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The Laser Interferometer Space Antenna (LISA) mission, scheduled for launch in the mid-2030s, is a gravitational wave space observatory designed to detect sources emitting in the millihertz band. LISA is an European Space Agency flagship mission, currently entering the Phase-B development phase. It is expected to help us improve our understanding of our Universe by measuring gravitational wave sources of different types, with some of the sources being at very high redshifts (z ∼ 2 0). On February 23, 2022, we organized the first LISA in Greece Workshop. This Workshop aimed to inform the Greek scientific and tech industry communities about the possibilities of participating in LISA science and the LISA mission, with the support of the Hellenic Space Center. In this White Paper, we summarize the outcomes of the Workshop, the most important aspect of it being the inclusion of 1 5 Greek researchers to the LISA Consortium, raising our total number to 2 2. At the same time, we present a road map with the future steps and actions of the Greek Gravitational Wave community with respect to the LISA mission. [ABSTRACT FROM AUTHOR]

The document is a response to a paper by Gruber, Block, and Montemayor (GBM) on the topic of time. The author admires GBM's inventive experiments but raises concerns about the philosophical foundations of their ideas. They discuss the use of James Hartle's IGUS model to incorporate subjective experience of time within a 4D Minkowski spacetime framework. The author suggests that thinking in terms of second-order cybernetics and considering a wider range of features could help address the problem GBM is discussing. They also question the assumption that our theories of physics and cosmology can provide a straightforward temporal worldview. The author proposes a dual-aspect monist view, where both subjective and objective time arise from a deeper structure. They believe that the resolution to GBM's problem lies in this deeper domain. [Extracted from the article]

In his groundbreaking 1905 paper on special relativity, Einstein distinguished between local and global time in inertial systems, introducing his famous definition of distant simultaneity to give physical content to the notion of global time. Over the following decade, Einstein attempted to generalize this analysis of relativistic time to include accelerated frames of reference, which, according to the principle of equivalence, should also account for time in the presence of gravity. Characteristically, Einstein's methodology during this period focused on simple, intuitively accessible physical situations, exhibiting a high degree of symmetry. However, in the final general theory of relativity, the a priori existence of such global symmetries cannot be assumed. Despite this, Einstein repeated some of his early reasoning patterns even in his 1916 review paper on general relativity and in later writings. Modern commentators have criticized these arguments as confused, invalid, and inconsistent. Here, we defend Einstein in the specific context of his use of global time and his derivations of the gravitational redshift formula. We argue that a detailed examination of Einstein's early work clarifies his later reasoning and demonstrates its consistency and validity. [ABSTRACT FROM AUTHOR]

It is commonly accepted that superluminal travel may be used to facilitate time travel. This is a purely special-relativistic argument, using the fact that for observers in two frames of reference, separated by a spacelike interval, the non-causal (spacelike) future of one observer includes part of the causal past of the other. In this paper we provide a concrete realization of this argument in a curved general-relativistic spacetime, using warp drives as the means of faster-than-light travel. By generalizing the usual warp drive metric to allow for a non-unit lapse function, we allow the warp drive to switch between reference frames in a purely geometric way. With an additional modification allowing the warp drive to have compact support, this permits us to glue two warp drives together to construct a closed timelike geodesic, such that a test particle following the geodesics of the two warp drives travels back to its own past. This provides a precise mathematical model for the connection between faster-than-light travel and time travel in general relativity, and the first such model to be explicitly formulated using two warp drives. We also give a detailed discussion of weak energy condition violations in the non-unit-lapse warp drive. [ABSTRACT FROM AUTHOR]

Gravitational memory effects are predictions of general relativity that are characterized by an observable effect that persists after the passage of gravitational waves. In recent years, they have garnered particular interest, both due to their connection to asymptotic symmetries and soft theorems and because their observation would serve as a unique test of the nonlinear nature of general relativity. Apart from the more commonly known displacement and spin memories, however, there are other memory effects predicted by Einstein's equations that are associated with more subleading terms in the asymptotic expansion of the Bondi-Sachs metric. In this paper, we write explicit expressions for these higher memory effects in terms of their charge and flux contributions. Further, by using a numerical relativity simulation of a binary black hole merger, we compute the magnitude and morphology of these terms and compare them to those of the displacement and spin memory. We find that, although these terms are interesting from a theoretical perspective, due to their small magnitude they will be particularly challenging to observe with current and future detectors. [ABSTRACT FROM AUTHOR]

This document contains commentaries on two papers that examine the concept of time from different angles. The first paper argues against the Block Universe theory, which suggests a static reality, and proposes a multilayered concept of time instead. The second paper takes a pragmatic approach and suggests that the brain reflects the temporal parameters of its external environment. The commentaries raise questions about the nature of reality, the validity of physical theories, and the perception of time. The text explores different perspectives on the flow of time, including the idea that it is a perceptual construct and the belief that consciousness and time are interconnected. It also discusses the arrow of time, entropy, and different interpretations of the IGUS model. The authors suggest three areas for further exploration: clarifying definitions, recognizing the desire to attribute reality to subjective experiences, and incorporating falsifiability into the debate. [Extracted from the article]

A recent JRASC paper (Brissenden 2020) demonstrated that a kinematic doppler interpretation of cosmological redshift can match Type 1a supernova measurements without expanding space or dark energy. Tis result is reviewed, and the omission of gravitational redshift, implications for general relativity, and the relevance of Milne cosmology are discussed. A new cosmological model is described where radius r replaces coordinate time-based ct. With this model, expansion of the Universe is associated with a kinematic increase in radius, and not the Friedmann-Robertson-Walker expanding space scale factor, a(t). A new metric tensor is proposed, to replace the FRW metric of standard cosmological theory. [ABSTRACT FROM AUTHOR]

