Flat Minkowski Spacetime Research Articles

On the gravitational hysteresis in the kinetic theory

General theory of relativity is non-linear in nature and therefore can result in hysteresis-like effects and cause systems to remember the footprint of the gravitational field. Here we have investigated this effect using the Kinetic theory in curved spacetime. It is shown that the entropy rate experiences this hysteresis behavior. The effect is then considered for some special spacetimes, including Schwarzschild black hole, Friedmann-Lemaître-Robertson-Walker cosmological solution, and the flat Minkowski spacetime perturbed by a gravitational wave pulse. It is shown that there is some hysteresis effect for the entropy rate.

Thin-shell wormholes with non-collapsing dark energy throats connecting flat Minkowski spacetimes

This research revisits the thin-shell wormhole connecting two Minkowski spacetimes — originally introduced by Matt Visser. Upon setting a particular timelike hypersurface with a de-sitter-induced line element, the corresponding thin-shell wormhole (TSW) possesses a minimum radius and a uniform surface energy–momentum tensor in the form of dark energy. The bounded from below radius for the throat implies that it does not collapse. The r−τ profile curve of the hypersurface is a Catenary in r−τ plane where r and τ are the radial coordinate and the proper time on the throat, respectively. It is also shown that while the throat is dynamic, the surface energy–momentum tensor of the dark energy is in the form of an effective cosmological constant in the spherically symmetric TSW. The 4-dimensional cylindrically symmetric TSW with a similar throat profile shares the same features as its spherical counterpart, however, its uniform surface energy–momentum tensor does not mimic an effective cosmological constant. The higher-dimensional generalization of the spherically symmetric TSW admits the same properties as in the 4-dimensional one.

Rotational influence on fermions within negative curvature wormholes

In this research, we examine relativistic fermions within the rotating frame of negative curvature wormholes. Initially, as is typical in our context, we introduce the wormholes by embedding a curved surface into a higher-dimensional flat Minkowski spacetime. Subsequently, we derive the spacetime metric that characterizes the rotating frame of these wormholes. We then investigate analytical solutions of the generalized Dirac equation within this framework. Through exploring a second-order non-perturbative wave equation, we seek exact solutions for fermions within the rotating frame of hyperbolic and elliptic wormholes, also known as negative curvature wormholes. Our analysis provides closed-form energy expressions, and we generalize our findings to Weyl fermions. By considering the impact of the rotating frame and curvature radius of wormholes, we discuss how these factors affect the evolution of fermionic fields, offering valuable insights into their behavior.

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.

Gravitoelectromagnetic Field Strength Tensor in Flat Spacetime Frame: Dynamics of a Gyroscope in the Earth’s Gravitational Field

In this article, we develop gravitoelectromagnetism (GEM) as a formal relativistic theory of gravitation characterized by a field potential fourvector in a flat (Minkowski) spacetime frame. By reorganizing the Lense-Thirring spacetime metric of linearized general relativity, we have determined the appropriate field potential four-vector and the field strength tensor which generates dynamics in the GEM field. The general covariant equation of motion of the spin four-vector of a gyroscope driven by the GEM field strength tensor provides the expected form of the frame-dragging and geodetic effects after introducing a gyromagnetic ratio η = 4 as an internal dynamical property of the gyroscope.

Souriau’s general covariant formulation of Relativistic Hyperelasticity revisited

We present and modernize Souriau’s 1958 geometric framework for Relativistic continuous media, and enlighten the necessary and the ad hoc modeling choices made since. We focus as much as possible on the Continuum Mechanics point of view and describe the general covariant formulation of Hyperelasticity in (Variational) General Relativity. At this level of generality, different relativistic strain and stress tensors are formulated and discussed. Then, the choice of an observer, through the introduction of a spacetime structure allows us to make deeper insights into the foundations of Continuum Mechanics. We extend Souriau’s calculations, initially performed in the flat Minkowski spacetime, to the Schwarzschild spacetime accounting for gravitation. Finally, we recover the Classical Galilean Hyperelasticity with gravity, as the Newton–Cartan infinite light speed limit of this formulation.

