Emergent modified gravity: The perfect fluid and gravitational collapse
Erick I. Duque
Erick I. Duque
Emergent modified gravity is a canonical theory based on general covariance where the spacetime is not fundamental, but rather an emergent object. This feature allows for modifications of the classical theory and can be used to model new effects, such as those suggested by quantum gravity. We discuss how matter fields can be coupled to emergent modified gravity, realize the coupling of the perfect fluid, identify the symmetries of the system, and explicitly obtain the Hamiltonian in spherical symmetry. We formulate the Oppenheimer-Snyder collapse model in canonical terms, permitting us to extend the model to emergent modified gravity and obtain an exact solution to the dust collapsing from spatial infinity including some effects suggested by quantum gravity. In this solution the collapsing dust forms a black hole, then the star radius reaches a minimum with vanishing velocity and finite positive acceleration, and proceeds to emerge out now behaving as a white hole. While the geometry on the minimum-radius surface is regular in the vacuum, it is singular in the presence of dust. However, the fact that the geometry is emergent, and the fundamental fields that compose the phase-space are regular, allows us to continue the canonical solution in a meaningful way, obtaining the global structure for the interior of the star. The star-interior solution is complemented by the vacuum solution describing the star-exterior region by a continuous junction at the star radius. This gluing process can be viewed as the imposition of boundary conditions, which is non-unique and does not follow from the equations of motion. This ambiguity gives rise to different possible physical outcomes of the collapse. We discuss two such phenomena: the formation of a wormhole and the transition from a black hole to a white hole.