Field Equations Of Relativity Research Articles

Whence Nonlocality? Removing Spooky Action-at-a-Distance from the de Broglie Bohm Pilot-Wave Theory Using a Time-Symmetric Version of the de Broglie Double Solution

In this work, we review and extend a version of the old attempt made by Louis de Broglie for interpreting quantum mechanics in realistic terms, namely, the double solution. In this theory, quantum particles are localized waves, i.e., solitons, that are solutions of relativistic nonlinear field equations. The theory that we present here is the natural extension of this old work and relies on a strong time-symmetry requiring the presence of advanced and retarded waves converging on particles. Using this method, we are able to justify wave–particle duality and to explain the violations of Bell’s inequalities. Moreover, the theory recovers the predictions of the pilot-wave theory of de Broglie and Bohm, often known as Bohmian mechanics. As a direct consequence, we reinterpret the nonlocal action-at-a-distance in the pilot-wave theory. In the double solution developed here, there is fundamentally no action-at-a-distance but the theory requires a form of superdeterminism driven by time-symmetry.

Cosmological solutions of chameleon scalar field model

We investigate cosmological solutions of the chameleon model with a non-minimal coupling between the matter and the scalar field through a conformal factor with gravitational strength. By considering the spatially flat FLRW metric and the matter density as a non-relativistic perfect fluid, we focus on the matter-dominated phase and the late-time accelerated-phase of the universe. In this regard, we manipulate and scrutinize the related field equations for the density parameters of the matter and the scalar fields with respect to the e-folding. Since the scalar field fluctuations depend on the background and the field equations become highly non-linear, we probe and derive the governing equations in the context of various cases of the relation between the kinetic and potential energies of the chameleon scalar field, or indeed, for some specific cases of the scalar field equation of state parameter. Thereupon, we schematically plot those density parameters for two different values of the chameleon non-minimal coupling parameter, and discuss the results. In the both considered phases, we specify that, when the kinetic energy of the chameleon scalar field is much less than its potential energy (i.e., when the scalar field equation of state parameter is ≃-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\simeq - 1 $$\\end{document}), the behavior of the chameleon model is similar to the ΛCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda CDM$$\\end{document} model. Such compatibility suggests that the chameleon model is phenomenologically viable and can be tested with the observational data.

On generalized Rayleigh waves in a pre-stressed piezoelectric medium

This research aims to study the different phenomena of generalized Rayleigh waves (RWs) in composite structures with piezoelectric material and corrugated surfaces. A thin piezoelectric layer that is precisely attached to an elastic substrate with initial stresses makes up the structure under consideration. By resolving the related electromechanical field equations, expressions for the displacement potential function are produced for both the elastic substrate and the piezoelectric layer. The frequency equations of the studied wave have been discovered as determinants for electrically open and short conditions. There have been both numerical illustrations and graphical demonstrations. On the stage speed of the combined RW, the impact of the grooved border, initial pressure, piezoelectric constant, dielectric constant, and thickness of the piezoelectric layer have been studied. Additionally, the analytical solution to the issue is compared to and shown to be in good agreement with the stiffness matrix approach result. This study offers a theoretical foundation for creating and developing piezoelectric composite-based devices. It has been found that the generalized RW velocity declines with the increase of the values of [Formula: see text] and [Formula: see text] and an inverse relationship has been found with the increase of the value of [Formula: see text]. In addition, it has also been noticed that the velocity profile of the generalized RW is greatly influenced by the size of the corrugation (measured at the upper layer).

Relativistic modeling of stellar objects in a Schwarzschild’s coordinates with embedded class one spacetime

In this study, we investigate a new relativistic anisotropic Einstein field equations solution for compact stars under embedding class 1 conditions. In order to do this, we apply the Karmarkar condition and the embedding class one technique. By taking Buchdahl type metric potential g_{rr} into consideration, the precise analytical solution has been investigated. We have studied physical characteristics of various compact star using this analytical solution. Central singularities are absent from the solution. We have explored thermodynamic observables inside the stellar models, such as radial and tangential pressures, matter density, anisotropic factor, energy conditions, TOV, red-shift, and the speed of sound, etc., after establishing this space-time geometry for the stellar models. From the graphical representation of various physical characteristics, it is demonstrated that our model meets all the specification for ultra-high density compact bodies.