A viable relativistic scalar theory of gravitation

We build a self-consistent relativistic scalar theory of gravitation on a flat Minkowski spacetime from a general field Lagrangian. It is shown that, for parameters that satisfy the equivalence principle, this theory predicts the same outcome as general relativity (GR) for every classical solar-system test. This theory also admits gravitational waves that propagate at the speed of light, and the gravitational radiation energy loss in a binary system is shown to be very similar to the GR prediction. We then analyze the strong gravity regime of the theory for a spherically symmetric configuration and find that there is an effective ‘singularity’ near the Schwarzschild radius. The main goal of this work is to show that, contrary to what is commonly believed, there are relativistic scalar theories of gravitation defined on a Minkowski spacetime that are not ruled out by the classical solar system tests of GR.

Particles of Negative and Zero Energy in Black Holes and Cosmological Models

Particles with negative energies are considered for three different cases: inside the horizon of a Schwarzschild black hole, Milne’s coordinates in flat Minkowski space–time (Milne’s universe using nonsynchronous coordinates) and in the cosmological Gödel model of the rotating universe. It is shown that, differently from the Gödel model with a nondiagonal term, where it occurs that negative energies are impossible, they are present in all other cases considered in the paper. Particles with zero energy are also possible in the first two cases.

Gravidynamics, spinodynamics and electrodynamics within the framework of gravitational quantum field theory

By noticing the fact that the charged leptons and quarks in the standard model are chirality-based Dirac spinors since their weak interaction violates maximally parity symmetry though they behave as Dirac fermions in electromagnetic interaction, we show that such a chirality-based Dirac spinor possesses not only electric charge gauge symmetry U(1) but also inhomogeneous spin gauge symmetry WS(1,3) = SP(1,3)$\rtimes$W$^{1,3}$, which reveals the nature of gravity and spacetime. The gravitational force and spin gauge force are governed by the gauge symmetries $W^{1,3}$ and SP(1,3), respectively, and a biframe spacetime with globally flat Minkowski spacetime as base spacetime and locally flat gravigauge spacetime as a fiber is described by the gravigauge field through emergent non-commutative geometry. The gauge-geometry duality and renormalizability in gravitational quantum field theory (GQFT) are carefully discussed. A detailed analysis and systematic investigation on gravidynamics and spinodynamics as well as electrodynamics are carried out within the framework of GQFT. A full discussion on the generalized Dirac equation and Maxwell equation as well as Einstein equation and spin gauge equation is made in biframe spacetime. New effects of gravidynamics as extension of general relativity are particularly analyzed. All dynamic equations of basic fields are demonstrated to preserve the spin gauge covariance and general coordinate covariance due to the spin gauge symmetry and emergent general linear group symmetry GL(1,3,R), so they hold naturally in any spinning reference frame and motional reference frame.

Near-horizon quantum dynamics of 4D Einstein gravity from 2D Jackiw-Teitelboim gravity

We study quantum fluctuations in the light-cone metric of the 4D Einstein-Hilbert action via dimensional reduction to Jackiw-Teitelboim (JT) gravity. In particular, we show that, in Einstein gravity, the causal development of a region in flat Minkowski spacetime, near a horizon defined by light sheets, can be described by an effective two-dimensional dilaton theory. This enables us to make use of known solutions of the JT action, where the spacetime position of a horizon has quantum uncertainty due to metric fluctuations. This quantum uncertainty can be then directly related to the original 4D light-cone coordinates, allowing us to compute the uncertainty in the time of a photon to travel from tip-to-tip of a causal diamond in flat 4D Minkowski space. We find that both Planck and infrared scales (with the latter set by the size of the causal diamond) enter the uncertainty in photon travel time, such that the quantum fluctuation in the arrival time may be observably large.

