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  • 1
    Electronic Resource
    Electronic Resource
    Einstein-Fokker-Planck Equation for a Collapsing Perfect Fluid Star in a Thermal Noise Bath: Static Thermal Black Hole as the Equilibrium Solution (1999)
    Springer
    General relativity and gravitation 31 (1999), S. 1519-1537 
    Details
    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
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  • 2
    Electronic Resource
    Electronic Resource
    Towards a Probabilistic Paradigm for Gravitational Collapse, Black Hole Creation and Singularity Smearing (1999)
    Springer
    General relativity and gravitation 31 (1999), S. 425-442 
    Details
    ISSN: 1572-9532
    Keywords: OPPENHEIMER-SNYDER MODEL ; GRAVITATIONAL COLLAPSE ; BLACK HOLE ; SINGULARITY ; QUANTUM FLUCTUATIONS
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A prototype probability interpretation ispresented for the Oppenheimer-Snyder model ofspherically symmetric, gravitational collapse of apressureless ensemble of n point particles. A transitionprobability P(R(t), t; R1, t1) isderived for an initial sphere or fluid star of radius Rat comoving time t, collapsing smoothly andhomogeneously to any finite radii R(t, r) 〈 R atcomoving t 〉 t1 and R(t) = 0 at t = tf. The transitionprobability is evaluated in two cases. In the firstcase, Planck's constant is assumed zero and smoothdifferential limits exist for space and matter on alllength scales down to zero. The probability for singularityformation converges smoothly to unity as R → 0 ort → tf: the collapse is deterministic atall scales. There is also a finite, nonzero probabilityof event horizon formation at R = Rh = 2GM, but the starcontinues to collapse through this radius since there isalways a higher probability of reaching any smallerradius R 〈 Rh. An event horizon forms sothe collapsed state is still a black hole. In the classical limit(as ℏ → 0) the singularity returns with unitprobability. Finally, we briefly discuss how the final,fuzzy, collapsed state may be related to aspects ofstring theory. The emphasis of the paper is on theconceptual ideas and general possibilities which couldarise when incorporating stochastic mechanics andanalysis into general relativistic collapse.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026657120463
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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