Stochastic Gravity

TL;DR

This paper models gravity as a stochastic process, deriving equations that suggest metric fluctuations can prevent singularities like black holes and the big bang, challenging classical deterministic predictions.

Contribution

It introduces a stochastic formalism for gravity using metric fluctuations, leading to new insights on singularity avoidance in gravitational collapse and cosmology.

Findings

Singularities in gravitational collapse are probabilistically avoided.

The big bang singularity has zero probability of occurring.

Black hole event horizons are unlikely to form during collapse.

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 $\theta$ in terms of the proper time $s$. 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, the singularity in gravitational collapse and the big-bang have a zero probability of occurring. Moreover, as a star collapses the probability of a distant observer seeing an infinite red shift at the Schwarzschild radius of the star is zero. Therefore, there is a vanishing probability of a Schwarzschild black hole event horizon forming during gravitational collapse.