STOCHASTIC GRAVITY

Gravity is treated as a stochastic phenomenon based on fluctuations of the metric tensor of general relativity. By using a 3+1 slicing of sp acetime, 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 geodes ics leads to a stochastic differential equation for the expansion para meter theta in terms of the proper time s. For sufficiently strong met ric fluctuations, it is shown that caustic singularities in spacetime can be avoided for converging geodesics. The formalism is applied to t he 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 whi te-noise limit for the metric fluctuations, the singularity in gravita tional collapse, and the big bang has a zero probability of occurring. Moreover, within the same approximation scheme, as a star collapses t he probability of a distant observer seeing an infinite redshift at th e Schwarzschild radius of the star is zero, and there is a vanishing p robability of a Schwarzschild black hole event horizon forming during gravitational collapse. [S0556-2821(97)07122-1].