https://youtu.be/uAVksa2dJv0?si=Hqx8CP5vsApll5yB https://youtu.be/BlcryjCFScw?si=S3Hx3cufesTIHbnV Classical General Relativity predicts spacetime singularities characterized by divergent curvature invariants and geodesic incompleteness, notably in cosmological and black-hole spacetimes. Such singularities are widely regarded as signaling the breakdown of the classical theory. In this work, we present a strictly second-order Palatini framework in which curvature dynamically self-regulates and remains bounded without introducing higher derivatives, additional propagating degrees of freedom, or explicit quantum discreteness. The spacetime metric and affine connection are treated as independent variables, and curvature invariants enter the field equations algebraically, enabling intrinsic curvature saturation. We demonstrate that physical observables measured by freely falling observers—specifically tidal forces—remain finite everywhere. As a result, both timelike and null geodesics are extendable to arbitrary affine parameter values, establishing geodesic completeness in the physical metric. In homogeneous and isotropic cosmologies, the theory admits a dynamically stable finite-curvature fixed point, replacing the classical Big Bang singularity with a nonsingular bounce. In static, spherically symmetric spacetimes, black-hole interiors develop universal de Sitter cores whose radius scales with mass. Linear tensor perturbations propagate exactly as in General Relativity, ensuring ghost freedom and luminal gravitational-wave speed. The theory preserves all low-energy predictions of General Relativity while yielding concrete, falsifiable predictions for primordial tensor modes and strong-field gravitational dynamics. This framework provides a conservative and structurally grounded resolution of physical spacetime singularities, arising directly from the algebraic structure of the Palatini field equations and the Bianchi identity, without resorting to fine-tuning or ad hoc modifications of gravity.
Seunghyun Hong (Tue,) studied this question.