Unimodular gravity traversable wormholes

Wormholes are outstanding solutions of Einstein’s General Relativity. They were worked out in the late 1980s by Morris and Thorne, who have figured out a recipe that wormholes must obey in order to be traversable, that is, safely crossed by travelers. A remarkable feature is that General Relativity Theory wormholes must be filled by exotic matter, which Morris and Thorne define as matter satisfying $$-p_r>\rho$$ , in which $$p_r$$ is the radial pressure and $$\rho$$ is the energy density of the wormhole. In the present article, we introduce, for the first time in the literature, traversable wormhole solutions of Einstein’s Unimodular Gravity Theory. Unimodular Gravity was proposed by Einstein himself as the theory for which the field equations are the traceless portion of General Relativity field equations. Later, Weinberg has shown that this approach elegantly yields the solution of the infamous cosmological constant problem. The wormhole solutions here presented satisfy the metric conditions of “traversability” and remarkably evade the exotic matter condition, so we can affirm that Unimodular Gravity wormholes can be filled by ordinary matter.

Diffraction for the Dirac–Coulomb Propagator

The Dirac equation in $$\mathbb {R}^{1,3}$$ with potential $${\textsf{Z}}/r$$ is a relativistic field equation modeling the hydrogen atom. We analyze the singularity structure of the propagator for this equation, showing that the singularities of the Schwartz kernel of the propagator are along an expanding spherical wave away from rays that miss the potential singularity at the origin, but also may include an additional spherical wave of diffracted singularities emanating from the origin. This diffracted wavefront is $$1-{\epsilon }$$ derivatives smoother than the main singularities, for all $${\epsilon }>0,$$ and is a conormal singularity.

Simulation of Closed Timelike Curves in a Darwinian Approach to Quantum Mechanics

Closed timelike curves (CTCs) are non-intuitive theoretical solutions of general relativity field equations. The main paradox associated with the physical existence of CTCs, the so-called grandfather paradox, can be satisfactorily solved by a quantum model named Deutsch-CTC. An outstanding theoretical result that has been demonstrated in the Deutsch-CTC model is the computational equivalence of a classical and a quantum computer in the presence of a CTC. In this article, in order to explore the possible implications for the foundations of quantum mechanics of that equivalence, a fundamental particle is modelled as a classical-like system supplemented with an information space in which a randomizer and a classical Turing machine are stored. The particle could then generate quantum behavior in real time in case it was controlled by a classical algorithm coding the rules of quantum mechanics and, in addition, a logical circuit simulating a CTC was present on its information space. The conditions that, through the action of evolution under natural selection, might produce a population of such particles with both elements on their information spaces from initial sheer random behavior are analyzed.

How Classical, Quantum-Mechanical, and Relativistic Wave and Field Equations Are Uniformly Generated by Velocity-Field Divergence Equations

How Classical, Quantum-Mechanical, and Relativistic Wave and Field Equations Are Uniformly Generated by Velocity-Field Divergence Equations

Matter and antimatter asymmetry in a rainbow universe

In rainbow gravity, the ordinary general relativity (GR) field equations can be modified by a parametric set of equations and thus the cosmology of this scenario may give new sounds about the physics of the early universe. As we know in the radiation-dominated universe the gravitational baryogenesis mechanism (GBM) cannot occur in the GR context. In this regard, by assuming the flat Friedmann–Robertson–Walker (FRW) metric we study GBM in the rainbow gravity. We obtain that for a rainbow universe filled with radiation, the baryon-to-entropy ratio from the GBM can have a non-zero value. In this work, we study the baryon-to-entropy ratio for the corresponding cosmological models of two suggested dispersion relations and we obtain that in the first case the baryogenesis mechanism occurs and also the results are compatible with the observational constraints while the second case is not consistent with the observational constraints.

