Energy-momentum Conservation Law Research Articles

Black bounces in conformal Killing gravity

In this work, we analyse black bounce solutions in the recently proposed “Conformal Killing gravity” (CKG), by coupling the theory to nonlinear electrodynamics (NLED) and scalar fields. The original motivation of the theory was essentially to fulfill specific criteria that are absent in existing gravitational theories, namely, to obtain the cosmological constant as an integration constant, derive the energy–momentum conservation law as a consequence of the gravitational field equations, rather than assuming it, and not necessarily considering conformally flat metrics as vacuum solutions. In this work, we extend the static and spherically symmetric solutions obtained in the literature, and explore the possibility of black bounces in CKG, coupled to NLED and scalar fields. We find novel NLED Lagrangian densities and scalar potentials, and extend the class of black bounce solutions found in the literature. Furthermore, within black bounce geometries, we find generalizations of the Bardeen-type and Simpson–Visser geometries and explore the regularity conditions of the solutions.

Flat from anti de Sitter

Ricci-flat solutions to Einstein’s equations in four dimensions are obtained as the flat limit of Einstein spacetimes with negative cosmological constant. In the limiting process, the anti-de Sitter energy-momentum tensor is expanded in Laurent series in powers of the cosmological constant, endowing the system with the infinite number of boundary data, characteristic of an asymptotically flat solution space. The governing flat Einstein dynamics is recovered as the limit of the original energy-momentum conservation law and from the additional requirement of the line-element finiteness, providing at each order the necessary set of flux-balance equations for the boundary data. This analysis is conducted using a covariant version of the Newman-Unti gauge designed for taking advantage of the boundary Carrollian structure emerging at vanishing cosmological constant and its Carrollian attributes such as the Cotton tensor.

Variational formulation of higher-order guiding-center Vlasov–Maxwell theory

Extended guiding-center Vlasov–Maxwell equations are derived under the assumption of time-dependent and inhomogeneous electric and magnetic fields that obey the standard guiding-center space-timescale orderings. The guiding-center Vlasov–Maxwell equations are derived up to second order, which contains dipole and quadrupole contributions to the guiding-center polarization and magnetization that include finite-Larmor-radius corrections. Exact energy-momentum conservation laws are derived from the variational formulation of these higher-order guiding-center Vlasov–Maxwell equations.

Estimation of air-bubble-induced wave height and set-up using representative wave approach

ABSTRACT This study aimed to investigate the possibility of modeling the wave height and set-up by using the representative wave method caused by air bubbles in irregular waves in the surf zone. Two regular wave-breaking models with air bubble effects were directly employed in the irregular waves and modified to obtain new irregular wave-breaking models. These models can be used to compute the root mean square (RMS) wave height and wave set-up based on the conservation laws of energy flux and momentum. Model I was solved analytically for a beach with a plane slope and numerically for a beach with an irregular slope for spilling and plunging breakers, separately. Additionally, model II was solved numerically for both slope types and breaking conditions. The modified models were calibrated and validated using a large amount of experimental data and a broad range of trial situations. These conditions included large-scale, small-scale, and field experiments. Finally, it was discovered that the modified models had excellent accuracy in computing the wave heights and set-ups. In terms of accuracy, Model I outperformed Model II for the computation of the RMS wave height and set-up of wave breakers in irregular waves.

Thermodynamic stability and holographic heat engine efficiency of a Kerr–Newmann-NUT-Kiselev-AdS black hole in Rastall gravity

Einstein’s general relativity was modified to the Rastall gravity by generalizing the energy–momentum conservation law to T;μμν=λRν and for this change in the covariant conservation of Tμν the thermodynamic characteristics also show some interesting properties. Here we discuss the thermodynamics, phase transition, stability and heat engine construction of a Kerr–Newman-NUT-Kiselev-AdS black hole in 4D Rastall gravity. We consider the space to be surrounded by dark energy, a specific perfect fluid matter. The dark energy has significant effects on the thermodynamic variables of the black hole. Here, the energy condition constraints the Rastall parameter (λ). We finally find that the equation-of-state is related to the Rastall parameter (λ) even when it is reduced to the critical point. The cosmological constant leads us to consider the black hole as a heat engine and determine the efficiency of the Carnot cycle for the black hole. In conclusion, we discuss possible methodologies for constraining the black hole parameters from astrophysical observations.

Wormhole solution in modified teleparallel-Rastall gravity and energy conditions

The possibility of static and spherically symmetric traversable wormhole solution in modified teleparallel Rastall gravity (MTRG) in a non-diagonal tetrad is investigated. Rastall assumption modifies the field equations and energy-momentum conservation law. These modifications lead to different exact asymptotically flat traversable wormhole solutions. By imposing different constraints on modified energy-momentum conservation law, different exact solutions are found and the obtained results for teleparallel Rastall gravity (TRG), with specific choices of $f(T)$, are studied. It is shown that the Rastall parameters have a key role in these models and in all of those exact traversable wormhole solutions the null energy condition (NEC) and weak energy condition (WEC) of matter or energy which has surrounded the wormhole are valid at the throat of the wormhole and through the space time as well.

