Space-time Equation Research Articles

Plasma magnetosphere of deformed magnetized neutron star

The plasma magnetosphere surrounding a rotating magnetized neutron star described by non-Kerr spacetime metric in slow rotation approximation has been studied. First we have studied the vacuum solutions of the Maxwell equations in spacetime of slowly rotating magnetized non-Kerr star with dipolar magnetic configuration. Then for the magnetospheric model we have derived second-order differential equation for electrostatic potential from the system of Maxwell equations in spacetime of slowly rotating magnetized non-Kerr star. Analytical solutions of Goldreich-Julian (GJ) charge density along open field lines of slowly rotating magnetized non-Kerr neutron star have been obtained which indicate the modification of an accelerating electric field, charge density along the open field lines and radiating losses of energy of the neutron star by the deformation parameter.

Global solutions for semilinear Klein–Gordon equations in FLRW spacetimes

We consider waves, which obey the semilinear Klein–Gordon equation, propagating in the Friedmann–Lemaître–Robertson–Walker spacetimes. The equations in the de Sitter and Einstein–de Sitter spacetimes are the important particular cases. We show the global in time existence in the energy class of solutions of the Cauchy problem.

Newton, Einstein and Barth on time and eternity

AbstractFor two hundred years after 1687, Newton's notion of absolute time dominated the world of physics. However, Newtonian metaphysical absolute time is so ideal that it may only be realised and actualised by God. In the early twentieth century, Einstein breaks this dominant understanding of time fundamentally by his Special Theory of Relativity and General Theory of Relativity. In the Einsteinian paradigm, we are forced to think no longer of space and time but rather to look at a four-dimensional space-time continuum, in which time appears to be more space-like than temporal. The Newtonian theory implies that there is an absolute, dominant point from which the universe can be observed, whereas Einstein argues for the opposite: there can be no vantage perspective and no universal present by which God can divide past and future.Barth takes a trinitarian approach to interpret the concept of time. For Barth, the Father is coeternal with the Son and the Holy Spirit. The eternal immanent Trinity acts concretely as the temporal economic Trinity, thus the triune God is pre-, supra- and post- to us. In actual temporality, the Father, Son and Holy Spirit transcend time concretely in our history and penetrate time absolutely from divine eternity. God's eternity is both transcendent and immanent to human time.Such a trinitarian temporality might serve as a ‘dynamic privileged perspective’ since time, energy and movement are all created by God from eternity. On the one hand, the triune Creator transcends his creature and its creaturely form – time absolutely; on the other hand, even when God enters time and moves together with the time ‘uniformly’ in the Son and the Holy Spirit, he becomes concretely simultaneous with all time. Also the Barthian perspective might provide something which is lacking in Einstein's relative time, i.e. the direction of time from the past to the future. Since every historical event in Einsteinian four-dimensional continuum is posited as a static space-time slice and Einstein equations are time-reversible, there is no ontological difference between time dimensions at all. However, in Barth's trinitarian opinion, such extraordinary events as the creation, resurrection and Pentecost are ontologically superior to other events in human history because they do change our temporality in an absolute way. Penetrated by the trinitarian eternity, those discrete space-time slices also become communicable and hence take genuine temporal characteristics, i.e. the past, present and future.

Algebra of Symmetry Operators and Integration of the Klein–Gordon Equation in an External Electromagnetic Field

The structure of the algebra of first-order differential symmetry operators of the Klein-Gordon equation in an external electromagnetic field is investigated from positions of the theory of cohomologies of Lie algebras. A method for integrating the given equation is proposed, based on noncommutative reduction, and, as a consequence, the corresponding integrability condition is obtained. An example of an integrable Klein- Gordon equation in a spacetime with a Steckel metric is considered, which does not admit separation of variables when an electromagnetic field is switched on. tensor of which is invariant with respect to the group of motions of the spacetime metric. The goal of this work is to describe the structure of the algebra of first-order symmetry operators of the equation under consideration from positions of the theory of cohomologies of Lie algebras, and also to propose a method of integration using the indicated symmetry algebra. An integrability condition for the Klein-Gordon equation in an electromagnetic field is derived, expressed in terms of the dimensionality of the Lie algebra of the group of motions of the metric and the so-called cohomology index of this algebra, this index depending on the class of cohomologies defined by the electromagnetic field. Note that in contrast to the well-known method of separation of variables, the integration method proposed in this work is based on the idea of noncommutative reduction (1), which makes more effective use of the algebra of first-order differential symmetry operators. In a number of cases, this eliminates the necessity of investigating hidden symmetries of the problem, associated with Killing tensors of second rank (and higher), which must often be done in the case of separation of variables (2, 3). To wrap things up, this paper considers an example of the Klein-Gordon equation in spacetime with a four- dimensional group of motions of the metric, which is integrable with the help of the approach proposed here. An interesting qualitative aspect of the example is the possibility of separation of variables in this equation in the absence of an external electromagnetic field and the impossibility of doing so in its presence.