Sources of irregular energy density in energy–momentum squared gravity with charge

This manuscript studies the inhomogeneity in the energy density for the relativistic dynamical charged system by invoking the outcomes coming from the considered anisotropic distribution of radiating fluid. We use newly developed f(G,T2) theory, which was proposed by the addition of T2=TζξTζξ in the usual action of f(G,) gravity. We construct relativistic field equations for a specific model f(G,T2)=λT2+G(1+Gα), to examine the gravitational structure in the influence of electromagnetic filed. We use dynamical expressions and differential equations for Weyl tensor for the inspection of sources of irregularities. By exploring special cases in the non-radiating and radiating scenarios, the irregularity elements for a fluid are examined. These special cases show that modified terms and charge have a considerable impact on the fluid inhomogeneity.

Confirming the Existence of Twin Stars in a NICER Way

We demonstrate that future radius measurements of the NICER mission have the potential to reveal the existence of a strong phase transition in dense neutron star matter by confirming the existence of so-called twin stars, compact star configurations with the same mass but different radii. The latest radius constraints from NICER for the pulsars J0740+6620 as well as J0030+0451 are discussed using relativistic mean field equations of state with varying stiffness, connected with a first-order phase transition to quark matter. We show that twin star solutions are compatible with the new radius constraint but are located at radii below the present constraints from NICER, serving as a smoking gun for a strong phase transition in neutron star matter. This scenario is realized if a strong phase transition takes place in neutron stars of the first branch with masses above 2 M ⊙.

On the Field Equations of General Relativity

In this work, we examine the geometric character of the field equations of general relativity and propose to formulate relativistic field equations in terms of the Riemann curvature tensor. The resulted relativistic field equations are also integrated into the general framework that we have presented in our previous works that all known classical fields can be expressed in the same dynamical form. We also discuss a possibility to reformulate the field equations of general relativity so that the Ricci curvature tensor and the energy-momentum tensor can appear symmetrically in the field equations without violating the conservation law stated by the covariant derivative.

A pedagogical review of the vacuum retarded dipole model of pulsar spin down

Abstract Pulsars are rapidly spinning highly magnetised neutron stars. Their spin period is observed to decrease with time. An early analytical model for this process was the vacuum retarded dipole (VRD) by Deutsch (1955, AnAp, 18). This model assumes an idealised star and it finds that the rotational energy is radiated away by the electromagnetic fields. This model has been superseded by more realistic numerical simulations that account for the non-vacuum like surroundings of the neutron star. However, the VRD still provides a reasonable approximation and is a useful limiting case that can provide some qualitative understanding. We provide detailed derivations of the spin down and related electromagnetic field equations of the VRD solution. We also correct typographical errors in the general field equations and boundary conditions used by Deutsch (1955, AnAp, 18).

In search of a variational formulation of the relativistic Navier‐Stokes equations

AbstractDrawing an analogy with Maxwell theory a new Lagrangian is proposed for a variational formulation of the relativistic Navier‐Stokes equations which to‐date has remained elusive. A key feature is the use of tensor potentials, whose degrees of gauge freedom allow for the reformulation of the energy‐momentum equations in a self‐adjoint form. An already existing potential‐based representation of the relativistic field equations is a suitable starting point for the present considerations, which in turn are guided by the already successfully solved case of non‐relativistic, stationary and incompressible flow.

