Field Equations Of Relativity Research Articles

High Index SMES Device for Gravitomagnetic Field Generation

A method is described for creating a measurable unbalanced gravitational acceleration using a gravitomagnetic field surrounding a superconducting toroid as described by Forward (1962). An experimental Superconducting Magnetic Energy Storage (SMES) toroid configuration of wound superconducting nanowire is proposed to create a measurable acceleration field along the axis of symmetry, providing experimental confirmation of the additive nature of a Lense-Thirring derived gravitomagnetic field. In the present paper, gravitational coupling enhancement of this effect is explored using a high index or high permittivity material, as predicted by Sarfatti (2020) using his modification to Einstein’s General Relativity Field Equations for gravitational coupling in matter.

Gravitational waves in higher order teleparallel gravity

The teleparallel equivalent of higher order Lagrangians like L □R = −R + a 0 R 2 + a 1 R□R can be obtained by means of the boundary term B = 2∇ μ T μ . In this perspective, we derive the field equations in presence of matter for higher-order teleparallel gravity considering, in particular, sixth-order theories where the □ operator is linearly included. In the weak field approximation, gravitational wave solutions for these theories are derived. Three states of polarization are found: the two standard + and × polarizations, namely 2-helicity massless transverse tensor polarizations, and a 0-helicity massive, with partly transverse and partly longitudinal scalar polarization. Moreover, these gravitational waves (GWs) exhibit four oscillation modes related to four degrees of freedom: the two classical + and × tensor modes of frequency ω 1, related to the standard Einstein waves with ; two mixed longitudinal-transverse scalar modes for each frequencies ω 2 and ω 3, related to two different 4-wave vectors, and . The four degrees of freedom are the amplitudes of each individual mode, i.e. , , , and . To describe a general teleparallel gravity model of order (2p + 2), we used the teleparallel Lagrangian which demonstrates to be not equivalent to . By varying its action, the related field equations in the presence of matter are derived. Hence we obtain the GWs for these teleparallel gravity models, i.e. , that are exactly the Einstein GWs as in f(T) teleparallel gravity. In conclusion, the boundary term B generates extra polarizations and additional modes beyond the standard ones. In particular B 2 and B□B terms generate both the additional scalar polarization and the extra scalar modes.

Stability, dark energy parameterization and swampland aspect of Bianchi type-V Ih cosmological models with f(R,T)-gravity

Stability, dark energy (DE) parameterization and swampland aspects for the Bianchi form-[Formula: see text] universe have been formulated in an extended gravity hypothesis. Here, we have assumed a minimally coupled geometry field with a rescaled function of [Formula: see text] replaced in the geometric action by the Ricci scalar [Formula: see text]. Exact solutions are sought under certain basic conditions for the related field equations. For the following theoretically valid premises, the field equations in this scalar-tensor theory have been solved. It is observed under appropriate conditions that our model shows a decelerating to accelerating phase transition property. Results are observed to be coherent with recent observations. Here, our models predict that the universe’s rate of expansion will increase with the passage of time. The physical and geometric aspects of the models are discussed in detail. In this model, we also analyze the parameterizations of DE by fitting the EoS parameter [Formula: see text] with redshift. The results obtained would be useful in clarifying the relationship between DE parameters. In this, we also explore the correspondence of quintessence DE with swampland criteria. The swampland criteria have been also shown the nature of the scalar field and the potential of the scalar field.

Local self-tuning mechanism for the cosmological constant

Recently the global variation of the Planck mass in the General Relativistic Einstein-Hilbert action was proposed as a self-tuning mechanism of the cosmological constant preventing vacuum energy from freely gravitating. We show that this global mechanism emerges for generic local scalar-tensor theories with additional coupling of the scalar field to the field strength of a three-form gauge field that turns the scalar field constant on the domain of the action. Evaluation of the resulting integral constraint equation over the observable Universe yields a self-consistent framework with General Relativistic field equations and arbitrary radiatively stable residual cosmological constant. We argue that the expectation value for this residual is in good agreement with the magnitude of the observed cosmic acceleration.

