Dust Collapse in Quadratic Gravity

This thesis explores the gravitational collapse in quadratic gravity, a higher-curvature extension of general relativity. Starting with a review of classical general relativity and the motivations for modifying the Einstein-Hilbert action, the study presents the theoretical foundations of quadratic gravity, characterized by terms quadratic in the spacetime curvature. Subsequently, the work focuses on the classical collapse of a pressureless, spherically symmetric dust ball, extending the traditional Oppenheimer-Snyder model into a regime governed by quadratic curvature corrections. The interior solution is modelled by a FLRW metric, and the evolution of the scale factor is obtained numerically. A comparison with general relativity reveals that the quadratic corrections can accelerate the collapse, especially at higher densities. The study further examines the apparent horizon formation, indicating the presence of both inner and outer horizons. Although no explicit time-dependent exterior solution is found, several ansätze are ruled out, and no-go theorems are estabilished. Constraints on the exterior metric are investigated via the junction conditions at the stellar surface at τ = 0, highlighting the incompatibility between a FLRW interior solution and a stationary exterior solution. This research provides new insights into dynamical black hole formation beyond general relativity and outlines directions for future investigations into time and radial-dependent solutions in quadratic gravity.