The General Theory of Singularity

A Unified Geometric Vision on Gravity and Fundamental Interactions

The General Theory of Singularity offers a profound extension of Einstein’s relativity by rethinking the very geometry of spacetime. Instead of assuming that the connection (the mathematical tool that describes how spacetime curves and how vectors or spinors are transported) must be symmetric—as is done in classical General Relativity—this theory allows for an additional, twisting component known as torsion.

By incorporating torsion into the framework, the theory aims to:

• Eliminate or Regularize Singularities: Instead of having points of infinite curvature (such as the centers of black holes), the torsion-based approach smooths out these singularities.

• Unify Fundamental Interactions: Gravity, electromagnetism, and the nuclear forces are seen as emerging naturally from the geometry of a higher-dimensional spacetime, with quantized properties arising from intrinsic topological conditions.

• Explain Discrete Observables: Features such as the quantization of electric charge, specific coupling constants, and even the masses of particles can be understood as direct consequences of integral (whole-number) topological fluxes in the extra-dimensional geometry.

A New Look at Spacetime Geometry

In this model, spacetime is conceived as a manifold with extra dimensions (typically “4+n” dimensions). Both the metric (which tells you how distances are measured) and a more general connection (which now includes an antisymmetric part, or torsion) work together to define the structure of the universe. The torsion represents a natural “twist” in spacetime that can account for physical properties—such as mass, charge, and spin—without having to add external fields or particles.

Unification of Interactions

One of the most exciting aspects of the General Theory of Singularity is its potential to unify the forces of nature in a single geometric framework:

• Gravity: The theory not only reproduces the familiar predictions of General Relativity but also removes the problematic singularities (like those in black holes) by smoothing out the geometry.

• Gauge Interactions: Electromagnetic and nuclear interactions emerge from the way extra dimensions are “compacted.” Topological fluxes in these extra dimensions naturally yield quantized charges and coupling constants.

• Quantization: Discrete values for particle properties (such as the electric charge and the masses of fermions) are explained as a consequence of integral topological conditions imposed on the structure of spacetime.

Implications for Astrophysics and Cosmology

The theory also offers alternative explanations for several astrophysical and cosmological observations:

• Black Holes: In this framework, the inner regions of black holes are regularized so that the infinite curvature predicted by classical models is avoided. This suggests that information might be preserved in a topologically stable structure.

• Galactic Rotation Curves: The additional geometric effects from torsion can mimic the influence traditionally attributed to dark matter, explaining the flat rotation curves observed in spiral galaxies.

• Cosmic Acceleration: The theory provides a natural mechanism for the accelerated expansion of the Universe. The effective “vacuum energy” needed to drive cosmic acceleration may emerge from the same topological fluxes, eliminating the need for a finely tuned cosmological constant.

These works provide an in-depth exploration of how a torsion-inclusive geometry can lead to the unification of fundamental forces, remove classical singularities, and explain phenomena ranging from particle quantization to cosmic acceleration.

The General Theory of Singularity represents a new approach to understanding the universe. By allowing spacetime to have a torsion component and by imposing integral topological conditions, the theory unifies gravity and the other fundamental interactions into one coherent geometric framework. It removes classical singularities, offers fresh insights into the nature of dark matter and dark energy, and explains why many physical constants appear in discrete, quantized values—all without the need to introduce additional, ad hoc fields.

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