ISSN:
1572-9532
Keywords:
GRAVITATION
;
FLUID STARS
;
STOCHASTIC PROCESS
;
BLACK HOLE
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract This paper considers sphericalOppenheimer-Snyder gravitational collapse of dust orperfect fluid “stars” immersed within aspacetime containing a thermal bath of (Gaussian) whitenoise at a temperature T, obeying the autocorrelations of thefluctation-dissipation theorem. Candidates for theresulting non-linear Einstein-Langevin (EL) stochasticdifferential field equations are developed. A collapsing fluid or dust star coupled to the stochastic,external thermal bath of fluctuations is theninterpreted as an example of a non-linear, noisy system,somewhat analogous to a non-linear Brownian motion in a viscous, thermal bath at temperature T. AnEinstein-Fokker-Planck (EFP) hydrodynamical continuityequation, describing the collapse as a probability flowwith respect to the exterior standard time ts outside the collapsing body, is developed. Thethermal equilibrium or stationary solution can bederived in the infinite standard time relaxation limit.This limit (ts → ∞) only exists for a static, external observer within thenoise bath viewing the collapsing sphere such that R→ 1 (the event horizon) with unit probability asts → ∞. The stationary or thermalequilibrium solution of the efp equations therefore seemsto correspond to a static black hole in a Hartle-Hawkingstate at the Hawking temperature tH. The OSmodel first predicted event horizons and singularities. It is interesting that through a simplestochastic extension of the model, one can conclude thatthe final collapsed, static, equilibrium state of thebody must be a thermal black hole at the Hawkingtemperature.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1026730420347
Permalink