Gravitational waves are being shown to derive directly from Newtonian dynamics for a continuous mass distribution, e.g. compressible fluids or equivalent. It is shown that the equations governing a continuous mass distribution, i.e. the inviscid Navier–Stokes equations for a general variable gravitational field g(t,x) , are equivalent to a form identical to the Maxwell equations from electromagnetism, subject to a specified condition. The consequence of this equivalence is the creation of gravity waves that propagate at a finite speed. The latter implies that Newtonian gravitation as presented in this paper is not 'spooky action at a distance' but rather is similar to electromagnetic waves propagating at finite speed, despite the apparent form appearing in the integrated field formula. In addition, this proves that, in analogy to the Maxwell equations, the Newtonian gravitation equations are Lorentz invariant for waves propagating at the speed of light. Since gravitational waves were so far derived only from Einstein's general relativity theory, it becomes appealing to check if there is a connection between the Newtonian waves presented in this paper and the general relativity type of waves at least in a certain limit of overlapping validity, i.e. as a flat-space approximation. The latter is left for follow-up research. [ABSTRACT FROM AUTHOR]

This document is an editorial for a special issue of the journal AIMS Mathematics on "Mathematical Coding Theory and its Applications." The issue includes 8 papers that explore various aspects of coding theory, which involves techniques from commutative algebra, discrete mathematics, and the geometry of numbers. The papers cover topics such as codes over rings (including non-commutative and non-unitary rings), codes for alternative metrics, and codes as ideals in special rings. The issue also includes papers on codes over fields, including finite fields and number fields. The guest editor for the special issue is Professor Patrick Solé from the University of Aix-Marseille in France. [Extracted from the article]

Disk galaxies have a typical dimension of a few tens of kiloparsecs. It follows from the theory of general relativity that any signal originating from the galactic center will be noticed at the outskirts of the galaxy only tens of thousands of years later. This retardation effect, however, is absent in modelling used to calculate rotation curves throughout entire galaxies and their external gas. The considerable differences between Newtonian predictions and observed velocities are currently removed either by assuming dark matter or by suggesting various modifications to the laws of gravity, MOND being a long standing alternative to Newtonian gravity. In previous papers we have shown that by applying general relativity in a rigorous fashion, without neglecting retardation, one can explain the rotational velocities of galactic matter without modifying gravity or adding dark matter. Moreover, it was shown that dark matter effects, as they appear in gravitational lensing, the Tully-Fisher relation, and mass estimations based on the virial theorem could also be explained as retarded-gravity effects. It must be noted, however, that the proposed theory relies on the existence of a mass flow (of a changing rate) into the galaxy; a requirement that was not directly observed. In the original paper on the subject only one galaxy (M33) was analysed in detail. This was later amended with a published study of eleven galaxies. Here we give a more comprehensive retardation analysis of 143 galaxies of different types from the SPARC Galaxy collection. We show that in most cases we obtain very accurate fits to the data. [ABSTRACT FROM AUTHOR]

This paper is the fourth in a series dedicated to the mathematically rigorous asymptotic analysis of gravitational radiation under astrophysically realistic set-ups. It provides an overview of the physical ideas involved in setting up the mathematical problem, the mathematical challenges that need to be overcome once the problem is posed, as well as the main new results we will obtain in upcoming work. From the physical perspective, this includes a discussion of how post-Newtonian theory provides a prediction on the gravitational radiation emitted by N infalling masses from the infinite past in the intermediate zone, i.e. up to some finite advanced time. From the mathematical perspective, we then take this prediction, together with the condition that there be no incoming radiation from I− , as a starting point to set up a scattering problem for the linearized Einstein vacuum equations around Schwarzschild and near spacelike infinity, and we outline how to solve this scattering problem and obtain the asymptotic properties of the scattering solution near i0 and I+. The full mathematical details will be presented in the sequel to this paper. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'. [ABSTRACT FROM AUTHOR]

The general theory of relativity predicts the relativistic effect in the orbital motions of S-stars which are orbiting around our Milky-way Galactic Center. The post-Newtonian or higher-order approximated Schwarzschild black hole models have been used by GRAVITY and UCLA Galactic Center groups to carefully investigate the S2 star's periastron precession. In this paper, we investigate the scalar field effect on the orbital dynamics of S2 star. Hence, we consider a spacetime, namely Janis-Newman-Winicour (JNW) spacetime which is seeded by a minimally coupled, mass-less scalar field. The novel feature of this spacetime is that one can retain the Schwarzschild spacetime from JNW spacetime considering zero scalar charge. We constrain the scalar charge of JNW spacetime by best fitting the astrometric data of S2 star using the Monte-Carlo–Markov-Chain (MCMC) technique assuming the charge to be positive. Our best-fitted result implies that similar to the Schwarzschild black hole spacetime, the JNW naked singularity spacetime with an appropriate scalar charge also offers a satisfactory fitting to the observed data for S2 star. Therefore, the JNW naked singularity could be a contender for explaining the nature of Sgr A* through the orbital motions of the S2 star. [ABSTRACT FROM AUTHOR]