Some Exact Blow-up Solutions of Landau-Lifshitz Equations Without Gilbert Term

Abstract: In this paper, we construct some exact blowup solutions of multi-dimensional space-time Landau-Lifshitz equations under the radially symmetric coordinates. Among these solutions, two blowup finite energy solutions on S are proposed. The question of whether a solution of the inhomogeneous isotropic Landau-Lifshitz equations can develop a finite time singularity on S from smooth initial data with finite energy is not clear. Our results show that the blowup phenomenon can really happen on this initial data.

Radion cosmology and stabilization

We solve the Einstein's equation in five-dimensional spacetime for Randall Sundrum Brane world model with time dependent radion field to study variation of brane scale factor with time. We have shown that as radion field decreases with time compactifying the extra dimension, the scale factor increases exponentially with time leading to inflationary scenario. We have also proposed a time dependent generalization of Goldberger-Wise moduli stabilization mechanism to explain the time evolution of the radion field to reach a stable value after which the scale factor on the brane exits from inflationary expansion.

A New Solution to the Structure Equation in Noncommutative Spacetime

In this paper, starting from the common foundation of Connes' noncommutative geometry ( NCG)\cite{Connes1, Connes2, CoLo, Connes3}, various possible alternatives in the formulation of atheory of gravity in noncommutative spacetime are discussed indetails. The diversity in the final physical content of the theory is shown to be the consequence of the arbitrary choices in each construction steps. As an alternative in the last step, when the structure equations are to be solved, a minimal set of constraints on the torsion and connection is found to determine all the geometric notions in terms of the metric. In the Connes-Lott model of noncommutative spacetime, in order to keep the full spectrum of the discretized Kaluza-Klein theory \cite{VW2}, it is necessary to include the torsion in the generalized Einstein-Hilbert-Cartan action.

New Discovery about Prediction of a Particle 'K-Suryon' as Basic Building Block of Mass

With the help of 'Heart of the God model of the universe' (1),'Siva's classical Equation for space time' (2) and 'Siva's Theory of quantum Gravity' (3) a new particle 'K-Suryon' has been predicted. It is the elementary particle with mass 1.15 x 10 -64 kg and radius 8.15 x 10 -134 mts. It is described as the basic building block of 'space- time' & mass. Mass of real particle 'K-Suryon' is 4.6x10 -64 Kgs. It has to be incorporated in standard model. This discovery will explain how the Quantum Gravity is synchronizing with General Relativity. It will open new ways of research in 'dark matter' and 'black hole' physics. It reveals the concept of mass creation more profoundly than 'Higgs mechanism'.

Siva’s Theory of Quantum Gravity

With the help of ‘space time fluid’ concept and ‘Siva’s equation for space time & matter’ it is concluded that the space time fluid density of a mass varies with distance from its centre. Not only that ,space time density of any mass exists in its space time fluid vicinity will also be affected . An equation has been derived to explain the concept. Conceptual analysis of this equation concluded a new model of quantum gravity showing that the space time fluid which plays a major role in creating gravity effect and is quantized. There will be quantized energy levels of space time fluid around a mass. Their energy distribution depends on the distance from the mass. Particles with mass exist in a specific energy level only. If the energy level is not suitable to its mass, that particle will have a tendency to move either to lower level or higher level. And at the same time when a particle jumps from higher energy level to lower energy level, it loses energy and if it moves from lower to higher level it absorbs energy. This is similar to Bohr’s atomic theory.

Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative

An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented. The order of the derivative is considered as0<β,γ≤1for the space and time domain, respectively. The fractional derivative of Caputo type is considered. In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case. In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form. In order that the equation preserves the physical units of the system two auxiliary parametersσxandσtare introduced characterizing the existence of fractional space and time components, respectively. A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parametersβandγ. The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior.

A Nuclear Reactor Transient Methodology Based on Discrete Ordinates Method

With the rapid development of nuclear power industry, simulating and analyzing the reactor transient are of great significance for the nuclear safety. The traditional diffusion theory is not suitable for small volume or strong absorption problem. In this paper, we have studied the application of discrete ordinates method in the numerical solution of space-time kinetics equation. The fully implicit time integration was applied and the precursor equations were solved by analytical method. In order to improve efficiency of the transport theory, we also adopted some advanced acceleration methods. Numerical results of the TWIGL benchmark problem presented demonstrate the accuracy and efficiency of this methodology.