A general relativity formulation for the Doplicher-Fredenhagen-Roberts noncommutative space-time

The Doplicher, Fredenhagen and Roberts (DFR) noncommutative (NC) formalism was proposed in a curved space-time. In the DFR approach, the NC parameters are promoted to a set of space-time coordinates. Consequently, the field theory defined on this space contains extra dimensions. We propose a metric containing the new coordinates to explain the length measurements of this extended space. We promote the Minkowski part of this extended metric to a metric defined in a curved manifold. Thus, we can build up a NC gravitation model with extra dimensions. Based on the curved metric, we propose an Einstein-Hilbert action to describe the NC general relativity model on the DFR space. It is a new result in the literature since there is not a general relativity formalism in the DFR approach. We also introduce the NC version of the general relativistic field equations. As an application of the formalism, the weak-field approximation is considered in the field equations to generate the wave equations for the graviton propagation in DFR space.

De Sitter field equations from quadratic curvature gravity: A group theoretical approach

In this paper, the linearized field equations related to the quadratic curvature gravity theory have been obtained in the four-dimensional de Sitter (dS) space–time. The massless spin-2 field equations have been written in terms of the Casimir operators of dS group making use of the ambient space notations. By imposing some simple constraints, arisen from group theoretical interpretation of the field equations, a new four-dimensional Gauss–Bonnet (GB-)like action has been introduced with the related field equations transforming according to the unitary irreducible representations (UIRs) of dS group. Since, the field equations transform according to the UIRs of dS group, the GB-like action, we just obtained, is expected to be a successful model of modified gravity. For more clarity, the gauge invariant field equations have been solved in terms of a gauge-fixing parameter [Formula: see text]. It has been shown that the solution can be written as the multiplication of a symmetric rank-2 polarization tensor and a massless minimally coupled scalar field on dS space. The Krein–Gupta–Bleuler quantization method has been utilized and the covariant two-point function has been calculated in terms of the massless minimally coupled scalar two-point function, using the ambient space notations. It has been written in terms of dS intrinsic coordinates from the ambient space counterpart. The two-point functions are dS invariant and free of any theoretical problems. It means that the proposed model is a successful model of modified gravity and it can produce significant results in the contexts of classical theory of gravity and quantum gravity toy models.

Relativistic compact stars in the Kuchowicz space-time

We present an anisotropic charged analogue of Kuchowicz (1971) solution of the general relativistic field equations in curvature coordinates by using simple form of electric intensity $E$ and pressure anisotropy factor $\Delta$ that involve charge parameter $K$ and anisotropy parameter $\alpha$ respectively. Our solution is well behaved in all respects for all values of $X$ ( $X$ is related to the radius of the star ) lying in the range $0< X \le 0.6$, $\alpha$ lying in the range $0 \le \alpha \le 1.3$, $K$ lying in the range $0< K \le 1.75$ and Schwarzschild compactness parameter "$u$" lying in the range $0< u \le 0.338$. Since our solution is well behaved for a wide range of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We present some models of super dense quark stars and neutron stars corresponding to $X=0.2,~\alpha=0.2$ and $K=0.5$ for which $u_{max}=0.15$. By assuming surface density $\rho_b=4.6888\times 10^{14}~ g/cc$ the mass and radius are $0.955 M_\odot$ and $9.439 km$ respectively. For $\rho_b=2.7\times 10^{14}~ g/cc$ the mass and radius are $1.259 M_\odot$ and $12.439 km$ respectively and for $\rho_b=2\times 10^{14}~ g/cc$ the mass and radius are $1.463 M_\odot$ and $14.453 km$ respectively. It is also shown that inclusion of more electric charge and anisotropy enhances the static stable configuration under radial perturbations. The $M-R$ graph suggests that the maximum mass of the configuration depends on the surface density {\bf i.e. with the increase of surface density} the maximum mass and corresponding radius decrease. This may be because of existence of exotic matters at higher densities that soften the EoSs.

