Eicheons instead of Black holes

Abstract

A new spherically-symmetric solution for a gravitational field is found in the conformally-unimodular metric. It is shown, that the surface of the black hole horizon in the standard Schwarzschild metric can be squeezed to a point by converting coordinates to the conformally-unimodular metric. In this new metric, there is no black hole horizon, while the naked singularity corresponds to a point massive particle. The reason for the study of this particular gauge (i.e., conformally-unimodular metric) is its relation to the vacuum energy problem. That aims to relate it to other physical phenomena (including black holes), and one could argue that they should be considered in this particular metric. That means the violation of the gauge invariance of the general theory of relativity. As a result, the nonsingular "eicheons" appear as the non-point compact objects with different masses and structures. They are a final product of the stellar collapse, with the masses exceeding the Tolman-Oppenheimer-Volkoff limit.

arXiv comment18 pages. The term "eicheon" refers to the fundamental work "Gravitation und Elektrizitat" by Hermann Weyl where the concept of gauge field theory ("Eichfeldtheorie") was invented for the first time

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• Rotational Curves of the Milky Way Galaxy and Andromeda Galaxy in Light of Vacuum Polarization around Eicheon
• Scalar Product for a Version of Minisuperspace Model with Grassmann Variables