Minkowski Space Research Articles

The Discovery of Accelerating Expansion of Universe 8.8 Billion Years after the Big Bang Vindicates M1 World One Out of the Six Solutions of Einstein’s General Theory of Relativity

This paper gives the mathematical methodology (Tensor mathematics) of describing the surfaces of our Universe in General Theory of Relativity. It expresses the mass energy equivalence formula. It introduces the concept of time dilation, length contraction and mass increment in high speed frame of reference. Minowski space time 4D manifold is illustrated for representing the flat spacetime fabric Reimannian Metric is enumerated. Schwarzschild metric and how mass is accounted for is given.

Singularities of worldsheets along framed particle trajectories in Minkowski three-space

Modeling the worldsheets along the trajectory (a string) of a point particle (a 0-brane) as two timelike surfaces in 3-subspace of Minkowskian spacetime, respectively, the work aims at analyzing the topological structures of these two worldsheets along the trajectory of the point particle from the view point of singularity theory. Different from the regular curves, the traveling trajectory (modeled as framed timelike curve) of the particle is allowed to be singular, two worldsheets are generated by the traveling trajectories of the particle. As applications of singularity theory, we classify the singularities of these two worldsheets along the traveling trajectory of the particle. Using the approach of the unfolding theory in singularity theory, we find two new geometric invariants which are useful for characterizing the local topological structures of singularities of these two worldsheets along the particle. It is revealed that there exist cuspidal edge type and swallowtail type of singularities for these two worldsheets under the appropriate conditions of geometric invariants. Meanwhile, it is also pointed out that the types of singularities of these two worldsheets have a close relationships to the order of contacts between these two worldsheets and two timelike planes, respectively. Finally, some examples are presented to interpret our theoretical results.

Eikonal amplitudes on the celestial sphere

Celestial scattering amplitudes for massless particles are Mellin transforms of momentum-space scattering amplitudes with respect to the energies of the external particles, and behave as conformal correlators on the celestial sphere. However, there are few explicit cases of well-defined celestial amplitudes, particularly for gravitational theories: the mixing between low- and high-energy scales induced by the Mellin transform generically yields divergent integrals. In this paper, we argue that the most natural object to consider is the gravitational amplitude dressed by an oscillating phase arising from semi-classical effects known as eikonal exponentiation. This leads to gravitational celestial amplitudes which are analytic, apart from a set of poles at integer negative conformal dimensions, whose degree and residues we characterize. We also study the large conformal dimension limits, and provide an asymptotic series representation for these celestial eikonal amplitudes. Our investigation covers two different frameworks, related by eikonal exponentiation: 2 → 2 scattering of scalars in flat spacetime and 1 → 1 scattering of a probe scalar particle in a curved, stationary spacetime. These provide data which any putative celestial dual for Minkowski, shockwave or black hole spacetimes must reproduce. We also derive dispersion and monodromy relations for these celestial amplitudes and discuss Carrollian eikonal-probe amplitudes in curved spacetimes.

Existence of traversable wormholes in the minimally coupled gravity model

The objective of this study is to examine the possible existence of traversable wormhole geometries within the context of [Formula: see text] gravity. To meet this objective, we employ the Karmarkar condition to construct the shape function that aids in identifying the wormhole configurations. This developed function is found to satisfy the essential conditions and provides a link between two asymptotically flat spacetime regions. We then assume the Morris–Thorne line element that expresses the wormhole configuration and formulate the anisotropic gravitational equations for a particular minimal matter-spacetime coupled model of the modified theory. Afterward, we develop three solutions and determine their viability by analyzing whether they violate the null energy conditions. Different stability methods are applied to the resulting geometries to explore the acceptance of the considered modified model. We conclude that the developed wormhole structures potentially fulfill the required criteria and thus exist in this modified gravity under all choices of the matter Lagrangian density.