The firewall transformation put forward by 't Hooft in recent years has made ambitious claims of solving the firewall problem and the black hole information paradox while maintaining unitary evolution. However, the theory has received limited attention from the community, especially in regards to its foundations in purely classical gravitational physics. This paper investigates the underlying assumptions of 't Hooft's firewall transformation before quantization. We find that the limiting procedure used by 't Hooft in order to obtain an identification of the quantum operators for ingoing and outgoing particles near a black hole is not consistent. We propose a correction, which involves a more relaxed approximation regime. In the new approximation regime, we find a new classical analog for the firewall transformation for spherical shells, which allows evolving the spherical shells' dynamics past their point of collision. In the classical theory, no firewall is removed, as both ingoing and outgoing matter is present on every spacelike hypersurface, and it does not appear that any firewalls will be removed after a canonical quantization. [ABSTRACT FROM AUTHOR]

Aggregative moral theories face a series of devastating problems when we apply them in a physically realistic setting. According to current physics, our universe is likely infinitely large, and will contain infinitely many morally valuable events. But standard aggregative theories are ill-equipped to compare outcomes containing infinite total value. So, applied in a realistic setting, they cannot compare any outcomes a real-world agent must ever choose between. This problem has been discussed extensively, and non-standard aggregative theories proposed to overcome it. This paper addresses a further problem of similar severity. Physics tells us that, in our universe, how remotely in time an event occurs is relative. But our most promising aggregative theories, designed to compare outcomes containing infinitely many valuable events, are sensitive to how remote in time those events are. As I show, the evaluations of those theories are then relative too. But this is absurd; evaluations of outcomes must be absolute! So we must reject such theories. Is this objection fatal for all aggregative theories, at least in a relativistic universe like ours? I demonstrate here that, by further modifying these theories to fit with the physics, we can overcome it. [ABSTRACT FROM AUTHOR]

The limited velocity in a geometry of Lorentzian signature seem to prevent the universe to reach thermodynamic equilibrium as suggested by the cosmic microwave background. Thus it was suggested that the universe which was initially minuscule has reached a more considerable radius in a short duration by a process known as cosmic inflation. However, to drive such a process have led to the suggestion of an ad-hoc scalar field the inflaton, which has no purpose in nature other than driving the cosmic inflation field and then stopping it once the universe reached the right size. In a recent paper it was shown that rapid expansion can occur without postulating an inflation by following Hawking's suggestion and assuming that primordially the metric of the universe had an Euclidean signature, in which case velocity is not limited and thermalization and rapid expansion are derived without the need to assume an ad-hoc field. However, while in the previous work emphasis was put on the dynamics and physical statistics of the particles in a Euclidean space versus Lorentzian space in which both spaces were given. No mathematical model was given regarding the development of current Lorentzian space-time from the early Euclidean space-time, and how fundamental problems such as the space-time singularity and the homogeneity of the CMB can be solved in the hybrid Euclidean–Lorentzian picture. This lacuna is to be rectified in this paper. [ABSTRACT FROM AUTHOR]

Our aim in this paper is two-fold. We establish a novel geometric characterization of the Robertson–Walker (RW) spacetime and, along the process, we find a canonical form of the RW metric associated to an arbitrary timelike curve and an arbitrary space frame. A known characterization establishes that a spacetime foliated by constant curvature leaves whose orthogonal flow (the cosmological flow) is geodesic, shear-free, and with constant expansion on each leaf, is RW. We generalize this characterization by relaxing the condition on the expansion. We show it suffices to demand that the spatial gradient and Laplacian of the cosmological expansion on a single arbitrary timelike curve vanish. In General Relativity these local conditions are equivalent to demanding that the energy flux measured by the cosmological flow, as well as its divergence, are zero on a single arbitrary timelike curve. The proof allows us to construct canonically adapted coordinates to the arbitrary curve, thus well-fitted to an observer with an arbitrary motion with respect to the cosmological flow. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the existence of Ricci solitons and the nature of curvature inheritance as well as collineations on the Robinson–Trautman (briefly, RT) spacetime. It is shown that under certain conditions RT spacetime admits almost-Ricci soliton, almost- η -Ricci soliton, almost-gradient η -Ricci soliton. As a generalization of curvature inheritance [K. L. Duggal, Curvature inheritance symmetry in Riemannian spaces with applications to fluid space times, J. Math. Phys. 33(9) (1992) 2989–2997] and curvature collineation [G. H. Katzin, J. Livine and W. R. Davis, Curvature collineations: A fundamental symmetry property of the space-times of general relativity defined by the vanishing Lie derivative of the Riemann curvature tensor, J. Math. Phys. 10(4) (1969) 617–629], in this paper, we introduce the notion of generalized curvature inheritance and examine if RT spacetime admits such a notion. It is shown that RT spacetime also realizes the generalized curvature (resp., Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) inheritance. Finally, several conditions are obtained, under which RT spacetime possesses curvature (resp., Ricci, conharmonic, Weyl projective) inheritance as well as curvature (resp., Ricci, Weyl conformal, concircular, conharmonic, Weyl projective) collineation, and we have also introduced the concept of generalized Lie inheritance and showed that RT spacetime realizes such a notion. [ABSTRACT FROM AUTHOR]