Proposed method of combining continuum mechanics with Einstein Field Equations

The paper proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress–energy tensor for a system with an electromagnetic field leads to the solution of Einstein Field Equations indicating a relationship between the electromagnetic field tensor and the metric tensor. In this EFE solution, the cosmological constant is related to the invariant of the electromagnetic field tensor, and additional pulls appear, dependent on the vacuum energy contained in the system. In flat Minkowski spacetime, the vanishing four-divergence of the proposed stress–energy tensor expresses relativistic Cauchy’s momentum equation, leading to the emergence of force densities which can be developed and parameterized to obtain known interactions. Transformation equations were also obtained between spacetime with fields and forces, and a curved spacetime reproducing the motion resulting from the fields under consideration, which allows for the extension of the solution with new fields.

Accelerated motion in general relativity: fate of the singularity

Under general relativity, the paths of accelerated test particles are taken into account. It is examined whether such accelerations have any influence on the ‘singularity’ of the spacetime. The Raychaudhuri equation for the congruence of the time-like curves describing the paths of the accelerated particles is considered to calculate a few physical attributes. It is shown that if the acceleration of the test particles exceeds a particular value, then the congruences of the accelerated time-like curves do not encounter any singularity although the usual energy conditions are violated or modified. It is shown further that in the curved spacetime of general relativistic framework one may generate a system of transformations that is a generalization of the Rindler coordinates related to accelerated frame in the flat Minkowski spacetime. To show the influence of the acceleration of test particle on singularity of a particular spacetime the Schwarzschild spacetime is considered. Taking tidal deviation related acceleration term, it is shown that the acceleration may attain a specific value for which the modified Kretschmann scalar vanishes in a spherical neighbourhood of the singularity and thus the Schwarzschild singularity disappears. In the context of singularity as ‘geodesic incompleteness’ of the spacetime manifold it is also proved that prescribing an appropriate acceleration term on the maximal geodesic defined in a finite interval one may extend it up to infinite proper time and hence the spacetime becomes singularity free. Such results hold at the price of violating the usual energy conditions.

Quantum theory of Weyl-invariant scalar-tensor gravity

We perform a manifestly covariant quantization of a Weyl-invariant (i.e., a locally scale-invariant) scalar-tensor gravity in the extended de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance and a new scalar gauge for Weyl invariance within the framework of the BRST formalism. We show that choral symmetry, which is a Poincar\'e-like $IOSp(8|8)$ supersymmetry in the case of Einstein gravity, is extended to a Poincar\'e-like $IOSp(10|10)$ supersymmetry. We point out that there is a gravitational conformal symmetry in quantum gravity and account for how conventional conformal symmetry in a flat Minkowski space-time is related to the gravitational conformal symmetry. Moreover, we examine the mechanism of the spontaneous symmetry breaking of the choral symmetry, and show that the gravitational conformal symmetry is spontaneously broken to the Poincar\'e symmetry and the corresponding massless Nambu-Goldstone bosons are the graviton and the dilaton. We also prove the unitarity of the physical $S$ matrix on the basis of the BRST quartet mechanism.

Analogue Metric in a Black-Bounce Background

The conventional approach of embedding an effective acoustic metric for sound motion in a background flat Minkowski space-time has recently been extended to incorporate more general curved background metrics, which might contain a black hole. Though the observational aspects of these kinds of acoustics horizons, including the sonic shadow structure and quasi normal modes, have received significant attention in the literature, there is room left for discussions about embedding more general classes of curved background space-times without optical horizons. Here, we propose and study a new class of acoustic metrics that is embedded in a black-bounce space-time, thereby giving a suitable tuneable system to understand possible observational effects of the presence or absence of acoustic horizons. After showing that the metric can represent five types of different effective backgrounds for sound motion, including a novel “acoustic wormhole–optical wormhole” branch, we discuss how the distinctive features of sonic shadows can appear even in the absence of any acoustic horizon due to the wormhole throat present in the acoustic metric.

The effective Dirac algebra by gauge field interaction in relativistic electrodynamics

Conventional relativistic electrodynamics is set on flat Minkowski spacetime, where all computable quantities are calculated from the flat metric [Formula: see text]. We can redefine the metric of spacetime from the Dirac algebra. In this paper, we study how an electrodynamic interaction can alter the normal gamma matrix to an effective one and result in a shift in the metric perturbatively. The curvature properties inferred from the curved metric are also investigated. We also study how the spin operator is changed under the interaction that contributes to an effective spin operator and how the spin of an electron will be slightly deviated from [Formula: see text]. Then we perform canonical quantization of the effective Dirac algebra. Finally, we apply our results to the relativistic hydrogen case and demonstrate how such system curves the spacetime metric.