On the non-flatness nature of noncommutative Minkowski spacetime and the singular behavior of probes

It is more than a century-old concept that the Minkowski spacetime is flat. From the pure geometric point of view, we explicitly address the issue of whether a noncommutative Minkowski spacetime is flat or not. In the framework of the twisted-diffeomorphism approach to noncommutative gravity with canonical type noncommutative (NC) coordinate structure, one important result that we get is that the NC Minkowski spacetime parametrized either with spherical polar coordinates or with parabolic coordinates has nontrivial NC corrections to Riemann curvature tensor, Ricci tensor and curvature scalars. Another crucial result is that the curvature scalars have singular behavior at certain points, and these singularities are not coordinate singularities. The nature of these singularities clearly points towards the idea of high-energetic probes turning into black holes. The absence of any such noncommutative corrections, and thus any such singularities, in the cases of Cartesian coordinates and cylindrical coordinates leads to the conclusion that high-energetic probes do not turn into black holes when the canonical NC structure is considered for these coordinates.

A five-dimensional vacuum-defect wormhole space-time

In this study, we present a novel extension to the Klinkhamer vacuum-defect model by incorporating a fifth spatial dimension. This modification results in the formulation of a comprehensive five-dimensional wormhole space-time. Crucially, this extension preserves its classification as a vacuum solution to the field equations, thereby automatically satisfying all energy conditions. We demonstrate that this five-dimensional vacuum-defect space-time can be expressed in a pure canonical form, and thus, locally reduces to five-dimensional Minkowski space. Finally, we explore the geodesic equations in the vicinity of this five-dimensional vacuum-defect wormhole, offering insights into its intriguing properties.

A connection between massive electrodynamics and the Einstein-Maxwell equations

Quaternions are the best mathematical construct for creatingvarious equations in electrodynamics, which has led to the emergence of new terms with unique physical implications. Since quaternions also have noncommutative properties that are reflected in curved space-time too, a formulation of a theory using quaternions can be compared with that formulated in some curved space-time. Furthermore, we calculate the Maxwell equations in curved space-time and observe the presence of extra terms that are not present in flat space-time. An electric current arises because of the coupling between the magnetic field and curvature. Upon comparing the outcomes of the two methods, we discovered a correlation between mass and gravity, indicating their similarity. Equations formulated via quaternions are equivalent to those formulated in curved space-time. The optical chirality and its flux are generalized to massive electrodynamics.

Maximum acceleration and quantum clock: on the existence of a new universal constant

In the pseudo-Euclidean Minkowski space, the four-dimensional volume element is invariant under Lorentz transformations. By hypothesising that in this space there is a minimum volume, it is possible to demonstrate the existence of a maximum acceleration. The volume element cannot be derived from the theory and must be obtained through direct measurement, thus it assumes the role of a bona fide universal constant. Two different estimates of the elementary volume are given, which differ by several orders of magnitude: the first is obtained in a pseudo-Euclidean space for particles with mass, and the second represents an absolute minimum volume, independent of the mass.

Relativity of the event: examples in JT gravity and linearized GR

Observables in quantum gravity are famously defined asymptotically, at the boundary of AdS or Minkowski spaces. However, by gauge fixing a coordinate system or suitably dressing the field operators, an approximate, “quasi-local” approach is also possible, that can give account of the measurements performed by a set of observers living inside the spacetime. In particular, one can attach spatial coordinates to the worldlines of these observers and use their proper times as a time coordinate. Here we highlight that any such local formulation has to face the relativity of the event, in that changing frame (= set of observers) implies a reshuffling of the point-events and the way they are identified. As a consequence, coordinate transformations between different frames become probabilistic in quantum gravity. We give a concrete realization of this mechanism in Jackiw-Teitelboim gravity, where a point in the bulk can be defined operationally with geodesics anchored to the boundary. We describe different ways to do so, each corresponding to a different frame, and compute the variances of the transformations relating some of these frames. In particular, we compute the variance of the location of the black hole horizon, which appears smeared in most frames. We then suggest how to calculate this effect in Einstein gravity, assuming knowledge of the wavefunction of the metric. The idea is to expand the latter on a basis of semiclassical states. Each element of this basis enjoys standard/deterministic coordinate transformations and the result is thus obtained by superposition. As a divertissement, we sabotage Lorentz boosts by adding to Minkoswki space a quantum superposition of gravitational waves and compute the probabilistic coordinate transformation to a boosted frame at linear order. Finally, we attempt to translate the relativity of the event into the language of dressed operators.