The spin-torsion theory is a gauge theory approach to gravity that expands upon Einstein's general relativity (GR) by incorporating the spin of microparticles. In this study, we further develop the spin-torsion theory to examine spherically symmetric and static gravitational systems that involve free-falling macroscopic particles. We posit that the quantum spin of macroscopic matter becomes noteworthy at cosmic scales. We further assume that the Dirac spinor and Dirac equation adequately capture all essential physical characteristics of the particles and their associated processes. A crucial aspect of our approach involves substituting the constant mass in the Dirac equation with a scale function, allowing us to establish a connection between quantum effects and the scale of gravitational systems. This mechanism ensures that the quantum effect of macroscopic matter is scale-dependent and diminishes locally, a phenomenon not observed in microparticles. For any given matter density distribution, our theory predicts an additional quantum term, the quantum potential energy (QPE), within the mass expression. The QPE induces time dilation and distance contraction, and thus mimics a gravitational well. When applied to cosmology, our theory yields a static cosmological model. The QPE serves as a counterpart to the cosmological constant introduced by Einstein to balance gravity in his static cosmological model. The QPE also offers a plausible explanation for the origin of Hubble redshift (traditionally attributed to the universe's expansion). The predicted luminosity distance–redshift relation aligns remarkably well with SNe Ia data from the cosmological sample of SNe Ia. In the context of galaxies, the QPE functions as the equivalent of dark matter. The predicted circular velocities align well with rotation curve data from the SPARC (Spitzer Photometry and Accurate Rotation Curves database) sample. Importantly, our conclusions in this paper are reached through a conventional approach, with the sole assumption of the quantum effects of macroscopic matter at large scales, without the need for additional modifications or assumptions. [ABSTRACT FROM AUTHOR]

Since the development of Brans–Dicke gravity, it has become well-known that a conformal transformation of the metric can reformulate this theory, transferring the coupling of the scalar field from the Ricci scalar to the matter sector. Specifically, in this new frame, known as the Einstein frame, Brans–Dicke gravity is reformulated as General Relativity supplemented by an additional scalar field. In 1959, Hans Adolf Buchdahl utilized an elegant technique to derive a set of solutions for the vacuum field equations within this gravitational framework. In this paper, we extend Buchdahl's method to incorporate the cosmological constant and to the scalar-tensor cases beyond the Brans–Dicke archetypal theory, thereby, with a conformal transformation of the metric, obtaining solutions for a version of Brans–Dicke theory that includes a quadratic potential. More specifically, we obtain synchronous solutions in the following contexts: in scalar-tensor gravity with massless scalar fields, Brans–Dicke theory with a quadratic potential, where we obtain specific synchronous metrics to the Schwarzschild–de Sitter metric, the Nariai solution, and a hyperbolically foliated solution. [ABSTRACT FROM AUTHOR]

In a recent series of papers new exact analytical interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. A fluid with an axially directed pressure has been first considered, then a perfect fluid, followed by a fluid with an azimuthally directed pressure, and, finally, by a fluid where the pressure is radially oriented. The perfect fluid configuration has subsequently been extended to the case of differential rotation. In the present paper, three different cases of anisotropic pressure analogous to those studied for rigidly rotating motion are considered in turn for differentially rotating fluids. General methods for generating mathematical solutions to the field equations and physically well-behaved examples are displayed for the axial and azimuthal pressure cases. As regards radial pressure fluids, four classes of solutions naturally emerge from the corresponding Einstein's equations, among which one class, after being fully integrated, exhibits physically well-behaved solutions. [ABSTRACT FROM AUTHOR]

Einsteinian cubic gravity (ECG) is the most general theory up to cubic order in curvature, which has the same graviton spectrum as the Einstein theory. In this paper, we investigate the geodesic motions of timelike particles around the four dimensional asymptotically flat black holes in ECG, and discuss their potential applications when connecting them with recent observational results. We first explore the effects of the cubic couplings on the marginally bound orbits (MBO), innermost stable circular orbits (ISCO) and on the periodic orbits around the Einsteinian cubic black hole. We find that comparing to Schwarzschild black hole in general relativity, the cubic coupling enhances the energy as well as the angular momentum for all the bound orbits of the particles. Then, we derive the relativistic periastron precessions of the particles and give a preliminary bound on the cubic coupling employing the observational result of the S2 star's pericenter precession in SgrA*. Finally, after calculating the periodic orbits' configurations, we preliminarily evaluate the gravitational waveform radiated from several periodic orbits in one complete period of a test object which orbits a supermassive Einsteinian cubic black hole. Our studies could be helpful for us to better understand the gravitational structure of the theory with high curvatures. [ABSTRACT FROM AUTHOR]

In his paper 'Bridging the neuroscience and physics of time' with Dean Buonomano (2021) in a forthcoming book Rovelli makes claims that I question because they rely uncritically on theoretical frameworks employed when the laws of thermodynamics and general relativity were discovered. Their reconsideration suggests growth of entropy is not the origin of time's arrow and identifies a notion of universal simultaneity within general relativity. [ABSTRACT FROM AUTHOR]

The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin foam models of quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality is encoded in such models. The quest unveils the physical meaning of the orientation of the two-complex and its role as a dynamical variable. We propose a causal version of the EPRL spin foam model and discuss the role of the causal structure in the reconstruction of a semiclassical space–time geometry. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the incorporation of aspects of the nature of science in primary and secondary education, specifically for the teaching of general relativity. The PRISMA protocol is applied in a systematic review of scientific articles between 2018 and 2022, provided by databases such as Web of Science, Scopus and Dialnet. Articles in Spanish, English and Portuguese were chosen to account for pedagogical interventions addressing aspects of the nature of science for training students in primary and secondary education. Forty-one studies were analyzed, including reflections of science’ epistemological and sociological characteristics. Regarding the teaching of general relativity, we found that using scientific news is privileged to include elements of the nature of science. The research allows us to conclude that there is an interest in introducing epistemic and non-epistemic aspects in the teaching of science at these educational levels, and specifically, teaching about general relativity empirical, tentative, gender and cooperation issues are included. [ABSTRACT FROM AUTHOR]