Discrete phase space, relativistic quantum electrodynamics, and a non-singular Coulomb potential

This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent relativistic quantum electrodynamics, the corresponding Feynman diagrams and [Formula: see text]-matrix elements are derived. In the special case of electron–electron scattering (Møller scattering), the explicit second-order element [Formula: see text] is deduced. Moreover, assuming the slow motions for two external electrons, the approximation of [Formula: see text] yields a divergence-free Coulomb potential.

Covariant BSSN formulation in bimetric relativity

Numerical integration of the field equations in bimetric relativity is necessary to obtain solutions describing realistic systems. Thus, it is crucial to recast the equations as a well-posed problem. In general relativity, under certain assumptions, the covariant BSSN formulation is a strongly hyperbolic formulation of the Einstein equations, hence its Cauchy problem is well-posed. In this paper, we establish the covariant BSSN formulation of the bimetric field equations. It shares many features with the corresponding formulation in general relativity, but there are a few fundamental differences between them. Some of these differences depend on the gauge choice and alter the hyperbolic structure of the system of partial differential equations compared to general relativity. Accordingly, the strong hyperbolicity of the system cannot be claimed yet, under the same assumptions as in general relativity. In the paper, we stress the differences compared with general relativity and state the main issues that should be tackled next, to draw a roadmap towards numerical bimetric relativity.

A Modified Dynamical Model of Cosmology I Theory

Wheeler (1964) had formulated Mach’s principle as the boundary condition for general relativistic field equations. Here, we use this idea and develop a modified dynamical model of cosmology based on imposing Neumann boundary condition on cosmological perturbation equations. Then, it is shown that a new term appears in the equation of motion, which leads to a modified Poisson equation. In addition, a modified Hubble parameter is derived due to the presence of the new term. Moreover, it is proved that, without a cosmological constant, such a model has a late time-accelerated expansion with an equation of state converging to w &lt; − 1 . Also, the luminosity distance in the present model is shown to differ from that of the Λ C D M model at high redshifts. Furthermore, it is found that the adiabatic sound speed squared is positive in radiation-dominated era and then converges to zero at later times. Theoretical implications of the Neumann boundary condition have been discussed, and it is shown that, by fixing the value of the conjugate momentum (under certain conditions), one could derive a similar version of modified dynamics. In a future work, we will confine the free parameters of the Neumann model based on hype Ia Supernovae, Hubble parameter data, and the age of the oldest stars.

Thermodynamics of scalar-tensor-Maxwell black holes

The action of the charged Einstein-dilaton gravity theory is obtained from that of the scalar-tensor gravity theory by use of the transformations defined as $ g_{\mu\nu}\rightarrow \Omega^{2}g_{\mu\nu}$ and $ A_{\mu}\rightarrow A_{\mu}$. It is shown that, under these conformal transformations, the Lagrangian of Maxwell’s electrodynamics remains invariant in four-dimensional space-times. The related field equations are solved in the framework of Einstein-dilaton theory, and the dilatonic potential is obtained as a linear combination of three Liouville-type potentials. Two classes of novel charged black holes are identified as the exact solution to the field equations of the Einstein-Maxwell-dilaton theory. We calculate the conserved and thermodynamic quantities of dilaton black holes and show that the first law of black hole thermodynamics is valid in its standard form. Also, the thermodynamic stability or the phase transition of dilaton black holes is analyzed by use of the canonical ensemble method. Then, making use of the inverse conformal transformations, two classes of charged scalar-tensor black holes are obtained from their Einstein-dilaton counterparts and their thermodynamic properties as well as thermodynamic phase transitions are investigated.

Validity of the Einstein hole argument

Arguing from his “hole” thought experiment, Einstein became convinced that, in cases in which the energy-momentum-tensor source vanishes in a spacetime hole, a solution to his general relativistic field equation cannot be uniquely determined by that source. After reviewing the definition of active diffeomorphisms, this paper uses them to outline a mathematical proof of Einstein's result. The relativistic field equation is shown to have multiple solutions, just as Einstein thought. But these multiple solutions can be distinguished by the different physical meaning that each metric solution attaches to the local coordinates used to write it. Thus the hole argument, while formally correct, does not prohibit the subsequent rejection of spurious solutions and the selection of a physically unique metric. This conclusion is illustrated using the Schwarzschild metric. It is suggested that the Einstein hole argument therefore cannot be used to argue against substantivalism.

