Shell-crossings and shock formation during gravitational collapse in effective loop quantum gravity
Francesco Fazzini, Viqar Husain, Edward Wilson-Ewing
Abstract
Effective models of gravitational collapse in loop quantum gravity for the Lema\^{\i}tre-Tolman-Bondi spacetime predict that collapsing matter reaches a maximum finite density, bounces, and then expands outward. We show that in the marginally bound case, shell-crossing singularities commonly occur for inhomogeneous initial profiles of the dust energy density; this is the case in particular for all profiles that are continuous and of compact support, including configurations arbitrarily close to the Oppenheimer-Snyder model. When a shell-crossing singularity occurs, it is necessary to seek weak solutions to the dynamics; we argue that weak solutions typically contain shock waves.
Topics & Concepts
Loop quantum gravityGravitational collapsePhysicsGravitationShock (circulatory)Loop (graph theory)Loop quantum cosmologyQuantumShell (structure)Classical mechanicsQuantum gravityTheoretical physicsMechanicsQuantum mechanicsEngineeringMathematicsMedicineMechanical engineeringCombinatoricsInternal medicineNoncommutative and Quantum Gravity TheoriesAdvanced Differential Geometry ResearchCosmology and Gravitation Theories