In this paper we use a modification of the Newtonian gravitational potential with a non-linear Yukawa-like correction, as it was proposed by C. Will earlier to obtain new bounds on graviton mass from the observed orbits of S-stars around the Galactic Center (GC). This phenomenological potential differs from the gravitational potential obtained in the weak field limit of Yukawa gravity, which we used in our previous studies. We also assumed that the orbital precession of S-stars is close to the prediction of General Relativity (GR) for Schwarzschild precession, but with a possible small discrepancy from it. This assumption is motivated by the fact that the GRAVITY Collaboration in 2020 and in 2022 detected Schwarzschild precession in the S2 star orbit around the Supermassive Black Hole (SMBH) at the GC. Using this approach, we were able to constrain parameter λ of the potential and, assuming that it represents the graviton Compton wavelength, we also found the corresponding upper bound of graviton mass. The obtained results were then compared with our previous estimates, as well as with the estimates of other authors. [ABSTRACT FROM AUTHOR]

In this paper we study the impact of a recent quasar datasample in the constraint of the free parameters of an extension of general relativity. As a ruler to test, we use Rastall gravity in the context of background cosmology being a simple extension to general relativity. We compare the results from quasars dataset with other known samples such as cosmic chronometers, supernovae of the Ia type, baryon acoustic oscillations, HII galaxies, and also a joint analysis. Results are consistent with the standard cosmological model emphasizing that Rastall gravity is equivalent to general relativity. According to the constraints provided from the joint sample, the age of the Universe is τ U = 12.601 − 0.066 + 0.067 Gyrs and the transition to an accelerated phase occurs at z T = 0.620 ± 0.025 in the redshift scale, being only the phase transition consistent with the standard paradigm and having a younger Universe. With the quasars sample, the Universe age differs with that expected in ΛCDM having a result of τ U = 11.958 − 0.109 + 0.139 Gyrs with a transition at z T = 0.652 ± 0.032 this last consistent with standard cosmology. A remarkable result is that quasars constraints has the capability to differentiate among general relativity and Rastall gravity due to the result for the parameter λ = − 2.231 − 0.546 + 0.785 . Moreover, the parameter j under quasars constraints suggests that the cause of the late Universe's acceleration is a dark energy fluid different from a cosmological constant. [ABSTRACT FROM AUTHOR]

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'. [ABSTRACT FROM AUTHOR]

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 I− and future null infinity I+ , one can identify two independent symmetry groups: BMS− at I− and BMS+ at I+. Associated with these symmetries are the so-called BMS charges. A recent conjecture by Strominger suggests that the generators of BMS− and BMS+ 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'. [ABSTRACT FROM AUTHOR]

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'. [ABSTRACT FROM AUTHOR]

Among about a thousand objects obtained by the Science Museum from Stephen Hawking's office is a blackboard full of cartoons and puns, both childishly silly and deeply scientifically meaningful. This blackboard is now one of the Museum's most popular objects thanks to its playful imagery and perhaps also its perceived fragility. But it is also one of the objects that best illustrates the scientific life of Stephen Hawking and his generation, and more broadly, it is an exemplar of the social and material culture of the postmodern epoch of theoretical physics in the decades around the turn of the twenty-first century. In this article, the curator of the Hawking Collection explains the importance of this blackboard, first through an account of its unexpected trajectory to becoming the Hawking Collection's most charismatic object, followed by a discussion of the general historical role of blackboards: their iconography, material culture, and value as historical sources and how their conservation requirements contribute to their perceived value. The author then delves deeper into the specific content of this blackboard, showing how it constitutes a window into the highs and lows of a generation of physicists inspired by Hawking's work, as they attempted, and ultimately failed, to unify the two great theories of the twentieth century: general relativity and quantum mechanics. What we now call the superspace and supergravity blackboard is a microcosm of one of those moments in physics when theory broke away from what was empirically verifiable. The scribblings on the blackboard were collectively drawn by an up-and-coming generation of supersymmetry theorists. It immortalises the promising early years of supergravity, one of the hopeful candidates at the time for the long-wished-for Theory of Everything. Preserved in chalk are the seeds of one of the most brilliant theoretical discoveries of the turn of the century: what is now called the holographic principle. But also, seen with the benefit of hindsight, supersymmetric approaches seeded the identity crisis that theoretical physics is experiencing today, especially around the role of empirical anchoring of proposed fundamental theories. The contested status of the blackboard's content and its humorous, self-ironic style, make it a key piece of a unique zeitgeist of physics at the turn of the twenty-first century, which one could call the era of postmodern physics. In addition to its significance to the history of specific ideas, this paper also argues that the blackboard reflects the collective, social nature of theoretical research, while also inviting reflection on what constitutes success and failure in the physical sciences. [ABSTRACT FROM AUTHOR]

