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Author: Augusto Espinoza

Post-Newtonian limit: second-order Jefimenko equations

AMADO AUGUSTO ESPINOZA GARRIDO Augusto Espinoza (2020)

The purpose of this paper is to get second-order

gravitational equations, a correction made to Jefimenko’s

linear gravitational equations. These linear equations were

first proposed by Oliver Heaviside in [1], making an analogy

between the laws of electromagnetism and gravitation. To

achieve our goal, we will use perturbation methods on Einstein field equations. It should be emphasized that the resulting system of equations can also be derived from Logunov’s

non-linear gravitational equations, but with different physical

interpretation, for while in the former gravitation is considered as a deformation of space-time as we can see in [2–5], in the latter gravitation is considered as a physical tensor field

in the Minkowski space-time (as in [6–8]). In Jefimenko’s

theory of gravitation, exposed in [9,10], there are two kinds

of gravitational fields, the ordinary gravitational field, due

to the presence of masses, at rest, or in motion and other

field called Heaviside field due to and acts only on moving

masses. The Heaviside field is known in general relativity as

Lense-Thirring effect or gravitomagnetism (The Heaviside

field is the gravitational analogous of the magnetic field in the

electromagnetic theory, its existence was proved employing

the Gravity Probe B launched by NASA (See, for example,

[11,12]). It is a type of gravitational induction), interpreted

as a distortion of space-time due to the motion of mass distributions, (see, for example [13,14]). Here, we will present our second-order Jefimenko equations for gravitation and its solutions.

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CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA Jefimenko equations gravitational equations gravitomagnetism

Special features of radio pulse spectral density analysis

AMADO AUGUSTO ESPINOZA GARRIDO Augusto Espinoza (2020)

The spectrum analysis of the periodic sequence radio pulses is often described in textbooks. However, if this method is applied to short radio pulses with a large period between them, then large errors occur. In this article, we described a new method of pulse gating. This method allows us to measure the spectral density of radio signals with high duty cycle. The main advantages of our method are a high signal-to-noise ratio, a large dynamic range of measurements, and a higher accuracy of spectral density measurements.

En los libros de texto se describe el análisis del espectro de la secuencia periódica de pulsos de radio. Sin embargo, si éste se aplica a pulsos de radio cortos con un periodo largo entre ellos, se producen grandes errores. En este artículo se describe el método de activación por pulso, el cual permite medir la densidad espectral de las señales de radio con un ciclo de trabajo alto. Entre las principales ventajas que posee está una alta relación señal/ruido, un amplio rango dinámico de mediciones y una mayor precisión de las mediciones de densidad espectral.

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CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA Spectral line amplitudes spectral density measurements LF-amplifier

Maxwell’s error and its consequences for physics

Andrew Chubykalo Augusto Espinoza (2019)

The analysis of errors in the theories of modern physics led us to an important conclusion. There are

initial errors, which then “generate” a spectrum of sec-ondary errors (erroneous consequences). We

found an error made by Maxwell in the mathematical formulation of Faraday studies. In

summarizing the experiments, Faraday Maxwell “lost” instantaneous action at a distance. The paper

presents a proof and considers some consequences for physical theories. For example, we must

consider the charge fields and the fields of electromagnetic waves as independent fields having

different (mutually exclusive) properties.

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CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA Occam’s principle equations of Maxwell

The origin of the energy–momentum conservation law

Andrew Chubykalo Augusto Espinoza (2017)

The interplay between the action–reaction principle and the

energy–momentum conservation law is revealed by the examples

of the Maxwell–Lorentz and Yang–Mills–Wong theories, and general

relativity. These two statements are shown to be equivalent in

the sense that both hold or fail together. Their mutual agreement

is demonstrated most clearly in the self-interaction problem by

taking account of the rearrangement of degrees of freedom appearing

in the action of the Maxwell–Lorentz and Yang–Mills–Wong

theories. The failure of energy–momentum conservation in general

relativity is attributed to the fact that this theory allows solutions

having nontrivial topologies. The total energy and momentum of a

system with nontrivial topological content prove to be ambiguous,

coordinatization-dependent quantities. For example, the energy of

a Schwarzschild black hole may take any positive value greater

than, or equal to, the mass of the body whose collapse is responsible

for forming this black hole. We draw the analogy to the paradoxial Banach–Tarski theorem; the measure becomes a poorly

defined concept if initial three-dimensional bounded sets are rearranged

in topologically nontrivial ways through the action of free

non-Abelian isometry groups.

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CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA Action–reaction Translation invariance Energy and momentum conservation Rearrangement of initial degrees of freedom

Andrew Chubykalo Augusto Espinoza (2016)

It is well known that the use of Helmholtz decomposition theorem for static vector fields C : R3 → R3 ,

when applied to the time dependent vector fields E : R4 → R3 , B : R4 → R3 which represent the

electromagnetic field, allows us to obtain instantaneous-like solutions all along R3 . For this reason,

some people thought (see e.g. [1] and references therein) that the Helmholtz theorem cannot

be applied to time dependent vector fields and some modification is wanted in order to get the retarded

solutions. However, the use of the Helmholtz theorem for static vector fields is correct even

for time dependent vector fields (see, e.g. [2]), so a relation between the solutions was required, in

such a way that a retarded solution can be transformed in an instantaneous one, and conversely.