Stationary black holes as holographs II

Within the generic null characteristic initial value problem a reduced set of the evolution equations are deduced from the coupled Newman–Penrose and Maxwell equations for smooth four-dimensional electrovacuum spacetimes allowing a non-zero cosmological constant. It is shown that these reduced equations make up a first-order symmetric hyperbolic system of evolution equations, and also that the solutions to this reduced system are also solutions to the full set of the Newman–Penrose and Maxwell equations provided that the inner equations hold on the initial data surfaces. The derived generic results are applied in carrying out the investigation of electrovacuum spacetimes distinguished by the existence of a pair of null hypersurfaces, and , generated by expansion and shear-free geodesically complete null congruences such that they intersect on a two-dimensional spacelike surface, . Besides the existence of this pair of null hypersurfaces, no assumption concerning the asymptotic structure is made. It is shown that both the spacetime geometry and the electromagnetic field are uniquely determined, in the domain of dependence of once a complex vector field ξA (determining the metric induced on ), the τ spin coefficient and the ϕ1 electromagnetic potential are specified on . The existence of a Killing vector field—with respect to which the null hypersurfaces and comprise a bifurcate-type Killing horizon—is also justified in the domain of dependence of . Since, in general, the freely specifiable data on do not have any sort of symmetry, the corresponding spacetimes do not possess any symmetry in addition to the horizon Killing vector field. Thereby, they comprise the class of generic ‘stationary’ distorted electrovacuum black hole spacetimes which for the case of a positive cosmological constant may also (or, in certain cases, only) contain a distorted de Sitter-type cosmological horizon to which our results equally apply. It is also shown that there are stationary distorted electrovacuum black hole configurations such that parallelly propagated curvature blow-up occurs both to the future and to the past ends of some of the null generators of their bifurcate Killing horizon, and also that this behavior is universal. In particular, it is shown that in the space of vacuum solutions to Einstein’s equations, in an arbitrarily small neighborhood of the Schwarzschild solution this type of distorted vacuum black hole configurations always exist. A short discussion on the relation of these results and some of the recent claims on the instability of extremal black holes is also given.

FERMION PERTURBATIONS IN HIGHER-DIMENSIONAL STRING-THEORY BLACK HOLES

In this paper, we report the results of a detailed investigation of the complete time evolution of massless fermion fields propagating in spacetimes of higher-dimensional stringy black hole solutions, obtained from intersecting branes in string/M theory. We write the Dirac equation in D-dimensional spacetime in a form suitable to perform a numerical integration of it, and using a Prony fitting of the time domain data, we determine the quasinormal frequencies that characterize the test field evolution at intermediary times. We also present the results obtained for the quasinormal frequencies using a sixth-order WKB approximation, that are in perfect agreement with the numerical results. The power-law exponents that describe the field relaxation at very late-times are also determined, and we show that they depends upon the dimensionality of spacetime, and are identical to that associated with the relaxation of boson fields for odd dimensions. The dependence of the frequencies and damping factor of the spinor field with the charges of the stringy black hole are studied.

Gaussian curvature and global effects: Gravitational Aharonov-Bohm effect revisited

Using the Gauss-Bonnet formula, integral of the Gaussian curvature over a 2-surface enclosed by a curve in the asymptotically flat region of a static spacetime was found to be a measure of a gravitational analogue of Aharonov-Bohm effect by Ford and Vilenkin in the linearized regime. Employing the 1+3 formulation of spacetime decomposition we study the same effect in the context of full Einstein field equations for stationary spacetimes. Applying our approach to static tube-like and cylindrical distributions of dust not only we recover their result but also obtain an extra term which is interpreted to be representing the classical version of the Colella-Overhauser-Werner effect (the COW experiment).

