\beginabstract Classical general relativity predicts the formation of spacetime singularities in gravitational collapse, signaling a breakdown of the theory at high curvature. This work investigates a class of singularity-free gravitational models guided by a principle of structural stability, in which curvature invariants remain finite and spacetime is geodesically complete. We construct a regular interior geometry that preserves the standard weak-field predictions of general relativity while modifying the strong-field regime in a controlled manner. Observable consequences are analyzed through particle dynamics, photon trajectories, and black hole shadow formation. The results demonstrate that singularity removal can be achieved without conflict with current experimental and observational constraints. \endabstract

Introduction

Motivation and Scope

General relativity has achieved remarkable empirical success across a wide range of physical regimes, from laboratory-scale tests to astrophysical and cosmological observations. Nevertheless, the theory predicts the inevitable formation of singularities under generic conditions of gravitational collapse. These singularities mark regions where curvature diverges and the classical description of spacetime ceases to be meaningful. The primary motivation of this work is to explore whether gravitational dynamics can be consistently extended to avoid such pathologies while preserving agreement with known tests of gravity. The scope of the paper is deliberately phenomenological: rather than proposing a fundamental quantum theory of gravity, we focus on constructing and analyzing effective, singularity-free spacetime geometries.

Singularities as a Breakdown of Classical Gravity

Spacetime singularities are commonly interpreted not as physical objects, but as indicators of the incompleteness of classical general relativity. At a singularity, geodesics terminate in finite proper time and curvature invariants diverge, rendering physical predictions ill-defined. From this perspective, singularities represent a structural failure of the theory rather than a genuine feature of nature. This view is reinforced by the expectation that new physics should regulate extreme curvature regimes, ensuring finite observables and well-defined evolution for all physical degrees of freedom.

Regular Black Holes and Existing Approaches

Over the past decades, numerous approaches to singularity resolution have been proposed, including regular black hole metrics, effective quantum gravity corrections, and modifications of the matter sector. Many of these models replace the central singularity with a regular core, often resembling a de Sitter-like region, while maintaining an exterior geometry close to the Schwarzschild or Kerr solutions. Although differing in motivation and construction, these approaches share the common goal of eliminating curvature divergences. The present work builds on this line of research, emphasizing minimal deviation from classical predictions and direct comparison with observational signatures.

Strategy and Structure of the Present Work

Our strategy is to impose structural stability and the absence of curvature singularities as guiding principles for model construction. We introduce a regular interior geometry matched smoothly to an asymptotically Schwarzschild exterior, ensuring consistency with weak-field tests. The consequences of this modification are then analyzed systematically in both weak-field and strong-field regimes. The paper is organized as follows: after introducing the guiding principles, we construct the regular spacetime geometry, analyze particle and photon dynamics, and compute observable quantities such as light deflection and black hole shadows. Numerical methods and observational implications are discussed in later sections, followed by a critical discussion and conclusions.