A semantic adjustment to what physicists mean by the terms 'special relativity' and 'general relativity' is suggested, which prompts a conceptual shift to a more unified perspective on physics governed by the Poincaré group and physics governed by the Galilei group. After exploring the limits of a unified perspective available in the setting of 4-dimensional spacetime, a particular central extension of the Poincaré group—analogous to the Bargmann group that is a central extension of the Galilei group—is presented that deepens a unified perspective on Poincaré and Galilei physics in a 5-dimensional spacetime setting. The immediate focus of this paper is classical physics on affine 4-dimensional and 5-dimensional spacetimes ('special relativity' as redefined here), including the electrodynamics that gave rise to Poincaré physics in the first place, but the results here may suggest the existence of a 'Galilei general relativity' more extensive than generally known, to be pursued in the sequel. [ABSTRACT FROM AUTHOR]

In this paper, we study a spatially homogeneous and anisotropic Bianchi type-III universe containing cold dark matter and Barrow holographic dark energy within the framework of General Relativity. We assume the cold dark matter and Barrow holographic dark energy to be non-interacting and obtain exact solutions of the Einstein field equations by considering a hybrid expansion law and assuming that the expansion scalar is proportional to the shear scalar. We examine the physical and kinematical properties of the resulting model using parameters such as the Hubble parameter, the anisotropic parameter, the deceleration parameter, the equation of state parameter, the jerk parameter etc. We also examine whether the energy conditions are violated or validated. We find that the Null, Weak, and Dominant energy conditions are fulfilled, while the Strong Energy Condition is violated, which supports the accelerated expansion of the universe. The Statefinder diagnostics have been conducted based on recent cosmological observations. In addition, we reformulated the correspondence between quintessence scalar field and Barrow holographic dark energy model. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to construct an anisotropic and spatially homogeneous Bianchi type-V I0 Kaniadakis holographic dark energy model in general relativity. For this purpose, we consider Hubble horizons as the IR cutoff. To obtain a deterministic solution of the model's field equations, we assume a relationship between the metric potentials which leads to an exponential solution and accelerated expansion. To investigate the physical behaviour of our dark energy model, we obtain some important cosmological parameters like Hubble, deceleration, equation of state and statefinder as well as ωkhde - ω' khde, r - s and r - q planes. We also included the stability analysis for the dark energy model through the squared speed of sound. It is observed that the equation of state parameter shows ΛCDM model at late times. Also, the squared speed of sound gives the stability of the Kaniadakis holographic dark energy model at the initial epoch and the model is unstable at late times. Statefinder diagnostic and deceleration parameters exhibit a smooth transition of the universe from the decelerating phase to the current accelerated expansion of the universe and also correspond to the ΛCDM model at late times. All these cosmological parameters support recent observational data. [ABSTRACT FROM AUTHOR]

This study examines Einstein's field equations in the context of general relativity, comparing five distinct methodologies: (a) vanishing complexity, (b) embedding class one or the Karmarkar condition, (c) conformally flat spacetime, (d) conformal killing symmetry, and (e) the Karmarkar scalar condition. The first four methods reveal a significant connection between two metric potentials, while the fifth method provides a coordinate-independent condition expressed in terms of structural scalars. The paper provides a comprehensive comparative analysis of a new exact solution derived by assuming a common metric function and solving the remaining metric functions through corresponding bridge equations to evaluate their effectiveness and validity. Critical parameters such as thermodynamic factors, causality conditions, stability, and mass function analysis are investigated. [ABSTRACT FROM AUTHOR]

The topic of gravitational lensing in the Mannheim–Kazanas solution of Weyl conformal gravity and the Schwarzschild–de Sitter solution in general relativity has featured in numerous publications. These two solutions represent a spherical massive object (lens) embedded in a cosmological background. In both cases, the interest lies in the possible effect of the background non-asymptotically flat spacetime on the geometry of the local light curves, particularly the observed deflection angle of light near the massive object. The main discussion involves possible contributions to the bending angle formula from the cosmological constant Λ in the Schwarzschild–de Sitter solution and the linear term γ r in the Mannheim–Kazanas metric. These effects from the background geometry, and whether they are significant enough to be important for gravitational lensing, seem to depend on the methodology used to calculate the bending angle. In this paper, we review these techniques and comment on some of the obtained results, particularly those cases that contain unphysical terms in the bending angle formula. [ABSTRACT FROM AUTHOR]

An electromagnetic-like model of gravitational radiation reproduces many features of the gravitational waves emitted by orbiting binary systems and observed by the LIGO-Virgo collaboration. However, that model predicts a total gravitational wave power emission which is smaller than that predicted by general relativity. In this paper, we improve the electromagnetic-like model by considering the energy-momentum tensor of the binary source and revisiting a numerical factor in the expressions that link the gravitational mass/energy currents to the vector potential. The enhanced model's results for the total gravitational wave power emitted by a binary source before coalescence are in complete agreement with general relativistic predictions. This approach makes gravitational wave physics accessible to a broad audience without requiring any knowledge of general relativity. Editor's Note: A deep understanding of gravitational waves requires knowledge of general relativity (which is notoriously difficult). Over the decades, and for various reasons, alternative theories/models of gravity have been developed. Even though such alternatives were eventually found to conflict with observations, they still can be used for pedagogical purposes. In this article, the author develops a vector theory of gravitational waves, reminiscent of electromagnetism, which leads to many of the same predictions as general relativity. Many calculations proceed by analogy with electromagnetism, and the context of this model may help learners build their intuition for gravitational radiation. Readers familiar with electromagnetic radiation will find the model presented here to be a helpful stepping stone to the full theory of general relativity. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper is devoted to observe the physical attributes of static spherically symmetric isotropic compact stellar candidates in the context of Rastall theory of gravity. In order to inspect the structural composition of compact objects, the Heintzmann ansatz is taken into account. The unknown parameters associated with Heintzmann ansatz are evaluated through matching conditions with derived values of radii and masses of some specific star models. The consistency of the adopted ansatz is analyzed via graphical interpretation of matter variables, equation of state parameter, mass components, energy constraints, causality condition, stellar equation and adiabatic index for several choices of Rastall parameter. It is observed that the stars under consideration manifest stable structures corresponding to Heintzmann ansatz in this framework. Moreover, it is shown that for vanishing Rastall coupling parameter, the standard outcomes of general relativity can be retrieved. [ABSTRACT FROM AUTHOR]

