Accelerated frames and galactic rotation curves

In this paper, the galactic rotation curve is analyzed as an effect of an accelerated reference frame. Such a rotation curve was the first evidence for the so-called dark matter. We show another possibility for this experimental data: non-inertial reference frame can fit the experimental curve. We also show that general relativity is not enough to completely explain that which encouraged alternatives paths such as the MOND approach. The accelerated reference frames hypothesis is well-suited to deal with the rotation curve of galaxies and perhaps has some role to play concerning other evidences for dark matter.

Accelerated frames

This chapter shows how, within the framework of special relativity, Newtonian inertial accelerations turn into mere geometrical quantities. In addition, the chapter states that labeling the points of Minkowski spacetime using curvilinear coordinates rather than Minkowski coordinates is mathematically just as simple as in Euclidean space. However, the interpretation of such a change of coordinates as passage from an inertial frame to an accelerated frame is more subtle. Hence, the chapter studies some examples of this phenomenon. Finally, it addresses the problem of understanding what the curvilinear coordinates actually represent. Or, similarly, it considers the question of how to realize them by a reference frame in actual, ‘relative, apparent, and common’ physical space.

Relativity in Modern Physics

Newton’s ideas about how to represent space and time, his laws of dynamics, and his theory of gravitation established the conceptual foundation from which modern physics developed. This book offers a modern view of Newtonian theory, emphasizing those aspects needed for understanding quantum and relativistic contemporary physics. In 1905, Albert Einstein proposed a novel representation of space and time, special relativity. The text also presents relativistic dynamics in inertial and accelerated frames, as well as a detailed overview of Maxwell’s theory of electromagnetism, thus providing the background necessary for studying particle and accelerator physics, astrophysics, and Einstein’s theory of general relativity. In 1915, Einstein proposed a new theory of gravitation, general relativity. Finally, the text develops the geometrical framework in which Einstein’s equations are formulated and presents several key applications: black holes, gravitational radiation, and cosmology.