Low temperature motion of hydrogen on metal surfaces signals breakdown of quantum mechanics in 3+1 dimensions

The low temperature motion of hydrogen on solid metal surfaces displays some unexplained experimental features: in the quantum diffusion regime more than nine orders of magnitude difference between the diffusion rates on different metal surfaces have been measured, the lowest diffusion rates being established in the low temperature scanning tunnelling microscope. Furthermore telegraph-signal-like adsorption site change, rather than Rabi oscillations predicted by Schrödinger equation in 3+1 dimensions, is observed, signaling the breakdown of quantum mechanics in 3+1 dimensions. A theory is presented to resolve these problems, involving the entanglement of the adsorbate motion to gravitons in high-dimensional spacetime. Soft local massive gravonons, induced in the presence of the adsorbate, determine the time scale for surface diffusion. The γη-model is used for the evaluation of the soft gravonon modes. Weak and local entanglement of the adsorbate motion with a nearly degenerate graviton continuum of high density of states are the conditions for the telegraph-signal-like time development of adsorption site change. In contrast to the Copenhagen interpretation of quantum mechanics, this apparent "classical" behaviour of the adsorbate in 3+1 dimensional spacetime is the result of the solution of Schrödinger's time dependent equation in high-dimensional spacetime.

G-Strands and Peakon Collisions on Diff(R)

A $G$-strand is a map $g:\mathbb{R}\times\mathbb{R}\to G$ for a Lie group $G$ that follows from Hamilton's principle for a certain class of $G$-invariant Lagrangians. Some $G$-strands on finite-dimensional groups satisfy 1+1 space-time evolutionary equations that admit soliton solutions as completely integrable Hamiltonian systems. For example, the ${\rm SO}(3)$-strand equations may be regarded physically as integrable dynamics for solitons on a continuous spin chain. Previous work has shown that $G$-strands for diffeomorphisms on the real line possess solutions with singular support (e.g. peakons). This paper studies collisions of such singular solutions of $G$-strands when $G={\rm Diff}(\mathbb{R})$ is the group of diffeomorphisms of the real line $\mathbb{R}$, for which the group product is composition of smooth invertible functions. In the case of peakon-antipeakon collisions, the solution reduces to solving either Laplace's equation or the wave equation (depending on a sign in the Lagrangian) and is written in terms of their solutions. We also consider the complexified systems of $G$-strand equations for $G={\rm Diff}(\mathbb{R})$ corresponding to a harmonic map $g: \mathbb{C}\to{\rm Diff}(\mathbb{R})$ and find explicit expressions for its peakon-antipeakon solutions, as well.

Equivalent Forms of Dirac Equations in Curved Space-times and Generalized de Broglie Relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved space-time. This canonical form is needed to apply Whitham’s Lagrangian method. The latter method, unlike the Wentzel–Kramers–Brillouin method, places no restriction on the magnitude of Planck’s constant to obtain wave packets and furthermore preserves the symmetries of the Dirac Lagrangian. We show by using canonical Dirac fields in a curved space-time that the probability current has a Gordon decomposition into a convection current and a spin current and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck’s constant. We further discuss the classical-quantum correspondence in a curved space-time based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved space-time are a direct consequence of Whitham’s Lagrangian method and not just a physical hypothesis as introduced by Einstein and de Broglie and by many quantum mechanics textbooks.

The Conservation of Energy Space-Time Metric for Space Outside Matter

By using experimentally determined measurements of potential energy together with the principle of conservation of energy and solving directly, the space-time geometry equation for space outside matter is obtained. That equation fits all the experimental observations that support the accepted Schwarzschild metric, yet predicts there isn’t a singularity at the Schwarzschild radius. The accepted Schwarzschild metric is the first approximation of the conservation of energy space-time metric. No observation yet made can distinguish between the predictions of the two metrics.

Numerical Simulations for the Space-Time Variable Order Nonlinear Fractional Wave Equation

The explicit finite-difference method for solving variable order fractional space-time wave equation with a nonlinear source term is considered. The concept of variable order fractional derivative is considered in the sense of Caputo. The stability analysis and the truncation error of the method are discussed. To demonstrate the effectiveness of the method, some numerical test examples are presented.

Siva’s Equation for Singularity of Black Holes

Classical equation for space time and matter gives the relation between a mass and the space time surrounded by its space time fluid. Mass of the basic building block of matter creation has been termed as ‘K-Suryon’. Mass of ‘K-Suryon’ has been calculated as 1.15x10-64 kgs. The density of its space time fluid is calculated as 3.32x10626 Kg/cum. Thus ‘K-Suryon’ is the most elementary mass that can exist in this universe. We know the minimum mass of anybody to become black hole is ‘Chandrasekhar’s Limit’ .For that mass we can calculate the space time fluid density. So we can find the density of space time fluid associated with it. With these calculations we have concluded that the physical singularity will not be there for a black hole. A physical singularity will exist below a critical density equal to K-Suryon where space time will not exist. It is concluded that velocity of light is reducing and space time fluid density of universe is increasing with the age of Universe. Experimental verification may be possible.