poetic imagination". A metaphor is a conceptual tool for categorising, organizing, thinking about, and ultimately shaping reality. Thus, metaphor underpins the way humans think. Our viewpoint is that metaphorical thought and communication contribute to "painogenicity", the tendency of socio-ecological environments (settings) to promote the persistence of pain. In this perspectives article, we explore the insidious nature of metaphor used in pain language and conceptual models of pain. We explain how metaphor shapes mental organisation to govern the way humans perceive, navigate and gain insight into the nature of the world, i.e., creating experience. We explain how people use metaphors to "project" their private sensations, feelings, and thoughts onto objects and events in the external world. This helps people to understand their pain and promotes sharing of pain experience with others, including health care professionals. We explore the insidious nature of "warmongering" and damage-based metaphors in daily parlance and demonstrate how this is detrimental to health and wellbeing. We explore how metaphors shape the development and communication of complex, abstract ideas, theories, and models and how scientific understanding of pain is metaphorical in nature. We argue that overly simplistic neuro-mechanistic metaphors of pain contribute to fallacies and misnomers and an unhealthy focus on biomedical research, in the hope of developing medical interventions that "prevent pain transmission [sic]". We advocate reconfiguring pain language towards constructive metaphors that foster a salutogenic view of pain, focusing on health and well-being. We advocate reconfiguring metaphors to align with contemporary pain science, to encourage acceptance of non-medicalised strategies to aid health and well-being. We explore the role of enactive metaphors to facilitate reconfiguration. We conclude that being cognisant of the pervasive nature of metaphors will assist progress toward a more coherent conceptual understanding of pain and the use of healthier pain language. We hope our article catalyses debate and reflection.

Past Adversity Influencing Now (PAIN): perspectives on the impact of temporal language on the persistence of pain.

Persistent pain is a significant healthcare issue, often unresponsive to traditional treatments. We argue for incorporating non-biomedical perspectives in understanding pain, promoting more comprehensive solutions. This article explores how language, specifically time-related terms, may affect the persistence (stickiness) of pain. We delve into how language influences one's experience of the world, especially in understanding pain through spatial metaphors. Notably, time perceptions differ across languages and cultures and there is no absolute construct of temporal pain experience. In English, time is viewed linearly as past, present, and future. We introduce a framework called Past Adversity Influencing Now (PAIN) which includes various temporal phases of pain; Past Perfect, Past Imperfect, Present, Future Imperfect, and Future Perfect. We suggest that past negative memories (emotional memory images) can "trap" individuals in a "sticky" pain state. We speculate that the process of diagnosing pain as "chronic" may solidify this "stickiness", drawing from the ancient Greek idea of "logos", where pain communicates a message across time and space needing recognition. Our PAIN framework encourages examining pain through a temporal lens, guiding individuals towards a more positive future.

Application of the replication-transmission relativity theory in the development of multiscale models of infectious disease dynamics.

Despite the existence of a powerful theoretical foundation for the development of multiscale models of infectious disease dynamics in the form of the replication-transmission relativity theory, the majority of current modelling studies focus more on single-scale modelling. The explicit aim of this study is to change the current predominantly single-scale modelling landscape in the design of planning frameworks for the control, elimination and even eradication of infectious disease systems through the exploitation of multiscale modelling methods based on the application of the replication-transmission relativity theory. We first present a structured roadmap for the development of multiscale models of infectious disease systems. The roadmap is tested on hookworm infection. The testing of the feasibility of the roadmap established a fundamental result which can be generalized to confirm that the complexity of an infectious disease system is encapsulated with a level of organization spanning a microscale and a macroscale.

Uncovering a population of gravitational lens galaxies with magnified standard candle SN Zwicky.