Transient dynamics of quasinormal mode sums

Quasinormal modes of spacetimes with event horizons are typically governed by a non-normal operator. This gives rise to spectral instabilities, a topic of recent interest in the black hole pseudospectrum programme. In this work we show that non-normality leads to the existence of arbitrarily long-lived sums of short-lived quasinormal modes, corresponding to localising packets of energy near the future horizon. There exist sums of M quasinormal modes whose lifetimes scale as log M. This transient behaviour results from large cancellations between non-orthogonal quasinormal modes. We provide simple closed-form examples for a massive scalar field in the static patch of dSd+1 and the BTZ black hole. We also provide numerical examples for scalar perturbations of Schwarzschild-AdSd+1, and gravitational perturbations of Schwarzschild in asymptotically flat spacetime, using hyperboloidal foliations. The existence of these perturbations is linked to certain properties of black hole pseudospectra. We comment on implications for thermalisation times in holographic plasmas.

Basic Mathematical form Of Nature of Space And Dimension of Observable Universe and Beyond

In this innovative research I have advanced the theory of space with definition of space, definition of types of space, and introduced energy-mass transformation, gravity and gravitation force. With this advance research, finally I have defined basic mathematical form of “Nature of space and Dimension of Observable Universe and beyond”.As we know the universe is defined as all space-time and their contents. However, several questions still remain open regarding higher dimension, singularity, gravity collapse at horizon of black hole, unified gravity, theory of everything, dark matter, dark energy, existence of observable universe and beyond, question for mathematical form of everything, question for matter itself, and question for the space itself. These open questions have driven this scientific research of “Basic Mathematical form Of Nature of Space and Dimension of Observable Universe and beyond”. My research findings indicate that the space itself is the entity with having physical properties. The space can be described by physical structure and its transformation. The space has two fundamental properties of energy and mass, and space can be described by energy- mass transformation. From these energy-mass transformation and physical structure transformation, I have defined the gravity, gravitation force and basicmathematical form of“Nature of space and Dimension of Observable Universe and beyond”. This basic mathematical form covers scope of higher dimension, unified gravity, singularity, horizon of black hole, and nature of space of observable universe and beyond. Several research have been conductedfor look into nature of space,space-time, gravity, unified gravity, higher dimensions, unified mathematical formof everything by Minkowski space,Higgs field, Aether medium, Newton’s law of universal gravitation, Electromagnetism, Planck constant,General relativity,Standard Model,Loop Quantum Gravity, Super symmetry, Super gravity, String theory and M-Theory. Despite these research, the questions still remain open for unified nature and for unified mathematical form of “Nature of space and Dimension of Observable Universe and beyond”. By researching the existence of matter, I found the existence of space was just accepted as the void, empty, and space-time background framework. My research reflects “Dimension of Observable Universe and beyond”encompasses all existence of observable universe and beyond it. The advance definition of space, definition of type of space, space transformation and energy-mass transformation perfectly describe existence of entire space & universe and its nature at very fundamental level. This very fundamental nature is presented in basic mathematical form. It is the most accurate foundation to answer those open questions. It is the novelty in astrophysics and foundation of entire existence.

