Singularity Analysis in f(R) Gravity and f(Q) Gravity

14 November 2024, Version 1
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

This paper systematically studies the singularity behavior in \( f(R) \) gravity and \( f(Q) \) gravity theories. By thoroughly deriving the gravitational equations and deeply analyzing the scalar curvature \( R \) and the asymmetry gravitational tensor \( Q \) under a spherically symmetric metric, we explore how the singular behaviors of these scalar fields in extreme conditions lead to the formation of singularities in the solutions of the gravitational equations. Furthermore, by comparing the modification terms and degrees of freedom in \( f(R) \) and \( f(Q) \) gravity, we analyze the impact of different functional forms on the gravitational field solutions and discuss the potential applications of these theories in cosmology and black hole physics. This paper also examines the effects of nonlinear corrections of scalar fields on dark energy and dark matter models, proposing related physical hypotheses and the possibilities for experimental verification.

Keywords

f(R) Gravity
f(Q) Gravity
Singularity
Scalar Curvature
Asymmetric Connection
Metric
Dark Energy
Black Hole

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Comment number 1, Aleksandr Rybnikov: Nov 24, 2024, 00:19

The occurrence of singularity is a consequence of consideration of the erroneous hypothesis of the existence of exclusively unambiguous charges. For example, at first sight, a diamond is a single-charge crystal. However, it consists of carbon atoms, each of which forms covalent bonds with four other carbon atoms, creating a strong three-dimensional structure. There are no ions with single charges in the diamond crystal lattice, as the carbon atoms share electrons uniformly without forming charged particles. The quantum theory of gravitation unambiguously indicates that the exchange of gravitons takes place exclusively between electrically neutral atoms, not their nuclei (see here “The a priori theory of everything”, paragraph “Quantum-relativistic of Newton's law of universal gravitation”). Gravitation disappears as soon as the atom is ionized completely or, as a result of high pressure, electrons are pressed into the nucleus, forming neutrons. This effect is seen in the final stage of a star's life, the Cepheid stage. Only it can explain the rapid and gigantic changes in the diameters of stars.