In this paper, we review the main features of modified theories of gravity containing higher-order curvature invariants in the action. After summarizing the main features of these theories, we consider their applications to cosmology, pointing out the differences with respect to general relativity that can eventually solve issues exhibited by the latter at low and high energy scales. Specifically, we explore a gravitational action that incorporates both the Ricci scalar R and the topological Gauss–Bonnet term, denoted as . Our investigation revolves around the cosmological properties of a specific category of modified gravity theories, chosen upon symmetry considerations. Within the framework of a spatially flat, homogeneous and isotropic cosmic background, we demonstrate that it is possible to account for the presently observed acceleration of the Universe by means of the extra geometric terms carried by the selected f (R ,) model. This approach offers a way to address the issues associated with the cosmological constant. To achieve this, we first examine the energy conditions and find that, under certain choices for the values of the cosmographic parameters, these conditions are all violated. In the second part of the work, to assess the feasibility of the selected f (R ,) model, we place observational constraints on its free parameters through a Bayesian Monte Carlo technique applied to late-time cosmic data. Our findings reveal that the f (R ,) model can effectively reproduce observations at low redshifts, providing an alternative to the standard Λ CDM scenario. [ABSTRACT FROM AUTHOR]

In this paper, we involve the galactic halo observational data to test the weak field General Relativity involving the cosmological constant. By using the data for 15 hydrogen (Hi) VLA super spirals and the Tully–Fisher relation, we obtain constraints for each galaxy. The results are consistent with previous results for spiral galaxies, as well as with the scaling relations for the halos, thus confirming the efficiency of the use of dark halo data and Tully–Fisher relation, including the baryonic Tully–Fisher index (BTFR), for testing modified gravity models. [ABSTRACT FROM AUTHOR]

The null-surface formulation (NSF) of general relativity differs markedly from the conventional approach. The conventional approach to general relativity is concerned with local fields such as the metric, whereas the NSF focuses on surfaces. The NSF has two distinct but mathematically equivalent interpretations: (a) Future-directed light rays leave a spacetime point and intersect future null-infinity. The resulting surface, known as a light-cone cut, encodes the properties of the spacetime; (b) The angular coordinates (Bondi coordinates) of null-infinity are used to label past light cones, thereby producing a family of null surfaces. These will satisfy the NSF field equations and a solution of these equations provides a description of spacetime. This paper features a new exact solution that, for the first time, directly links the two interpretations, thereby illustrating both approaches and demonstrating their equivalence. The solution and its properties are first explored in 2+1 dimensions, after which, the generalization to 3+1 is outlined. [ABSTRACT FROM AUTHOR]

In this paper, we explore a set of geometric properties of Mixed Super Quasi-Einstein (MSQE) manifolds and provide examples of both Riemannian and Lorentzian MSQE manifolds to demonstrate their existence. Furthermore, we examine MSQE spacetimes in the context of the space-matter tensor, discussing several related properties. Finally, we establish the existence of an MSQE spacetime through a nontrivial example. [ABSTRACT FROM AUTHOR]

In this paper, we have revisited the Berman's idea of the variation of Hubble parameter. While previously explored in the context of Λ-varying cosmologies, where scale factor variations yield linear universe expansion, this parametrization has undergone extensive scrutiny. Our investigation, however, explores into its implications in the context of late-time cosmic acceleration, within the framework of classical general relativity, adopting the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime as our background metric. Our analysis offers a precise solution to Einstein's field equations (EFEs) in a model-independent way, affording a thorough assessment of both geometrical and physical model parameters. Additionally, this study supplements its findings with graphical representations of the evolving cosmological parameters across flat, closed, and open universe scenarios, all subject to constraints derived from the model parameters. In synthesizing these results, we shed light on the intricate interplay between cosmic acceleration, dark energy, and the parametrization of the Hubble parameter, thereby providing valuable insights into the fundamental mechanics of our universe. [ABSTRACT FROM AUTHOR]

Inspired by high-energy physics and by considering standard gravity theory as the low-energy limit of quantum theory, the modification of general relativity as R + f (G) has been proposed. This paper is dedicated to investigating the cosmological model of modified Gauss–Bonnet gravity in four dimensions. General field equations for the four-dimensional Friedmann– Robertson–Walker metric are given in detail. Also, it is well known that Hubble parameter H (z) measurements are helpful for the inference of cosmological model parameters. We try to explain the MCMC statistical approach used to calculate Hubble's parameter. The resulting form of H (z) was limited using Cosmic Chronometric data, Standard Candles SN Ia from Pantheon, and Baryon Acoustic Oscillations to obtain the best match values by using the regression equation. Finally, to examine the late-time dynamics of our Universe, the behavior of physical and kinematic variables like the deceleration parameter (q) , State-finder parameters { r , s } , diagnostic parameter ( O m (z)), equation of state parameter as well as the behavior of energy conditions versus redshift with the parameter values are presented. [ABSTRACT FROM AUTHOR]

