Instability Trajectories in Stellar Evolution: From Molecular Clouds to Black Hole Collapse

Black holes represent the most extreme manifestation of gravitational collapse in the universe, transforming diffuse interstellar matter into ultra-compact objects governed by relativistic spacetime dynamics. In this work we propose a trajectory-based dynamical framework to describe the complete evolutionary pathway of massive stars, from the initial gravitational collapse of molecular clouds to compact-object formation. We introduce a generalized instability functional that characterizes the progressive departure from stellar equilibrium during successive nuclear burning stages. Within this framework, stellar evolution is interpreted as a continuous trajectory in a multidimensional phase space defined by structural organization, nuclear reaction complexity, and coherence of energy transport. This dynamical perspective provides a unified interpretation of stellar evolution, gravitational instability, and compact-object formation, linking early stellar formation processes to the onset of gravitational collapse and black hole formation. Future work will extend this framework through numerical simulations and observational constraints in order to reconstruct detailed dynamical trajectories of stellar collapse and compact-object formation.