Proportionality of gravitational and electromagnetic radiation by an electron in an intense plane wave

Accelerated charges emit both electromagnetic and gravitational radiation. Classically, it was found that the electromagnetic energy spectrum radiated by an electron in a monochromatic plane wave is proportional to the corresponding gravitational one. Quantum mechanically, it was shown that the amplitudes of graviton photoproduction and Compton scattering are proportional to each other at tree level. Here, by combining strong-field QED and quantum gravity, we demonstrate that the amplitude of nonlinear graviton photoproduction in an arbitrary plane wave is proportional to the corresponding amplitude of nonlinear Compton scattering. Also, introducing classical amplitudes we prove that the proportionality relies on the semiclassical nature of the electron's motion in a plane wave and on energy-momentum conservation laws, leading to the same proportionality constant in the classical and quantum case. These results deepen the intertwine between gravity and electromagnetism into both a nonlinear and a quantum level.

Mathematical foundations for field theories on Finsler spacetimes

This paper introduces a general mathematical framework for action-based field theories on Finsler spacetimes. As most often fields on Finsler spacetime (e.g., the Finsler fundamental function or the resulting metric tensor) have a homogeneous dependence on the tangent directions of spacetime, we construct the appropriate configuration bundles whose sections are such homogeneous fields; on these configuration bundles, the tools of coordinate free calculus of variations can be consistently applied to obtain field equations. Moreover, we prove that the general covariance of natural Finsler field Lagrangians leads to an averaged energy–momentum conservation law that, in the particular case of Lorentzian spacetimes, is equivalent to the usual pointwise energy–momentum covariant conservation law.

A new conservative finite difference scheme for 1D Cahn–Hilliard equation coupled with elasticity

Abstract In this article, we give analysis for a structure-preserving finite difference scheme to the Cahn–Hilliard system coupled with elasticity in one space dimension. In the previous article [K. Shimura and S. Yoshikawa, Error estimate for structure-preserving finite difference schemes of the one-dimensional Cahn–Hilliard system coupled with viscoelasticity, Regularity and Asymptotic Analysis for Critical Cases of Partial Differential Equations, RIMS Kôkyûroku Bessatsu B82, Research Institute for Mathematical Sciences (RIMS), Kyoto 2020, 159–175], we studied the system coupled with viscoelasticity, where we proposed a conservative numerical scheme for the system which inherits the total energy conservation and momentum conservation laws, and showed the error estimate. However, the error estimate can not be applied to the system without viscosity, due to the fact that the proof relies on the viscous term. Here, we show the error estimate for the system without viscosity by proposing a new structure-preserving finite difference scheme for the system. In addition, we also give the proof of existence of solution for the scheme.

Hidden Killing fields, geometric symmetries and black hole mergers

In the present work, using the recently introduced framework of local geometric deformations, special types of vector fields – so-called hidden Killing vector fields – are constructed, which solve the Killing equation not globally, but only locally, i.e. in local subregions of spacetime. Taking advantage of the fact that the vector fields coincide locally with Killing fields and therefore allow the consideration of integral laws that convert into exact physical conservation laws on local scales, balance laws in dynamical systems without global Killing symmetries are derived that mimic as closely as possible the conservation laws for energy and angular momentum of highly symmetric models. The utility of said balance laws is demonstrated by a concrete geometric example, namely a toy model for the binary merger of two extremal Reissner–Nordström black holes.

Discovering exact, gauge-invariant, local energy–momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds

Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas. However, exact local energy–momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite continuous effort. Without such local conservation laws, energy and momentum can be instantaneously transported across spacetime, which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory. The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic field reside on different manifolds. To overcome this difficulty, we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact, local conservation laws, in particular the energy–momentum conservation laws, for the electromagnetic gyrokinetic system. A weak Euler–Lagrange (EL) equation is established to replace the standard EL equation for the particles. It is discovered that an induced weak EL current enters the local conservation laws, and it is the new physics captured by the high-order field theory on heterogeneous manifolds. A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy–momentum conservation laws electromagnetic gauge-invariant.

Gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories

For electromagnetic field theories, canonical energy-momentum conservation laws can be derived from the underpinning spacetime translation symmetry according to the Noether procedure. However, the canonical Energy-Momentum Tensors (EMTs) are neither symmetric nor gauge-symmetric (gauge invariant). The Belinfante-Rosenfeld (BR) method is a well-known procedure to symmetrize the EMTs, which also renders them gauge symmetric for first-order field theories. High-order electromagnetic field theories appear in the study of gyrokinetic systems for magnetized plasmas and the Podolsky system for the radiation reaction of classical charged particles. For these high-order field theories, gauge-symmetric EMTs are not necessarily symmetric and vice versa. In the present study, we develop a new gauge-symmetrization method for EMTs in high-order electromagnetic field theories. The Noether procedure is carried out using the Faraday tensor F, instead of the 4-potential A, to derive a canonical EMT T_N. We show that the gauge-dependent part of T_N can be removed using the displacement-potential tensor \mathcal{F}=\mathcal{D}*A/4\pi, where \mathcal{D} is the anti-symmetric electric displacement tensor. This method gauge-symmetrize the EMT without necessarily making it symmetric, which is adequate for applications not involving general relativity. For first-order electromagnetic field theories, such as the standard Maxwell system, \mathcal{F} reduces to the familiar BR super-potential \mathcal{S}, and the method developed can be used as a simpler procedure to calculate \mathcal{S} without employing the angular momentum tensor in 4D spacetime. When the electromagnetic system is coupled to classical charged particles, the gauge-symmetrization method for EMTs is shown to be effective as well.

Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.

Four Bosons EM Conservation Laws

Electromagnetism is expressed from two basic postulates. They are light invarianceand charge conservation. At this work one extends the Maxwell scenario from macroscopic to microscopic electromagnetism by following the elementary particles electric charge microscopic behavior. It yields a triune electric charge interrelationship. Three charges {+, 0, −} be exchanged through a vector bosons quadruplet. It is called Four Bosons Electromagnetism. A systemic EM physics appears to be understood. Maxwell photon is not enough for describing the microscopic electric charge physics. An extension for electromagnetic energy is obtained. The fields quadruplet {Aµ, Uµ, Vµ±} are the porters of electromagnetic energy. They are the usual photon Aµ, massive photon Uµ and two charged photons Vµ±, A new understanding on EM phenomena has to be considered. A set determinism based on granular and collective fields is developed. A space-time evolution associated to a whole.Conservation laws are studied. The EM phenomena is enlarged to three charges interchanges to {+, 0, −}. Two novelties appear. New features on nonlinear fields acting as own sources and on electric charge physics. Properties as conservation, conduction, transmission, interaction are extended to a systemic electromagnetism. A whole conservation law for electric charge emerges from three charges interwoven. Electric charge has a systemic behavior. Although there is no Coulomb law for zero electric charge, the Four Bosons Electromagnetism contains an EM energy which provides a neutral electromagnetism. Particles with zero charge {Aµ, Uµ} are carrying EM energy. Another consideration is on EM energy being transported by four nonlinear fields. A new physicality appears. The abelian nonlinearity generates fields charges. Fields are working as own sources through mass terms, trilinear and quadrilinear interactions, spin couplings. Consequently the photon is more than being a consequence from electric charge oscillations. It is able to generate its own charge. Introduce the meaning of photonics.Thus, electric charge is no more the isolate electromagnetic source. There are another conservation laws. Fields sources appear through corresponding equations of motion, Bianchi identities, energy-momentum, Noether laws and angular momentum conservation laws. They move EM to a fields charges dependence. Together with electric charge they carrythe electromagnetic flux. Supporting the Ahranov-Bohm experiment of potential fields as primitive entities.

Exact conservation laws for gauge-free electromagnetic gyrokinetic equations

The exact energy and angular momentum conservation laws are derived by the Noether method for the Hamiltonian and symplectic representations of the gauge-free electromagnetic gyrokinetic Vlasov–Maxwell equations. These gyrokinetic equations, which are solely expressed in terms of electromagnetic fields, describe the low-frequency turbulent fluctuations that perturb a time-independent toroidally-axisymmetric magnetized plasma. The explicit proofs presented here provide a complete picture of the transfer of energy and angular momentum between the gyrocentres and the perturbed electromagnetic fields, in which the crucial roles played by gyrocentre polarization and magnetization effects are highlighted. In addition to yielding an exact angular momentum conservation law, the gyrokinetic Noether equation yields an exact momentum transport equation, which might be useful in more general equilibrium magnetic geometries.

Robustness of Noether’s Principle: Maximal Disconnects between Conservation Laws and Symmetries in Quantum Theory

To what extent does Noether's principle apply to quantum channels? Here, we quantify the degree to which imposing a symmetry constraint on quantum channels implies a conservation law, and show that this relates to physically impossible transformations in quantum theory, such as time-reversal and spin-inversion. In this analysis, the convex structure and extremal points of the set of quantum channels symmetric under the action of a Lie group $G$ becomes essential. It allows us to derive bounds on the deviation from conservation laws under any symmetric quantum channel in terms of the deviation from closed dynamics as measured by the unitarity of the channel. In particular, we investigate in detail the $U(1)$ and $SU(2)$ symmetries related to energy and angular momentum conservation laws. In the latter case, we provide fundamental limits on how much a spin-$j_A$ system can be used to polarise a larger spin-$j_B$ system, and on how much one can invert spin polarisation using a rotationally-symmetric operation. Finally, we also establish novel links between unitarity, complementary channels and purity that are of independent interest.