On this paper we want to suggest, following most of the time the mathematical formalism of Woodside

in [3], that: 1) there are many Helmholtz decompositions, all equally consistent, 2) each one is

naturally related to a space-time structure, 3) when we use the Helmholtz decomposition for the

electromagnetic potentials it is equivalent to a gauge transformation, 4) there is a natural methodological

criterion for choosing the gauge according to the structure postulated for a global spacetime,

5) the Helmholtz decomposition is the manifestation at the level of the fields that a gauge is

involved. So, when we relate the retarded solution to the instantaneous one what we do is to change

the gauge and the space-time. And, if the Helmholtz decompositions are related to a space-time

structure, and are equivalent to gauge transformations, each gauge transformation is natural for a

specific space-time. In this way, a Helmholtz decomposition for Euclidean space is equivalent to

the Coulomb gauge and a Helmholtz decomposition for the Minkowski space is equivalent to the

Lorenz gauge. This leads us to consider that the theories defined by different gauges may be mathematically

equivalent, because they can be related by means of a gauge transformation, but they

are not empirically equivalent, because they have quite different observational consequences due

to the different space-time structure involved.

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CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA Helmholtz Theorem Gauge Transformations Space-Time Transformations Symmetries of Differential Equations Underdetermination of Systems of Differential Equations Natural Covariance

On Some Unusual Properties of Wave Solutions of Free Maxwell Equations

Augusto Espinoza Andrew Chubykalo (2006)

Se descubren algunas propiedades

inusuales de las soluciones de las llamadas

ecuaciones libres de Maxwell. Mostramos la

existencia de soluciones que representan las

ondas electromagnéticas en el vacío para los

cuales el vector de Poynting no coincide con

el vector de Umov. Se presentan soluciones que

corresponden a ondas magnéticas estacionarias

de una configuración inusual en el vacío, que

describen en el vacio formaciones estables

anulares y esféricas de campo. Se demuestra

que en el vacío, de acuerdo a las soluciones

obtenidas el campo eléctrico E puede ser un

vector polar así como un vector axial; y el

campo magnético B, en su turno, puede ser un

vector axial así como también un vector polar.

Se muestra que tales soluciones existen

cuando los vectores E y B, no son vectores

polares ni axiales. Además, estas soluciones

corresponden a ondas electromagnéticas que

no transfieren energía ni momentos en

cualquier punto del vacío.

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CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA vector de Poynting vector de Umov vector axial vector polar soluciones ondulatorias

Relativistic analysis of application of Helmholtz theorem to classical electrodynamics

Andrew Chubykalo Augusto Espinoza (2014)

In this work we discuss the relationship between the instantaneous-action-at-a-distance solutions of Maxwell‟s equations obtained using Helmholtz theorem and the Lorentz‟s invariant solutions of the same equations obtained using Special Relativity postulates. We show that Special Relativity postulates are not consistent with Helmholtz‟s theorem in the presence of charges and currents, but in the vacuum, without charges and currents, Helmholtz‟s theorem and Special Relativity agree because the instantaneous-action-at-a-distance solutions can be eliminated using a gauge transformation.

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CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA Helmholtz theorem Lorentz gauge space-time theories

Spherical and Ring-Like Configurations for the Gravitodynamical Field

Augusto Espinoza Andrew Chubykalo (2018)

In the present work, we write a brief exposition of the Jefimenko’s theory of gravitation. This theory arose from the analogy between the laws of gravitation and electromagnetism, that is, exist a second gravitational field called cogravitational field, analogous to the magnetic field. We introduce a new system of units called Gravitational Gaussian System (GGS). This system allows us write the equations of gravitation in a simple form to solve them. Using the Jefimenko’s equations of gravitation, we obtain the wave equations for gravitational and cogravitational fields and we find wave solutions. We demonstrate there are configurations of the gravitodynamical field (that is, the set of gravitational and cogravitacional fields) in form of co gravitational field spheres and gravitational field rings. This phenomenon must be an analogue of the ball lightning in the electromagnetic field, but in this case the cogravitational field spheres serves as containers of matter (it could be a gas). We analyze how this configuration acts on the particles inside the spheres, and we investigate the physical properties of such configurations, namely, how behaves the density of energy and the Pointing vector of this solution.

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CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA Cogravitation Gravitational waves Gravitodynamical field

The Mathematical Justification of a Possible Wave Nature of the Time Flow of Kozyrev

Andrew Chubykalo Augusto Espinoza (2014)

In this brief note we do not prove or disprove the existence of the so-called time

flow in the conception of time offered by N.A. Kozyrev, here we merely give the

mathematical justification of the presumable wave nature Kosyrev’s time flow in

the case of the physical existence of the mentioned flow.

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CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA Kozyrev’s substantial time chronometry time waves

On the presumable wave nature of the time flow of Kozyrev

Andrew Chubykalo Augusto Espinoza (2014)

In this brief note we mathematically substantiate the presumable wave nature of the so-called

time flow in the conception of time offered by N.A. Kozyrev.

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CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA Kozyrev s substantial time Chronometry Time waves