![]() The metric is a tool that encapsulates the geometry of space and time. In order to be able to describe what happens in curved spacetime, we need to understand a very important tool from mathematics: the metric g. Another was that he realized that gravity, the force keeping us in bed every morning, was equivalent to the curvature of spacetime. Gravity is geometryįor the physics enthusiast today, the idea of space and time being one unit seems natural, but more than 100 years ago it was one of Albert Einstein’s greatest insights and gifts he left us. Maar wat gebeurt er als je écht het zwarte gat bereikt en over de rand valt? Afbeelding: ESO / L. Een zwart gat.Wat je ziet is alle materie die in het zwarte gat valt het zwarte gat zelf is een klein bolletje in het midden van de afbeelding dat nauwelijks zichtbaar is. $$\begin(x)\) with the single particle source term.Afbeelding 1. In the absence of the interaction between matter field, particle and radiation, the action is given by: In the present paper, we study some small distribution of matter to simplify our considerations. In the second one, we exclude the continuum structure of spacetime and introduce the spacetime network instead of manifold structure. In the first one, we exclude the point concept and introduce the extended object (string). So far we have two candidates for quantum gravity: string theory and loop quantum gravity. Thus the general relativity is not a complete theory by itself, it needs to join with the quantum theory, i.e., we need quantum gravity. On the other hand, we have point particle in the world (leptons). Choice of the point assumption causes a problem: the point matters are not compatible with general relativity, because it creates black hole (a spherical matter distribution with the fixed mass and charge when its radius vanishes becomes a black hole). We can principally obtain the extended matter’s fields from point’s field (even it is not the case for gravitational waves, because the Einstein equations are not linear). ![]() To avoid the complexity of extended charged matters, we turned to the point particles. ![]() 5 we have discussed the new mathematical concepts that are introduced in the problem. ![]() 4, the Conservation of energy is considered that is the extension of energy conservation theorem to the curved space. 3, the electromagnetic self-force is discussed by axiomatic approach. First we describe the charge particle motion in the curved spacetime and discuss some of its complexities then in Sect. We discuss some aspects of these new concepts in this paper. These new mathematical concepts need further research and studies. In this manner we come to a new mathematical concept in the formulation of the problem. The method we specially focus on it using another mathematical object: difference of two tensors belonging to two distinct tangent spaces. Bitensor is a mathematical object that is defined in two distinct points of a manifold. The Green functions that is appropriate for our problem are bitensors. One of the known ways to solve the differential equations is the use of Green functions. We focus on a particle that, even small, changes the spacetime geometry. The solution of Maxwell’s equation depends on several parameters, e.g., on the presence of other charged particles and the spacetime geometry. In this paper we only consider the first one. Radiation field of a charged particle motion in curved space, in general, can be divided into two parts: electromagnetic field and gravitational field. Apart from this, the very charged particle motion is an important problem that contains some mathematical complexity. For example, the first velocity moment cannot explain the Landau damping. Some physical phenomena come back to this mismatching. It is clear that every particle’s trajectory is not in full adjustment to the element’s trajectory. In the equation of first velocity moment we study the average motion of particles in all elements. In statistical formalism of such problem usually we just need the first velocity moment of Vlasov or Boltzmann equation. In considering the plasma around a neutron star, we encounter a charged gas in the curved space.
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