Stochastic gravity

J. W. Moffat
Phys. Rev. D 56, 6264 – Published 15 November 1997
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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 θ 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, 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

Authors & Affiliations

J. W. Moffat

  • Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7

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Issue

Vol. 56, Iss. 10 — 15 November 1997

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