Stochastic gravity
Oct, 199637 pages
Published in:
- Phys.Rev.D 56 (1997) 6264-6277
e-Print:
- gr-qc/9610067 [gr-qc]
Report number:
- UTPT-96-16
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Abstract: (arXiv)
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, 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.Note:
- Revised version. Eq. (108) has been modified. Additional comments have been added to text. Revtex 39 pages
- 97.60.Sm
- 04.20.Cv
- gravitation: stochastic
- nonlinear
- space-time: fluctuation
- Langevin equation
- Fokker-Planck equation
- Friedman model
- singularity
- statistics: density
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