2026-10-09T04:05:02Z https://api.figshare.com/v2/oai

oai:figshare.com:article/33342219 2026-10-06T10:34:57Z category_30103 item_type_12 month_year_10_2026

The Singularity Theory Shivanshu Sharma (24655371) High energy astrophysics and galactic cosmic rays Astrophysics and Astronomy, Cosmology and Nongalactic Astrophysics (astro-ph.CO), Astrophysics of Galaxies (astro-ph.GA) <p dir="ltr">The abstract for the theory presented in "The_Singularity_Theory_v3_with_AppendixI-1_TOC_updated.pdf" details a dimensionally consistent, non-minimally coupled scalar-tensor extension of general relativity. ​Core Derivation: The theory is motivated by a momentum-dependent propagation velocity, v(P)=c[1+KP/E_{Planck}]^{-1}. A spacetime scalar \varphi, which is sourced by the local average momentum of matter quanta, produces a derived correction tensor K_{\mu\nu}(\varphi) to Einstein's equations. ​Imposed Ansatz: By simply imposing a natural metric ansatz, m(r)=M(1-\varphi(r)/\varphi_{max})^{3} with \varphi(r)=\varphi_{max}r_{c}/(r+r_{c}), the theory produces everywhere-finite curvature at the black hole center (Kretschmann scalar K(r\rightarrow0)=96G^{2}M^{2}/(c^{4}r_{c}^{6})) and recovers classical Schwarzschild behavior as r_{c}\rightarrow0. ​Central Finding (The Obstruction): The paper proves that this single-function metric ansatz class cannot be an exact solution to the theory's coupled field equations. Consistency would force the condition \varphi^{\prime\prime}=\varphi^{\prime2}/2\xi, whose logarithmic solutions are structurally incompatible with vanishing at spatial infinity. To achieve an actual regular solution, structural assumptions must be relaxed by introducing a two-function metric, a non-canonical scalar sector, or an additional matter field. ​Two-Function Exploration: An exploratory two-function metric relaxes the rigid obstruction into a single constraint relating \varphi, A(r), and B(r). The derived second field equation (the 00 component) shows no asymptotic obstruction as r\rightarrow\infty, but leaves regularity at r\rightarrow0 as an open question because \varphi(r) is not an even function near the origin. ​Hawking Radiation & Observational Bounds: Independent of the metric obstruction, the kinematic relation v(P)\rightarrow0 as P\rightarrow\infty regularizes the terminal Hawking-temperature divergence, predicting a stable Planck-mass remnant. Fermi-LAT GRB 090510 bounds establish K\le O(1), while Solar System Cassini data bounds the non-minimal coupling to \xi<6.25\times10^{-6}. </p> 2026-10-06T10:34:57Z Text Preprint 10.6084/m9.figshare.33342219.v22 https://figshare.com/articles/preprint/The_Singularity_Theory/33342219 CC BY 4.0