Charged wormholes in f(R,T)-extended theory of gravity

Wormholes (WHs) are a solution for General Relativity field equations which characterize a passage or tunnel that connects two different regions of spacetime and is filled by some sort of exotic matter that does not satisfy the energy conditions. On the other hand, it is known that in extended theories of gravity, the extra degrees of freedom once provided may allow the energy conditions to be obeyed and, consequently, the matter content of the WH to be nonexotic. In this work, we obtain, as a novelty in the literature, solutions for charged WHs in the [Formula: see text]-extended theory of gravity. We show that the presence of charge in these objects may be a possibility to respect some stability conditions for their metric. Also, remarkably, the energy conditions are respected in the present approach. In addition, we argue that our framework can be very useful to study the possibility of evolving [Formula: see text] and [Formula: see text]-dimensional WH spacetime within the context of nonlinear electrodynamics, which open a new window to probe the physical quantities in a WH-type solution.

Decay of I-ball/oscillon in classical field theory

I-balls/oscillons are long-lived and spatially localized solutions of real scalar fields. They are produced in various contexts of the early universe in, such as, the inflaton evolution and the axion evolution. However, their decay process has long been unclear. In this paper, we derive an analytic formula of the decay rate of the I-balls/oscillons within the classical field theory. In our approach, we calculate the Poynting vector of the perturbation around the I-ball/oscillon profile by solving a relativistic field equation, with which the decay rate of the I-ball/oscillon is obtained. We also perform a classical lattice simulation and confirm the validity of our analytical formula of the decay rate numerically.

Brief report: Extremely dense general relativistic polytropes of index $$n=1$$ n = 1

Polytropic gas spheres of index 1 and extremely high central densities are analysed with the help of general relativistic field equations. Parameters such as the radius and mass are calculated for different central densities. The limiting values of these quantities are obtained and the physical nature of sound waves in these bodies is verified.

Anisotropic coupling of gravity and electromagnetism in Hořava-Lifshitz theory

We analyze the electromagnetic-gravity interaction in a pure Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz framework. To do so we formulate the Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity in $4+1$ dimensions and perform a Kaluza-Klein reduction to $3+1$ dimensions. We use this reduction as a mathematical procedure to obtain the $3+1$ coupled theory, which at the end is considered as a fundamental, self-consistent theory. The critical value of the dimensionless coupling constant in the kinetic term of the action is $\ensuremath{\lambda}=1/4$. It is the kinetic conformal point for the nonrelativistic electromagnetic-gravity interaction. In distinction, the corresponding kinetic conformal value for pure Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity in $3+1$ dimensions is $\ensuremath{\lambda}=1/3$. We analyze the geometrical structure of the critical and noncritical cases, they correspond to different theories. The physical degrees of freedom propagated by the noncritical theory are the transverse traceless graviton, the transverse gauge vector and two scalar fields. In the critical theory one of the scalars is absent, only the dilaton scalar field is present. The gravity and vector excitations propagate with the same speed, which at low energy can be taken to be the speed of light. The field equations for the gauge vector in the nonrelativistic theory have exactly the same form as the relativistic electromagnetic field equations arising from the Kaluza-Klein reduction of general relativity, and are equal to them for a particular value of one of the coupling constants. The potential in the Hamiltonian is a polynomial of finite degree in the gauge vector and its covariant derivatives.