Massless charged wormhole solution in Einstein\u2013Maxwell-Scalar theory

A new exact wormhole solution in Einstein–Maxwell-Scalar theory is introduced. The wormhole solution is accompanied by a non-black hole naked singular branch solution. Both of the solutions are massless such that with charge zero the spacetime coincides with the vacuum Minkowski flat spacetime. In addition to that, the wormhole solution seems to be the missing part of the class of solutions in the standard Einstein–Maxwell-Dilaton theory with an arbitrary dilaton parameter.

On the Vacuum Structure of the N=4 Conformal Supergravity

We consider N=4 conformal supergravity with an arbitrary holomorphic function of the complex scalar S which parametrizes the SU(1,1)/U(1) coset. Assuming non-vanishings vevs for S and the scalars in a symmetric matrix Eij of the 10¯ of SU(4) R-symmetry group, we determine the vacuum structure of the theory. We find that the possible vacua are classified by the number of zero eigenvalues of the scalar matrix and the spacetime is either Minkowski, de Sitter, or anti-de Sitter. We determine the spectrum of the scalar fluctuations and we find that it contains tachyonic states which, however, can be removed by appropriate choice of the unspecified at the supergravity level holomorphic function. Finally, we also establish that S-supersymmetry is always broken whereas Q-supersymmetry exists only on flat Minkowski spacetime.

Electrodynamics in noninertial frames

The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relativistic formulation of Maxwell’s electrodynamics arises in the flat Minkowski spacetime when the general coordinate transformations are restricted to a class of transformations preserving the Minkowski line element. The particular attention is paid to the analysis of the electromagnetism in the noninertial rotating reference system. For the latter case, the general stationary solution of the Maxwell equations in the absence of the electric current is constructed in terms of the two scalar functions satisfying the Poisson and the biharmonic equations with an arbitrary charge density as a matter source. The classic problem of Schiff is critically revisited.

Restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry

In this paper, we elucidate the relation between the restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry. Using a scalar–tensor gravity, we show that the restricted Weyl symmetry leads to spontaneous symmetry breakdown of a global scale symmetry when the vacuum expectation value of a scalar field takes a nonzero value. It is then shown that this spontaneous symmetry breakdown induces spontaneous symmetry breakdown of special conformal symmetry in a flat Minkowski spacetime, but the resultant Nambu–Goldstone boson is not an independent physical mode but expressed in terms of the derivative of the dilaton which is the Nambu–Goldstone boson of the global scale symmetry. In other words, the theories which are invariant under the general coordinate transformation and the restricted Weyl transformation exhibit a Nambu–Goldstone phase where both special conformal transformation and dilatation are spontaneously broken while preserving the Poincaré symmetry.

Analyzing the Effects of Topological Defect (TD) on the Energy Spectra and Thermal Properties of LiH, TiC and I2 Diatomic Molecules.

In this study, the impacts of TD on the energy spectra and thermal properties of LiH, TiC and I2 diatomic molecules is considered. The Schrodinger equation in cosmic string spacetime is solved with the generalized Morse potential using the well-known (NU) method. The energy spectra and eigenfunction are obtained respectively. The energy spectra is used to obtain the partition function which is then used to evaluate the thermal properties of the system is evaluated accordingly. We find that the energy spectra in the presence of the TD differ from their flat Minkowski spacetime analogue. The effects of the deformation parameter and TD on the thermal properties of the system is also analysed in detail. We observe that the specific heat capacity of the system tends to exhibit quasi-saturation as the deformation parameter and topological defect approaches unity. The results of our study can be applied in the astrophysical situation where these modifications exist in the understanding of spectroscopical data and it may be used as a probe of the presence of a cosmic string or a global monopole in the Universe.