Energy and momentum conservation in spin transfer

We utilize simulations of spin-polarized electron scattering by a chain of localized quantum spins to show that energy and linear momentum conservation laws impose strong constraints on the properties of magnetic excitations induced by spin transfer. In turn, electron's orbital and spin dynamics depends on the dynamical characteristics of the local spins. Our results suggest the possibility to achieve precise control of spin transfer-driven magnetization dynamics by tailoring the spectral characteristics of the magnetic systems and the driving electrons.

On the 12C Hoyle state gamma decay

The γ-decays of 12C excited levels (the Hoyle state 0+ at 7.65 MeV and the 9.64 MeV 3) are essential for its production in the universe. We present here a new attempt to precisely measure such γ-decay probabilities. The measurement was performed at INFN-LNS in Catania using the 4π CHIMERA multidetector. In order to measure these low probability decay-channels we performed 4-fold coincidence measurements. The 12C target nuclei were excited by using a beam of 64 MeV α-particles produced by the Superconducting Cyclotron (CS) of INFN-LNS. The scattered α-particles and the 12C recoils were detected and identified by? E-E and ToF methods using CHIMERA telescopes. The two emitted γ-rays in the decay chain were detected and identified by using the second stage of the telescopes, CsI(Tl) scintillators, by means of fast-slow and rise time techniques. Kinematics and energy-momentum conservation laws were used to constrain the data analysis. Also the 3-α decay channel probability was measured. Such a simultaneous measurement of all known decay channels was useful to reduce the systematic errors. Preliminary results of the data analysis are reported.

Symmetries and Their Breaking in the Fundamental Laws of Physics

Symmetries in the Physical Laws of Nature lead to observable effects. Beyond the regularities and conserved magnitudes, the last few decades in particle physics have seen the identification of symmetries, and their well-defined breaking, as the guiding principle for the elementary constituents of matter and their interactions. Flavour SU(3) symmetry of hadrons led to the Quark Model and the antisymmetric requirement under exchange of identical fermions led to the colour degree of freedom. Colour became the generating charge for flavour-independent strong interactions of quarks and gluons in the exact colour SU(3) local gauge symmetry. Parity Violation in weak interactions led us to consider the chiral fields of fermions as the objects with definite transformation properties under the weak isospin SU(2) gauge group of the Unifying Electro-Weak SU(2) × U(1) symmetry, which predicted novel weak neutral current interactions. CP-Violation led to three families of quarks opening the field of Flavour Physics. Time-reversal violation has recently been observed with entangled neutral mesons, compatible with CPT-invariance. The cancellation of gauge anomalies, which would invalidate the gauge symmetry of the quantum field theory, led to Quark–Lepton Symmetry. Neutrinos were postulated in order to save the conservation laws of energy and angular momentum in nuclear beta decay. After the ups and downs of their mass, neutrino oscillations were discovered in 1998, opening a new era about their origin of mass, mixing, discrete symmetries and the possibility of global lepton-number violation through Majorana mass terms and Leptogenesis as the source of the matter–antimatter asymmetry in the universe. The experimental discovery of quarks and leptons and the mediators of their interactions, with physical observables in spectacular agreement with this Standard Theory, is the triumph of Symmetries. The gauge symmetry is exact only when the particles are massless. One needs a subtle breaking of the symmetry, providing the origin of mass without affecting the excellent description of the interactions. This is the Brout–Englert–Higgs Mechanism, which produces the Higgs Boson as a remnant, discovered at CERN in 2012. Open present problems are addressed with by searching the New Physics Beyond-the-Standard-Model.

Accelerating Model of a Flat Universe in $$\boldsymbol{f(R,T)}$$ Gravity

The $f(R,T)$ theory of gravitation is an extended theory of gravitation in which the gravitational action contains both the Ricci scalar $R$ and the trace of energy momentum tensor $T$ and hence the cosmological models based on $f(R,T)$ gravity are eligible to describing late time acceleration of present universe. In this paper, we investigate an accelerating model of flat universe with linearly varying deceleration parameter (LVDP). We apply the linearly time varying law for deceleration parameters that generates a model of transitioning universe from early decelerating phase to current accelerating phase. We carry out the state-finder and Om(z) analysis, and obtain that LVDP model have consistency with astrophysical observations. We also discuss profoundly the violation of energy-momentum conservation law in $f(R,T)$ gravity and dynamical behavior of the model.