A new development in quantum field equations of dyons

In this study, we describe a novel approach to quantum phenomena of the generalized electromagnetic fields of dyons with quaternionic analysis. Starting with quaternionic quantum wave equations, we have established a quantized condition for time coordinate that transforms microscopic to macroscopic fields. In view of the classical electromagnetic field equations, we propose a new set of quantized Proca–Maxwell’s equations for dyons. Furthermore, a quantized form of four-current densities and the quantized Lorentz gauge conditions for electric and magnetic potentials, respectively, of dyons are obtained. We have established the new quantized continuity equations for electric and magnetic densities of dyons, which are associated with a torque density result from the two spin states. The quantized Klein–Gordon-like field equations and the unified quaternionic electromagnetic potential wave equations for massive dyons are demonstrated. Moreover, we investigate the quaternionic quantized relativistic Dirac field equations for massive dyons, which indicate that the antiparticle of dyons will exist, called antidyons.

From Newtonian energy conservation in self-gravitating systems to General Relativity

A novel derivation of Einstein’s General Relativity is presented which sheds new light on its relation to Newton’s gravitational theory. The derivation is based on a one-parameter family of Newtonian energy-conservation equations for systems interacting gravitationally. The conservation equations make manifest the non-localizability of the gravitational energy. The introduction of a redundant Newtonian vector potential puts the gravitational energy and energy–current densities into a form with first derivatives of the Newtonian potentials only. The lift of the one-parameter family of the Newtonian energy-conservation equations to Minkowski space under the Einstein equivalence principle renders the Newtonian vector potential the relativistic gravitomagnetic field in harmonic coordinates. The coupling of light to the ‘Newtonian’ potentials gets derived. The relativistic gravitational field equations find straight derivation through quadratic-nonlinear order. The step from the quadratic-nonlinear field equations to the full Einstein field equations turns out stringent under general covariance.

O maior erro de Einstein? Debatendo o papel dos erros na ciência através de um jogo didático sobre cosmologia

A constante cosmológica de Einstein, introduzida por ele como uma estratégia para manter seu modelo de universo estático, tem sido divulgada como um dos maiores erros de sua carreira. Em 1922, Einstein avaliou o artigo enviado por Friedmann para um periódico alemão, mostrando que existe uma solução das equações de campo da relatividade geral em que o tamanho do universo aumenta com o tempo. Einstein considerou que Friedmann teria cometido um erro nos cálculos, mas após discutir a questão com um colega de Friedmann, reconheceu seu engano, declarando que a proposta do universo em expansão seria matematicamente possível. Contudo, acreditava que essa ideia dificilmente teria algum sentido físico. Este episódio histórico foi adaptado para o contexto do ensino de Física do ensino médio através da criação de um jogo didático. Neste artigo, analisamos argumentos envolvendo a oposição entre Einstein e Friedmann e as concepções dos alunos sobre o papel dos erros na ciência. Houve um equilíbrio entre o número de alunos que apoiou Einstein ou Friedmann. Muitos dos fãs de Einstein tinham uma admiração ingênua, acreditando que alguém tão inteligente como ele não poderia cometer erros. Por outro lado, os fãs de Friedmann valorizaram sua atitude crítica, desafiando a autoridade de um cientista renomado. Os alunos discutiram se o fato de que Einstein tenha admitido seu próprio erro deveria ou não ser valorizado. Com isso, notamos argumentos interessantes dos alunos sobre o papel dos erros na ciência, que motivaram a problematização do mito dos grandes gênios que nunca erram e cuja autoridade não deve ser questionada.

English

Einstein&#39;s general relativistic field equation is a nonlinear partial differential equation that lacks an easy way to obtain exact solutions. The most famous of which are Schwarzschild and Kerr&#39;s black hole solutions. Kerr metric has astrophysical meaning because most cosmic celestial bodies rotate. Kerr metric is even harder than Schwarzschild metric to be derived directly due to off-diagonal term of metric tensor. In this paper, a derivation of Kerr metric was obtained by ellipsoid coordinate transformation which causes elimination of large amount of tedious derivation. This derivation is not only physically enlightening, but also further deducing some characteristics of the rotating black hole. &nbsp; Key words: General relativity, Schwarzschild metric, Kerr metric, ellipsoid coordinate transformation, exact solutions.