Physical states and transition amplitudes in piecewise flat quantum gravity

In this paper, we show how the path integral for gravity and matter on a piecewise flat spacetime can be used to define the physical quantum gravity states and the related transition amplitudes. The physical states are given by the path integrals for open manifolds from a certain topological class, while the corresponding transition amplitudes are obtained by gluing two such open manifolds into a closed one and calculating the corresponding path integral. We also solve the problem of how to associate a quantum gravity state to an effective action. This is done by using the path integral for a closed manifold from the transition-amplitude topological class so that the state which corresponds to the effective action can be chosen to be the Hartle–Hawking or the Vilenkin wavefunction for the vacuum manifold component of the transition-amplitude manifold.

Tachyons in “momentum-space” representation

Obtaining the momentum space associated with tachyonic “particles” from the Poincaré group manifold proves to be rather intricate, departing very much from the ordinary dual to Minkowski space directly parametrized by space-time translations of the Poincaré group. In fact, although described by the constants of motion (Noether invariants) associated with space-time translations, they depend non-trivially on the parameters of the rotation subgroup. However, once the momentum space is parametrized by the Noether invariants, it behaves as that of ordinary particles. On the other hand, the evolution parameter is no longer the one associated with time translation, whose Noether invariant, Po, is now a basic one. Evolution takes place in a spatial direction. These facts not only make difficult the computation of the corresponding representation, but also force us to a sound revision of several traditional ingredients related to Cauchy hypersurface, scalar product and, of course, causality. After that, the theory becomes consistent and could shed new light on some special physical situations like inflation or traveling inside a black hole.

Cosmological particle creation using an equal-time Wigner formalism

It is well known that the expansion of the universe can create particles. However, due to ambiguities when defining particles during the expansion, there are still debates about how to choose vacuum and particle states. To clarify how particles are produced in an expanding universe, we study the creation of real scalar particles in flat Friedmann-Lemaître-Robertson-Walker spacetimes by using a recently developed equal-time Wigner formalism. By comparing this quantum kinetic formalism with the standard Bogoliubov approach, we make a natural definition of a particle number in terms of kinetic phase-space functions, which we then compare with common adiabatic particle numbers. With inspiration from flat spacetime QED, we perform numerical calculations and discuss the interpretation of the particle numbers in terms of a hypothetical switch-off in the expansion rate. Finally, we consider how this interpretation is affected by regularization. Published by the American Physical Society 2024

Gravitational redshift revisited: Inertia, geometry, and charge

Gravitational redshift effects undoubtedly exist; moreover, the experimental setups which confirm the existence of these effects—the most famous of which being the Pound–Rebka experiment—are extremely well-known. Nonetheless—and perhaps surprisingly—there remains a great deal of confusion in the literature regarding what these experiments really establish. Our goal in the present article is to clarify these issues, in three concrete ways. First, although (i) Brown and Read (2016) are correct to point out that, given their sensitivity, the outcomes of experimental setups such as the original Pound–Rebka configuration can be accounted for using solely the machinery of accelerating frames in special relativity (barring some subtleties due to the Rindler spacetime necessary to model the effects rigorously), nevertheless (ii) an explanation of the results of more sensitive gravitational redshift outcomes does in fact require more. Second, although typically this ‘more’ is understood as the invocation of spacetime curvature within the framework of general relativity, in light of the so-called ‘geometric trinity’ of gravitational theories, in fact curvature is not necessary to explain even these results. Thus (a) one can often explain the results of these experiments using only the resources of special relativity, and (b) even when one cannot, one need not invoke spacetime curvature. And third: while one might think that the absence of gravitational redshift effects would imply that spacetime is flat (indeed, Minkowskian), this can be called into question given the possibility of the cancelling of gravitational redshift effects by charge in the context of the Reissner–Nordström metric. This argument is shown to be valid and both attractive forces as well as redshift effects can be effectively shielded (and even be repulsive or blueshifted, respectively) in the charged setting. Thus, it is not the case that the absence of gravitational effects implies a Minkowskian spacetime setting.

