Abstract
Gravity is treated as a stochastic phenomenon based on fluctuations of the metric tensor of general relativity. By using a 3+1 slicing of spacetime, a Langevin equation for the dynamical conjugate momentum and a Fokker-Planck equation for its probability distribution are derived. The Raychaudhuri equation for a congruence of timelike or null geodesics leads to a stochastic differential equation for the expansion parameter in terms of the proper time . For sufficiently strong metric fluctuations, it is shown that caustic singularities in spacetime can be avoided for converging geodesics. The formalism is applied to the gravitational collapse of a star and the Friedmann-Robertson-Walker cosmological model. It is found that owing to the stochastic behavior of the geometry, and based on an approximate stationary, Gaussian white-noise limit for the metric fluctuations, the singularity in gravitational collapse, and the big bang has a zero probability of occurring. Moreover, within the same approximation scheme, as a star collapses the probability of a distant observer seeing an infinite redshift at the Schwarzschild radius of the star is zero, and there is a vanishing probability of a Schwarzschild black hole event horizon forming during gravitational collapse.
- Received 25 November 1996
DOI:https://doi.org/10.1103/PhysRevD.56.6264
©1997 American Physical Society