In general relativity, singularities, like those theorized to exist at the centres of black holes or at the origin of the Big Bang, present unique challenges to both mathematical and physical understanding. These singularities are characterized by conditions where physical laws as currently understood cease to be predictable or observable. This raises a fundamental question: Are singularities purely mathematical constructs that exist beyond the Planck scale, and thus beyond the scope of empirical validation?
General relativity predicts the existence of singularities, regions of infinite density where the gravitational field becomes infinite. Notably, the mathematical representation of these singularities involves values that approach division by zero, which is undefined and non-physical. For example, the Friedman-Robertson-Walker (FRW) solution to Einstein's field equations, which underpins the standard Big Bang model, indicates a singularity at the time of the universe's inception.
These singularities occur at scales smaller than the Planck scale, where the effects of quantum gravity are hypothesized to become significant, yet remain unquantified by existing theories. As such, singularities are not observable with current technology or provable by existing physical laws, which are based on empirical evidence. This limitation leads to the interpretation of singularities as mathematical abstractions rather than physical entities.
Given these considerations, should singularities be viewed solely as theoretical constructs within the mathematical frameworks of cosmology and black hole physics? How might advances in theoretical physics, particularly in quantum gravity, change our understanding of these enigmatic features? Whether and how singularities might bridge the gap between current mathematical theory and physical reality.
To my understanding of our universe...there is no singularity exist in the universe, because everything is duality, general relativity is about one sun, three planets and one moon, not the universe with billions of galaxies, and our physic does not describe nature with pressure, temperature, colors, taste, smells...., where it is changing constantly. Thus the quest is invalid.
Please read my articles for more understanding.
https://www.researchgate.net/post/Should_General_Relativity_now_be_considered_an_established_fiction_What_about_Silbersteins_objection3