Biquaternion algebra is an algebraic structure originating from a complex number and has mainly been used in quantum mechanics, special and general relativity, classical, relativistic, and covariant electrodynamics, and signal processing. In this paper, the problem of the diagonalization of a biquaternion matrix is studied, by means of a complex representation of a biquaternion matrix, and an algebraic algorithm for the diagonalization of a biquaternion matrix is presented. In addition, numerical examples demonstrate the effectiveness of the algebraic algorithm. [ABSTRACT FROM AUTHOR]

General theory of relativity can be equivalently formulated on a flat spacetime associating a torsion-free affine connection of non-vanishing non-metricity scalar Q. In this paper, we present an extension of this, viz., the f (Q) theory of gravity, and explore the early evolution of the universe in the background of anisotropic Bianchi-I model. The f (Q) theory in the current setting through its geometric modification is quite successful in explaining the late time accelerated expansion. Here, we note that it accommodates latest released constraints on the inflationary parameters by Planck's collaboration group with excellent precession, but fails to produce a viable decelerated expansion in the radiation dominated era. [ABSTRACT FROM AUTHOR]

In this paper we investigate the impact of lensing magnification on the analysis of Euclid's spectroscopic survey using the multipoles of the two-point correlation function for galaxy clustering. We determine the impact of lensing magnification on cosmological constraints as well as the expected shift in the best-fit parameters if magnification is ignored. We considered two cosmological analyses: (i) a full-shape analysis based on the Λ cold dark matter (CDM) model and its extension w0waCDM and (ii) a model-independent analysis that measures the growth rate of structure in each redshift bin. We adopted two complementary approaches in our forecast: the Fisher matrix formalism and the Markov chain Monte Carlo method. The fiducial values of the local count slope (or magnification bias), which regulates the amplitude of the lensing magnification, have been estimated from the Euclid Flagship simulations. We used linear perturbation theory and modelled the two-point correlation function with the public code coffe. For a ΛCDM model, we find that the estimation of cosmological parameters is biased at the level of 0.4–0.7 standard deviations, while for a w0waCDM dynamical dark energy model, lensing magnification has a somewhat smaller impact, with shifts below 0.5 standard deviations. For a model-independent analysis aimed at measuring the growth rate of structure, we find that the estimation of the growth rate is biased by up to 1.2 standard deviations in the highest redshift bin. As a result, lensing magnification cannot be neglected in the spectroscopic survey, especially if we want to determine the growth factor, one of the most promising ways to test general relativity with Euclid. We also find that, by including lensing magnification with a simple template, this shift can be almost entirely eliminated with minimal computational overhead. [ABSTRACT FROM AUTHOR]

This paper is devoted to observe the physical attributes of isotropic relativistic spherical objects in the context of Rastall theory of gravity. In order to inspect the structural composition of spherical objects, the Tolman IV solution is taken into account. The unknown parameters associated with Tolman IV solution are evaluated through matching conditions with derived values of radii and masses of some specific star models. The consistency of the adopted ansatz is analyzed via graphical interpretation of matter variables, equation of state parameter, mass components, energy constraints, causality condition and stellar equation for several choices of Rastall parameter. It is observed that the considered solution does not admit singularities in the matter variables. Moreover, in accordance with the graphical analysis, the stellar models satisfy all physical requirements anticipated in a realistic star. It is also shown that for vanishing Rastall coupling parameter, the standard outcomes of general relativity can be retrieved. [ABSTRACT FROM AUTHOR]

This paper focuses on the Einstein–Cartan theory, an extension of general relativity that incorporates a torsion tensor into spacetime. The differential form technique is employed to analyze the Einstein–Cartan theory, which replaces tensors with tetrads. A tetrad formalism, specifically the Newman–Penrose–Jogia–Griffiths formalism, is used to study the field equations. Also, the energy–momentum tensor is determined, considering a Weyssenhoff fluid with anisotropic matter. The spin density is derived in terms of the redshift function. Additionally, our findings demonstrate that the radial sound speed within the wormhole throat exceeds the speed of light, suggesting the existence of superluminal matter, while the tangential sound speed indicates near-light-speed propagation, particularly within the throat, emphasizing the significance of exotic matter in comprehending wormhole properties. The results also extend to examining the energy conditions at the throat of a Morris–Thorne wormhole, shedding light on the properties of wormholes within the context of the Einstein–Cartan theory, including the energy conditions at the throat. [ABSTRACT FROM AUTHOR]

We describe a general constitutive framework for a teleparallel extension of the general theory of relativity. This approach goes beyond the teleparallel equivalent of general relativity (TEGR) by broadening the analogy with the electrodynamics of media. In particular, the main purpose of this paper is to investigate in detail a local constitutive extension of TEGR that is the local limit of non-local gravity. Within this framework, we study the modified Friedmann–Lemaître–Robertson–Walker cosmological models. Of these, the most cogent turns out to be the modified Cartesian flat model which is shown to be inconsistent with the existence of a positive cosmological constant. Moreover, dynamic dark energy and other components of the modified Cartesian flat model evolve differently with the expansion of the universe as compared to the standard flat cosmological model. The observational consequences of the modified Cartesian flat model are briefly explored and it is shown that the model is capable of resolving the H 0 tension. [ABSTRACT FROM AUTHOR]