Quasinormal Modes and Stability Analysis of Rotating Hairy Black Holes in Asymptotically Flat Spacetime

Abstract Kerr black holes, characterized solely by their mass and angular momentum, are considered the predominant type in the universe. Recent studies, however, suggest that black holes may possess additional parameters, known as “hair”. This paper investigates the quasinormal modes (QNMs) of rotating hairy black holes in asymptotically flat spacetimes using the continued fraction method to analyze their stability. Our results demonstrate that the introduction of hair parameters modifies the QNM frequencies, indicating a nuanced stability profile that reduces to the classical Kerr solution under specific conditions. These findings provide new insights into the dynamic properties of hairy black holes and their potential astrophysical implications.

Causal completion of globally hyperbolic conformally flat spacetimes

In their paper Geroch, Kronheimer, and Penrose, “Ideal points in space-time,” [Proc. R. Soc. London, Ser. A 327, 545–567 (1972)] introduced a way to attach ideal points to a spacetime M, defining the causal completion of M. They established that this is a topological space which is Hausdorff when M is globally hyperbolic. In this paper, we prove that if, in addition, M is simply-connected and conformally flat, its causal completion is a topological manifold with boundary homeomorphic to S × [0, 1] where S is a Cauchy hypersurface of M. We also introduce three remarkable families of globally hyperbolic conformally flat spacetimes and provide a description of their causal completions.

A Riemannian geometric approach for timelike and null spacetime geodesics

The geodesic motion in a Lorentzian spacetime can be described by trajectories in a 3-dimensional Riemannian metric. In this article we present a generalized Jacobi metric obtained from projecting a Lorentzian metric over the directions of its Killing vectors. The resulting Riemannian metric inherits the geodesics for asymptotically flat spacetimes including the stationary and axisymmetric ones. The method allows us to find Riemannian metrics in three and two dimensions plus the radial geodesic equation when we project over three different directions. The 3-dimensional Riemannian metric reduces to the Jacobi metric when static, spherically symmetric and asymptotically flat spacetimes are considered. However, it can be calculated for a larger variety of metrics in any number of dimensions. We show that the geodesics of the original spacetime metrics are inherited by the projected Riemannian metric. We calculate the Gaussian and geodesic curvatures of the resulting 2-dimensional metric, we study its near horizon and asymptotic limit. We also show that this technique can be used for studying the violation of the strong cosmic censorship conjecture in the context of general relativity.

The harmonic background paradigm, or why gravity is attractive

In a work by Visser, Bassett and Liberati (VBL) (Nucl Phys B Proc Suppl 88:267, 2000) a relation was suggested between a null energy condition and the censorship of superluminal behaviour. Their result was soon challenged by Gao and Wald (Class Quantum Grav 17:4999, 2000) who argued that this relation is gauge dependent and therefore not appropriate to find such connections. In this paper, we clear up this controversy by showing that both papers are correct but need to be interpreted in distinct paradigms. In this context, we introduce a new paradigm to interpret gravitational phenomena, which we call the Harmonic Background Paradigm. This harmonic background paradigm starts from the idea that there exists a more fundamental background causality provided by a flat spacetime geometry. One of the consequences of this paradigm is that the VBL relation can provide an explanation of why gravity is attractive in all standard weak-field situations.

Kinetic theory of tilted Dirac cone materials

We formulate the Boltzmann kinetic equations for interacting electrons with tilted Dirac cones in two space dimensions characterized by a tilt parameter 0≤ζ<1. By solving the linearized Boltzmann equation, we find that the broadening of the Drude pole is enhanced by κ(ζ)×(1−ζ2)−1/2, where the κ is interaction-induced enhancement factor. The intensity of the Drude pole is also anisotropically enhanced by (1−ζ2)−1. The ubiquitous “redshift” factors (1−ζ2)1/2 can be regarded as a manifestation of an underlying spacetime structure in such solids. The additional broadening κ that arises from the interactions cannot be obtained from a simple coordinate change and are more pronounced for electrons in a ζ-deformed Minkowski spacetime of tilted Dirac fermions.