Post-Newtonian limit: second-order Jefimenko equations
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Regular Article - Theoretical Physics
Post-Newtonian limit: second-order Jefimenko equations David Pérez Carlos1,a , Augusto Espinoza2 , Andrew Chubykalo2 1 2
Unidad Académica de Física, Universidad Autónoma de Zacatecas, Campus II, Av. Preparatoria s/n, 98068 Zacatecas, Mexico Unidad Académica de Ciencia y Tecnología de Luz y Materia, Universidad Autónoma de Zacatecas, Ciudad Universitaria Campus Siglo XX1, 98160 Zacatecas, Mexico
Received: 28 October 2019 / Accepted: 10 July 2020 © The Author(s) 2020
Abstract 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.
1 Introduction In general relativity gravitational interaction is interpreted as deformation of space-time due to the presence and movement of masses. We can read in almost all books related to general relativity about the relationship existing between matter and space-time: ”space-time tells matter how to move, matter a e-mail:
tells to space-time how to curve” (see, [15]). This idea arose from the conclusion of Einstein that the field variable for the gravitational field must be the metric tensor of the Riemann space-time gμν , and that this quantity is determined by the distribution and motion of matter, this is the link between matter and geometry. General relativity theory is often mentioned by various authors as one of the most important theories developed in the last century. In words of the Nobel prize R. Feynman: “Einstein’s gravitational theory, which is said to be the greatest single achievement of theoretical physics, resulted in beautiful relatio
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