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Title: A Regularized Scalar-Tensor Formulation of Gravity: The Finite-Length Kernel and UV Singularity Resolution Abstract: "Standard General Relativity (GR) and Newtonian gravity both suffer from ultraviolet (UV) divergences at small length scales, manifesting as coordinate singularities. We propose a regularized gravitational framework wherein the fundamental metric potential is governed by a finite-length cutoff parameter L, representing a fundamental minimum spacetime interval. By modifying the Poisson equation via a Plummer-type potential kernel, F = k/(r^2 + L^2), we demonstrate that gravitational propagation remains strictly causal and finite, avoiding the pathological infinite jerk associated with instantaneous mass disappearance. We establish the correspondence principle, showing that the model recovers Newtonian dynamics in the limit r L, and derive constraints on L using gravitational wave event GW170817 and solar system ephemerides."
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sarmad khan (2026) studied this question.
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