Nonsingular collapse of a perfect fluid sphere within a dilaton-gravity reformulation of the Oppenheimer model

摘要

A generic four-dimensional dilaton gravity is considered as a basis for reformulating the paradigmatic Oppenheimer-Synder model of a gravitationally collapsing star modelled as a perfect fluid or dust sphere. Initially, the vacuum Einstein scalar-tensor equations are modified to Einstein-Langevin equations which incorporate a noise or micro-turbulence source term arising from Planck scale conformal, dilaton fluctuations which induce metric fluctuations. Coupling the energy-momentum tensor for pressureless dust or fluid to the Einstein-Langevin equations, a modification of the Oppenheimer-Snyder dust collapse model is derived. The Einstein-Langevin field equations for the collapse are of the form of a Langevin equation for a non-linear Brownian motion of a particle in a homogeneous noise bath. The smooth worldlines of collapsing matter become increasingly randomised Brownian motions as the star collapses, since the backreaction coupling to the fluctuations is non-linear; the input assumptions of the Hawking-Penrose singularity theorems are then violated. The solution of the Einstein-Langevin collapse equation can be found and is non-singular with the singularity being smeared out on the correlation length scale of the fluctuations, which is of the order of the Planck length. The standard singular Oppenheimer-Synder model is recovered in the limit of zero dilaton fluctuations. [References: 21]