Detecting gravitationally lensed supernovae is among the biggest challenges in astronomy. It involves a combination of two very rare phenomena: catching the transient signal of a stellar explosion in a distant galaxy and observing it through a nearly perfectly aligned foreground galaxy that deflects light towards the observer. Here we describe how high-cadence optical observations with the Zwicky Transient Facility, with its unparalleled large field of view, led to the detection of a multiply imaged type Ia supernova, SN Zwicky, also known as SN 2022qmx. Magnified nearly 25-fold, the system was found thanks to the standard candle nature of type Ia supernovae. High-spatial-resolution imaging with the Keck telescope resolved four images of the supernova with very small angular separation, corresponding to an Einstein radius of only θE = 0.167″ and almost identical arrival times. The small θE and faintness of the lensing galaxy are very unusual, highlighting the importance of supernovae to fully characterize the properties of galaxy-scale gravitational lenses, including the impact of galaxy substructures.

Quasi-Hyperbolically Symmetric γ-Metric.

We carry out a systematic study on the motion of test particles in the region inner to the naked singularity of a quasi-hyperbolically symmetric γ-metric. The geodesic equations are written and analyzed in detail. The obtained results are contrasted with the corresponding results obtained for the axially symmetric γ-metric and the hyperbolically symmetric black hole. As in this latter case, it is found that test particles experience a repulsive force within the horizon (naked singularity), which prevents them from reaching the center. However, in the present case, this behavior is affected by the parameter γ which measures the departure from the hyperbolical symmetry. These results are obtained for radially moving particles as well as for particles moving in the θ-r subspace. The possible relevance of these results in the explanation of extragalactic jets is revealed.

On truth and polarity in negation processing: language-specific effects in non-linguistic contexts.

Introduction: This study examines how negation is processed in a nonverbal context (e.g., when assessing ▲ ≠ ▲) by speakers of a truth-based system like Mandarin and a polarity-based system like English. In a truth-based system, negation may take longer to process because it is typically attached to the negation as a whole (it is not true that triangle does not equal triangle), whereas in polarity-based systems, negation is processed relatively faster because it is attached to just the equation symbol (triangle does not equal triangle), which is processed relatively faster. Our hypothesis was that negation processing routines previously observed for verbal contexts, namely that speakers of Mandarin get slowed down more when processing negative stimuli than positive stimuli compared to speakers of English, also extend to contexts when language use is not obligatory. Methods: To test this, we asked participants to agree/disagree with equations comprising simple shapes and positive '=' or negative '≠' equation symbols. English speakers showed a response-time advantage over Mandarin speakers in negation conditions. In a separate experiment, we also tested the contribution of equation symbols '≠'/'=' to the cognitive demands by asking participants to judge shape sameness in symbol-free trials, such as ▲ ■. This comparison allowed us to test whether crosslinguistic differences arise not because of shape congruence judgement but arguably due to negation attachment. Results and discussion: The effect of the '≠' symbol on shape congruence was language-specific, speeding up English speakers but slowing down Mandarin speakers when the two shapes differed. These findings suggest language-specific processing of negation in negative equations, interpreted as novel support for linguistic relativity.

Advancing physiology education by understanding the multiple dimensions of homeostasis.

Homeostasis of the internal environment has been considered the central organizing concept of physiology. However, current definitions of it in textbooks and online teaching sources do not sufficiently reflect how homeostasis serves its central unifying role. Meanwhile, scientific understanding of the functions of the body's structures at multiple levels (molecular, cell, tissue, organ, organ system, and organism) has advanced significantly, but the understanding of homeostasis is still in the same place. In this article, the author describes some issues and insufficiencies in teaching about homeostasis in physiology education and proposes that homeostasis needs to be understood in terms of four dimensions rather than a simple definition: internal, functional organization; functional manifestation; mechanism; and effect or consequence. Each dimension has two subdimensions or sides. Throughout the elucidation of these dimensions and subdimensions, the original meaning of homeostasis is reinforced, what is lost in current understanding of homeostasis becomes clear, some insufficiencies mentioned above are supplemented, new insights into homeostasis develop, and how the four dimensions of homeostasis can be applied to physiology education is exampled. This new, comprehensive conceptualization advances the understanding of homeostasis and can facilitate teaching and learning about homeostasis and physiology.