Accretion onto a quintessence contaminated rotating black hole: violating the lower limit for eta over s

Viscous accretion flow around a rotating supermassive black hole sitting in a quintessence tub is studied in this article. To introduce such a dark energy contaminated black hole’s gravitational force, a new pseudo-Newtonian potential is used. This pseudo-Newtonian force can be calculated if we know the distance from the black hole’s center, spin of the black hole and equation of state of the quintessence inside which the black hole is considered to lie. This force helps us to avoid complicated nonlinearity of general relativistic field equations. Transonic, viscous, continuous and Keplerian flow is assumed to take place. Fluid speed, sonic speed profile and specific angular momentum to Keplerian angular momentum ratio are found out for different values of spin parameter and quintessence parameter. Density variation is built and tallied with observations. Shear viscosity to entropy density ratio is constructed for our model and a comparison with theoretical lower limit is done.

New classes of exact interior nonvacuum solutions to the GR field equations for spacetimes sourced by a rigidly rotating stationary cylindrical anisotropic fluid

A double new class of solutions to the general relativity field equations describing interior spacetimes sourced by stationary cylindrical anisotropic fluids with principal stress directed along the symmetry axis is displayed. These solutions are required to satisfy regularity and junction conditions so that they can be possibly used to represent rotating astrophysical objects. Mathematical and physical properties are analyzed. The spacetime two independent parameters are physically interpreted, and they are shown to define two different solution classes together with stating the latters' properties.

The unitary representations of the Poincar\'e group in any spacetime dimension

An extensive group-theoretical treatment of linear relativistic field equations on Minkowski spacetime of arbitrary dimension D\geqslant 3D≥3 is presented. An exhaustive treatment is performed of the two most important classes of unitary irreducible representations of the Poincar'e group, corresponding to massive and massless fundamental particles. Covariant field equations are given for each unitary irreducible representation of the Poincar'e group with non-negative mass-squared.

To Conserve, or Not to Conserve: A Review of Nonconservative Theories of Gravity

Apart from the familiar structure firmly-rooted in the general relativistic field equations where the energy–momentum tensor has a null divergence i.e., it conserves, there exists a considerable number of extended theories of gravity allowing departures from the usual conservative framework. Many of these theories became popular in the last few years, aiming to describe the phenomenology behind dark matter and dark energy. However, within these scenarios, it is common to see attempts to preserve the conservative property of the energy–momentum tensor. Most of the time, it is done by means of some additional constraint that ensures the validity of the standard conservation law, as long as this option is available in the theory. However, if no such extra constraint is available, the theory will inevitably carry a non-trivial conservation law as part of its structure. In this work, we review some of such proposals discussing the theoretical construction leading to the non-conservation of the energy–momentum tensor.

A variational approach to relativistic fluid balls

This paper deals with spherically symmetric static solutions of the relativistic field equation which represents a perfect fluid ball with given equation of state and given baryon number. We prove existence of solutions for baryon numbers that do not exceed a limiting number determined by the equation of state. The proof is based on energy minimization under the given baryon number constraint.

Dilaton black holes with logarithmic source in gravity’s rainbow

Starting from the suitable action of four-dimensional Einstein gravity, which is coupled to a scalar dilaton field and logarithmic nonlinear electrodynamics, the related field equations have been solved in a spherically symmetric and energy-dependent spacetime. It has been found that the scalar potential, as the exact solution of the scalar field equations, must be written as the linear combination of two Liouville-type potentials. Three families of novel exact black holes have been introduced as the exact solutions to the gravitational equations, which are asymptotically non-flat and non-AdS. It has been illustrated that our solutions, recover their corresponding quantities in the Einstein–Maxwell-dilaton gravity theory when the nonlinearity parameter of electrodynamics is chosen very large. The thermodynamic and conserved quantities of the black holes have been calculated under the influence of the rainbow function. Then, through calculation of the Smarr mass formula, we have shown that the first law of black hole thermodynamics remain valid for all of the new dilatonic black holes. Thermal stability or phase transition of the black holes have been investigated by use of the canonical ensemble and thermodynamic geometry approaches, separately. By comparison of the results of these two alternative approaches, it has been found that they lead to the same results provided that the thermodynamic metric of HPEM is used.